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Math Videos on DVD for Individual/Home Study
- Basic Mathematical Skills Series
- Basic Mathematics Core
- Pre-Algebra Series
- Algebra I/Introductory Algebra Series
- Algebra II/Intermediate Algebra Series
- Advanced/College Algebra Series
- Trigonometry Series
- Geometry Series
- Calculus Series
- Probability and Statistics Series
Elementary Math DVD Series - 8 DVDs
The Elementary Math Series was developed to teach younger students math concepts in a fun, non-threatening way. The series is fully animated with bright colors and illustrations so students can easily follow and understand the material presented.
- DVD 1 - Patterns, Addition, Subtraction, Greater Than & Less Than
- DVD 2 - Money, Time, Measurement, Counting
- DVD 3 - Addition, Subtraction, Calendar, Sums to 18, Odd & Even
- DVD 4 - Subtraction Facts & Place Value, 2&3 Digit Addition & Subtraction
- DVD 5 - Understanding Multiplication, Factors, Multiplication
- DVD 6 - Understanding Division, Dividing by 2 & 3, Dividing by 4 & 5,
Division Review - DVD 7 - Multiplying with 2 Digit Factors, Finding 2 Digit Quotients,
Metric Measurement - DVD 8 - Understanding Fractions, Understanding Decimals
For a complete description of DVDs, see our Complete Series Listings.
Basic Mathematics Core - 20 DVDs
This series is extremely helpful to students who want to grasp or review the basic mathematics or who are enrolled in a basic mathematics course or a pre-algebra mathematics course. Topics in this series include whole numbers, fractions, decimals, ratio and proportion, percent and percent applications, perimeter and area, statistics, signed numbers, and the introduction to algebra.
- DVD 1 – Whole Numbers - Place Value, Addition, Subtraction and Rounding
- DVD 2 – Whole Numbers - Multiplication and Order of Operations
- DVD 3 – Whole Numbers - Division
- DVD 5 – Whole Numbers - Factors and Multiples
- DVD 6 – Fractions - Equivalent Fractions, Lowest Terms, Comparing
Fractions and Mixed Numbers - DVD 7 – Fractions - Multiplication and Division of Fractions
- DVD 8 – Fractions - Least Common Denominator, Addition and
Subtraction of Fractions - DVD 9 - Fractions - Real World Application of Fractions
- DVD 10 – Decimals - Addition, Subtraction, Multiplication and
Rounding of Decimals - DVD 11 – Decimals - Division of Decimals and Converting Decimals to Fractions
- DVD 12 – Ratio and Proportions - Fundamentals of Ratios and Proportions
- DVD 14 – Percent - Converting Among Fractions, Decimals and Percents
- DVD 15 – Percent – Real World Application of Percents
- DVD 17 - Measurement - U.S. Customary System
- DVD 20 – Geometry - Lines, Angles and Triangles
- DVD 24 – Geometry - Geometric Relationships
- DVD 25 – Geometry - Perimeter, Area and Volume
- DVD 26 – Statistics - Charts and Graphs
- DVD 27 - Statistics - Mean, Median, Mode and Organizing Data
- DVD 29 – Signed Numbers - Operations on Signed Numbers
For a complete description of DVDs, see our Complete Series Listings.
Algebra 1 Series - 16 DVDs
This Algebra 1 DVD tutor series was made to give students clear, concise explanations of topics in a manner that the student may enjoy while acquiring the skills necessary to be successful in current and future mathematical courses. Throughout each tape segment, pertinent definitions, theorems, and steps are shown and clearly explained. The lecturer then follows the introduction with a variety of examples, which are thoroughly explained step by step. These examples are graded in difficulty. Students are first exposed to examples that increase their confidence and problem-solving skills; then they are eased gradually through more difficult problems.
Algebra I consists of 89 video segments. Each segment is approximately 15 minutes in length. Topics include algebraic expressions, exponents, real numbers, solving equations and inequalities and applications, polynomials, factoring, rational expressions, graphing linear equations and inequalities in two variables, relations and functions, solving systems of linear equations, radicals, and solving quadratic equations.
DVD 1-Introduction to Real Numbers & Variables
- Variables and Algebraic Expressions
- Order of Operations
- Set of Real Numbers
- Comparing Real Numbers
- Exponents
DVD 2-Operations with Real Numbers
- Adding Real Numbers on the Number Line
- Adding Real Numbers
- Subtracting Real Numbers
- Multiplying Real Numbers
- Dividing Real Numbers
- Properties of Real Numbers
DVD 3-Algebraic Expressions
- Evaluating Algebraic Expressions
- Combining Like Terms
- Simplifying Algebraic Expressions
DVD 4-Solving Equations
- Solution Sets
- Solving Equations Using Addition and Subtraction Properties
- Solving Equations Using Multiplication and Division Properties
- Solving Equations Requiring More than One Step
- Solving Equations with Variables on Both Sides
- Solving Percent Equations
- Solving Literal Equations
- Solving Absolute Value Equations
DVD 5-Problem Solving
- Problem Solving: Using Formulas to Solve Applications
- Problem Solving: From Words to Symbols
- Problem Solving: Geometry
- Problem Solving: Percent
- Problem Solving: Mixtures
- Problem Solving: Distance/Rate/Time
DVD 6-Solving Inequalities
- Graphing Inequalities
- Solving Inequalities Using Addition and Subtraction Properties
- Solving Inequalities Using Multiplication and Division Properties
- Solving Inequalities Requiring More than One Step
- Solving Combined Inequalities
- Solving Absolute Value Inequalities
DVD 7-Exponents
- Multiplying Monomials
- Powers of Monomials
- Dividing Monomials
- Negative Exponents
- Scientific Notation
DVD 8-Operations With Polynomials
- Polynomials
- Adding and Subtracting Polynomials
- Multiplying Polynomials
- Multiplying Binomials
- Special Products
- Dividing Polynomials
DVD 9-Factoring Polynomials
- Factoring Integers
- The Greatest Common Factor
- Factoring by Grouping
- Factoring the Difference of Two Squares
- Factoring x2 + bx + c
- Factoring ax2 + bx + c
- Factoring Completely
- Solving Equations by Factoring
DVD 10-Rational Expressions
- Simplifying Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Least Common Denominator
- Adding and Subtracting Rational Expressions with Like Denominators
- Adding and Subtracting Rational Expressions with Unlike Denominators
- Operations on Rational Expressions
- Complex Fractions
- Solving Equations with Rational Expressions
DVD 11-Graphing Linear Equations & Inequalities
- Graphing Ordered Pairs
- Graphing Linear Equations in Two Variables
- x- and y- Intercepts
- Relations
- Functions
- Graphing Linear Inequalities in Two Variables
DVD 12-Slope and Forms of Equations of Lines
- Slope
- Slope-Intercept Form of a Linear Equation
- Point-Slope Form of a Linear Equation
- Using Two Points to write Equations of Lines
- DVD 13-Systems of Linear Equations
- Graphing Systems of Linear Equations
- The Substitution Method
- The Addition Method
- Using Multiplication with the Additional Method
DVD 14-Roots & Radicals, Part I
- Square Roots
- Simplifying Square Roots
- Simplifying Square Roots Containing Variables
- Addition and Subtraction of Radicals
- Multiplication of Radicals
DVD 15-Roots & Radicals, Part II
- Division of Radicals
- Rationalizing the Denominator
- Solving Radical Equations
- The Pythagorean Theorem
- The Distance Formula
DVD 16-Solving Quadratic Equations
- Solving Quadratic Equations by the Square Root Property
- Solving Quadratic Equations by Completing the Square
- Solving Quadratic Equations by the Quadratic Formula
For a complete description of DVDs, see our Algebra I Series Listings.
END OF DVD MATH PACK DESCRIPTION
The video series consists of 8 DVDs and was developed to teach younger students Pre-K through 4th grade math concepts in a fun, non-threatening way. The series is fully animated with bright colors and illustrations so students can easily follow and understand the material presented. A workbook accompanies each tape in the series.
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Basic Mathematics
Video Series on DVD
The Basic Mathematics video series consists of 40 DVDs. Each DVD is approximately 25-30 minutes in length. Topics in this series include whole numbers, fractions, decimals, ratio and proportion, percent and percent applications, the U.S. and metric systems of measurement, perimeter, area, statistics, probability, signed numbers, introduction to variables, solving equations and applications, and exponents.
This series is extremely helpful to students currently enrolled in a basic mathematics course, a prealgebra mathematics course, or for anyone wanting to review basic mathematics.
1001 - Whole Numbers - Place Value, Addition, Subtraction and Rounding . This segment covers place value in the usual base ten numbering system for whole numbers. Addition and subtraction in columns, lining up place values vertically, and carrying in addition as well as borrowing in subtraction are covered. Rounding whole numbers to any place value is covered.
1002 - Whole Numbers - Multiplication and Order of Operations. This segment covers multiplication of whole numbers. Order of operations is covered for computations involving several operations and removal of parentheses or grouping symbols.
1003 - Whole Numbers - Division. This segment covers long division of whole numbers using the division algorithm. Simple applications are also covered.
1004 - Whole Numbers - Estimating. This segment covers a review of rounding whole numbers as well as estimating sums, products, and quotients by rounding. Applications of estimating are also included.
1005 - Whole Numbers - Factors and Multiples. This segment covers factoring of whole numbers and the concept of one number being a multiple of another.
1006 - Fractions - Equivalent Fractions, Lowest Terms, Comparing Fractions and Mixed Numbers. This segment covers equivalence of fractions and reduction to lowest terms. Comparison of fractions and mixed numbers is also covered.
1007 - Fractions - Multiplication and Division. This segment covers multiplication of fractions as well as the use of dividing out common factors to simplify the multiplication. Division is covered via inversion of the divisor followed by multiplication.
1008 - Fractions - Least Common Denominator, Addition and Subtraction. This segment covers common denominators for pairs of fractions and addition and subtraction of fractions by first replacing fractions with equivalent fractions all having common denominators. The concept and use of least common denominators is also covered.
1009 - Fractions - Real World Applications of Fractions. This segment covers solving applications by adding, subtracting, multiplying, or dividing fractions.
1010 - Decimals - Addition, Subtraction, Multiplication and Rounding. This segment covers addition and subtraction of decimals by working in columns with decimal points lined up vertically, multiplication by addition of partial products and location of the decimal point for the product. Rounding of decimal numbers is also covered.
1011 - Decimals - Division, Converting to Fractions. This segment covers long division of decimals as well as conversion from decimals to fractions and fractions to decimals.
1012 - Ratio and Proportion - Fundamentals of Ratios and Proportions. This segment covers ratio, rate and proportion. Topics included are unit rates, three ways of writing a ratio, and solving proportions by cross multiplying.
1013 - Ratio and Proportion - Applications of Proportions. This segment covers applications solved by setting up and solving proportions. The importance of like units in the numerators and like units in the denominators is stressed.
1014 - Percent - Converting Among Fractions, Decimals and Percents. This segment covers percent, conversion of decimals to percents and percents to decimals as well as applications to everyday real problems.
1015 - Percent - Real World Applications of Percents This segment covers the more advanced applications of percents such as in problems of interest rates on loans and savings accounts.
1016 - Percent - Using Percents in Everyday Situations This segment is to be viewed after a study of percents. It is meant to help students become comfortable with percents as they might encounter them in real-life situations. estimating is encouraged. Applications include discount, restaurant tips, layaways, purchasing a home, and purchasing a car.
1017 - Measurement - U.S. Customary System. This segment covers units of length, capacity, and weight in the U.S. Customary System. Converting from one unit of measurement to another by unit fractions is included. An example of adding lengths is shown as well as an application.
1018 - Measurement - Metric System. This segment covers units of length, capacity, and mass in the Metric System. Converting from one unit of measurement to another by unit fractions is included as well as converting by using a table.
1019 - Measurement - Customary and Metric System Conversions. This segment covers converting between the Metric System and the U.S. Customary System. A large portion of this tape segment is devoted to converting through estimation.
1020 - Geometry - Lines, Angles and Triangles. This segment covers definitions and classifications of basic geometric terms including line segments, rays and right, acute, straight, and obtuse angles. The Pythagorean Theorem is introduced to find the unknown side of a right triangle. The concept of similar, congruent and perfect triangles is also covered.
1021 - Geometry - Line and Angle Relationships
1022 - Geometry - Polygons
1023 - Geometry - Transformations and Symmetry
1024 - Geometry - Geometric Relationships
1025 - Geometry - Perimeter, Area and Volume This segment covers methods of computing perimeter and area for elementary geometric figures such as squares, triangles, rectangles parallelograms, circles and trapezoids.
1026 - Statistics - Charts and Graphs. This segment introduces statistics and how it is used to describe the results of events using various graphing techniques including pictographs, bar graphs, line graphs, circle graphs and histograms.
1027 - Statistics - Mean, Median, Mode and Organizing Data. This segment explores ways to use statistics to organize data numerically including mean, median, mode and range. Techniques to organize data visually including stem-and-leaf plots, box-and-whisker plots and scatter plots are also introduced.
1028 - Probability - Introduction to Probability. This segment introduces using probability as a means to predict outcomes. Tree Diagrams and other practical applications of using probability to predict outcomes numerically are discussed.
1029 - Signed Numbers - Operations on Signed Numbers. This segment covers the notion of negative numbers as well as rules for signs in addition, subtraction, multiplication and division of numbers.
1030 - Signed Numbers - The Order of Operations and Signed Numbers. This segment covers order of operations. Some examples include exponents.
1031 - Introduction to Algebra - Variables and Like Terms. This segment covers an introduction to variables, expressions, and evaluating an expression if given replacement values. Also formulas are evaluated by substituting given replacement values.
1032 - Introduction to Algebra - Solving Equations. This segment covers solving the most elementary linear equations so as to provide an introduction to the beginning of algebra. The notion of keeping an equation in balance is covered as well as elementary techniques for isolation of the unknown.
1033 - Introduction to Algebra - Applications of Linear Equations. This segment covers translating phrases into expressions and solving applications by setting up and solving linear equations.
1034 - Rectangular Coordinate System and Distance Between Points
1035 - Graphing on the Rectangular Coordinate System
1036 - Slope and Forms of a Line
1037 - Linear Relationships and Scientific Notation
1038 - Relations And Functions
1039 - Exponents - Using Exponents. This segment covers the computation of numerical expressions involving whole number exponents as well as the elementary rules of exponents.
1040 - Exponents - Exponent Rules and Radicals. This segment covers the basic notions of roots and radicals and their relations to whole number exponents.
Basic Mathematics Core - 20 DVDs
This series is extremely helpful to students who want to grasp or review the basic mathematics or who are enrolled in a basic mathematics course or a pre-algebra mathematics course. Topics in this series include whole numbers, fractions, decimals, ratio and proportion, percent and percent applications, perimeter and area, statistics, signed numbers, and the introduction to algebra.
- DVD 1 – Whole Numbers - Place Value, Addition, Subtraction and Rounding
- DVD 2 – Whole Numbers - Multiplication and Order of Operations
- DVD 3 – Whole Numbers - Division
- DVD 5 – Whole Numbers - Factors and Multiples
- DVD 6 – Fractions - Equivalent Fractions, Lowest Terms, Comparing
Fractions and Mixed Numbers - DVD 7 – Fractions - Multiplication and Division of Fractions
- DVD 8 – Fractions - Least Common Denominator, Addition and
Subtraction of Fractions - DVD 9 - Fractions - Real World Application of Fractions
- DVD 10 – Decimals - Addition, Subtraction, Multiplication and
Rounding of Decimals - DVD 11 – Decimals - Division of Decimals and Converting Decimals to Fractions
- DVD 12 – Ratio and Proportions - Fundamentals of Ratios and Proportions
- DVD 14 – Percent - Converting Among Fractions, Decimals and Percents
- DVD 15 – Percent – Real World Application of Percents
- DVD 17 - Measurement - U.S. Customary System
- DVD 20 – Geometry - Lines, Angles and Triangles
- DVD 24 – Geometry - Geometric Relationships
- DVD 25 – Geometry - Perimeter, Area and Volume
- DVD 26 – Statistics - Charts and Graphs
- DVD 27 - Statistics - Mean, Median, Mode and Organizing Data
- DVD 29 – Signed Numbers - Operations on Signed Numbers
For a complete description of DVDs, see our Basic Math Series.
The Pre-Algebra video series consists of 31 DVDs. Each DVD is approximately 25-30 minutes in length. Topics include fractions, real numbers, exponents, solving linear equations and inequalities and applications, polynomials, factoring, rational expressions, ratio and proportions, graphing linear equations and inequalities and equations of lines, functions, systems of linear equations and inequalities, radicals, rational exponents, solving quadratic equations. Many of the topic titles are the same as for the intermediate algebra series, but at a level consistent with introductory algebra courses.
This series is extremely helpful to students currently enrolled in a prealgebra course, for review before enrolling in an introductory algebra course, or for anyone wanting a review from basic mathematics to the introduction of algebra.
1101 - Order of Operations. This segment covers order of operations for computations involving several operations and removal of parentheses or grouping symbols.
1102 - Factors and Multiples. This segment covers factoring of whole numbers and the concept of one number being a multiple of another.
1103 - Fractions - Equivalent Fractions, Lowest Terms, Comparing Fractions and Mixed Numbers. This segment covers equivalence of fractions and reduction to lowest terms. Comparison of fractions and mixed numbers is also covered.
1104 - Fractions - Multiplication and Division. This segment covers multiplication of fractions as well as the use of dividing out common factors to simplify the multiplication. Division is covered via inversion of the divisor followed by multiplication.
1105 - Fractions - Least Common Denominator, Addition and Subtraction. This segment covers common denominators for pairs of fractions and addition and subtraction of fractions by first replacing fractions by equivalent fractions all having common denominators. The concept and use of least common denominators is also covered.
1106 - Fractions and Problem Solving. This segment covers solving problems that contain fractions.
1107 - Decimals - Addition, Subtraction, Multiplication and Rounding. This segment covers addition and subtraction of decimals by working in columns with decimal points lined up vertically, multiplication by addition of partial products and location of the decimal point for the product. Rounding of decimal numbers is also covered.
1108 - Decimals - Division, Converting to Fractions. This segment covers long division of decimals as well as conversion from decimals to fractions and fractions to decimals.
1109 - Ratio and Proportion. This segment covers ratio, rate, and proportion. Topics included are writing equivalent ratios, three ways of writing a ratio, and cross multiplication.
1110 - Percent. This segment covers conversion between fractions, decimals and percents. Also included is how to find a percent of a number.
1111 - Integers - Addition and Subtraction. This segment covers addition and subtraction of integers.
1112 - Integers - Multiplication and Division. This segment covers multiplication and division of integers.
1113 - Introduction to Variables. This segment covers an introduction to variables, expressions, and evaluating an expression if given replacement values. Also, formulas are evaluated by substituting given replacement values.
1114 - Solving One Step Equations. This segment covers solving linear equations that can be solved in one step.
1115 - Solving Two Step Equations. This segment covers solving linear equations that can be solved in two steps.
1116 - Solving Equations in General. This segment covers solving the most elementary linear equations so as to provide an introduction to the beginning of algebra. The notion of keeping an equation in balance is covered as well as elementary techniques for isolation of the unknown.
1117 - Proportions and Problem Solving. This segment covers applications solved by setting up and solving proportions. The importance of like units in the denominators is stressed.
1118 - Percent and Problem Solving. This segment covers solving problems that contain percents. Included in this segment are percent increase and percent decrease problems.
1119 - Graphing Linear Equations. This segment covers the slope-intercept and point-slope forms for the equation of a line. The relationship of slope to steepness and methods of calculating slope via rise over run as well as rearrangement into slope-intercept form is covered. Parallel and perpendicular lines are also covered as well as graphing inequalities by graphing their boundary equations and using a test point off the boundary to determine the solution region.
1120 - Exponents. This segment covers the computation of numerical expressions involving whole number exponents as well as the elementary rules of exponents.
1121 - More Exponents and Introduction to Radicals. This segment covers the basic notions of roots and radicals and their relations to whole number exponents.
1122 - Lines, Angles, and Triangles. This segment contains definitions of line segments, rays, angles and their classifications, including right, acute, straight, and obtuse angles. The concept of similar and congruent triangles is also covered.
1123 - Square Roots and the Pythagorean Theorem. This segment covers an introduction to square roots along with simplifying the square root of a perfect square. The Pythagorean Theorem is also introduced to find the unknown side of a right triangle.
The Algebra I video series on DVD was made to give students clear, concise explanations of topics in a manner that the student may enjoy while acquiring the skills necessary to be successful in current and future mathematical courses. Throughout each DVD segment, pertinent definitions, theorems, and steps are shown and clearly explained. To reinforce these mathematical ideas, they are continually referenced and reviewed as examples are worked. Careful attention has been given to the NCTM Standards.
An ample number and variety of examples are solved on each tape segment by the lecturer. Each example solved is thoroughly explained step by step for the student. The examples on a single tape are graded in difficulty. Students are first exposed to examples that increase their confidence and problem-solving skills; then they are eased gradually through more difficult problems.
Algebra I consists of 89 video segments. Each segment is approximately 15 minutes in length. Topics include algebraic expressions, exponents, real numbers, solving equations and inequalities and applications, polynomials, factoring, rational expressions, graphing linear equations and inequalities in two variables, relations and functions, solving systems of linear equations, radicals, and solving quadratic equations.
Algebra I is made primarily for the junior high school or high school student. Objectives are clearly stated at the beginning of each segment. This series is extremely helpful to students enrolled in an algebra I mathematics course, students wanting to prepare before enrolling an algebra I course, students wanting a comprehensive review before enrolling in an algebra II course, or anyone wanting to review their basic algebra skills.
A1 Introduction to Real Numbers and Variables
Variables and Algebraic Expressions
Order of Operations
Set of Real Numbers
Comparing Real Numbers
Exponents
A2 Operations with Real Numbers
Adding Real Numbers on the Number Line
Adding Real Numbers
Subtracting Real Numbers
Multiplying Real Numbers
Dividing Real Numbers
Properties of Real Numbers
A3 Algebraic Expressions
Evaluating Algebraic Expressions
Combining Like Terms
Simplifying Algebraic Expressions
A4 Solving Equations
Solution Sets
Solving Equations Using Addition and Subtraction Properties
Solving Equations Using Multiplication and Division Properties
Solving Equations Requiring More than One Step
Solving Equations with Variables on Both Sides
Solving Percent Equations
Solving Literal Equations
Solving Absolute Value Equations
A5 Problem Solving
Problem Solving: Using Formulas to Solve Applications
Problem Solving: From Words to Symbols
Problem Solving: Geometry
Problem Solving: Percent
Problem Solving: Mixtures
Problem Solving: Distance/Rate/Time
A6 Solving Inequalities
Graphing Inequalities
Solving Inequalities Using Addition and Subtraction Properties
Solving Inequalities Using Multiplication and Division Properties
Solving Inequalities Requiring More than One Step
Solving Combined Inequalities
Solving Absolute Value Inequalities
A7 Exponents
Multiplying Monomials
Powers of Monomials
Dividing Monomials
Negative Exponents
Scientific Notation
A8 Operations with Polynomials
Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials
Multiplying Binomials
Special Products
Dividing Polynomials
A9 Factoring Polynomials
Factoring Integers
The Greatest Common Factor
Factoring by Grouping
Factoring the Difference of Two Squares
Factoring x2 + bx + c
Factoring ax2 + bx + c
Factoring Completely
Solving Equations by Factor
A10 Rational Expressions
Simplifying Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions
Least Common Denominator
Adding and Subtracting Rational Expressions with Like Denominators
Adding and Subtracting Rational Expressions with Unlike Denominators
Operations on Rational Expressions
Complex Fractions
Solving Equations with Rational Expressions
A11 Graphing Linear Equations and Inequalities
Graphing Ordered Pairs
Graphing Linear Equations in Two Variables
x- and y- Intercepts
Relations
Functions
Graphing Linear Inequalities in Two Variables
A12 Slope and Forms of Equations of Lines
Slope
Slope-Intercept Form of a Linear Equation
Point-Slope Form of a Linear Equation
Using Two Points to write Equations of Lines
A13 Systems of Linear Equations
Graphing Systems of Linear Equations
The Substitution Method
The Addition Method
Using Multiplication with the Additional Method
A14 Roots and Radicals, Part I
Square Roots
Simplifying Square Roots
Simplifying Square Roots Containing Variables
Addition and Subtraction of Radicals
Multiplication of Radicals
A15 Roots and Radicals, Part II
Division of Radicals
Rationalizing the Denominator
Solving Radical Equations
The Pythagorean Theorem
The Distance Formula
A16 Solving Quadratic Equations
Solving Quadratic Equations by the Square Root Property
Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations by the Quadratic Formula
The Algebra II video series on DVD consists of 31 DVDs. Each DVD is approximately 25-30 minutes in length. Topics include exponents, solving linear equations and inequalities and applications, polynomials, factoring, rational expressions, complex fractions, graphing linear equations and inequalities, and equations of lines, radicals, rational exponents, solving quadratic equations.
3001 - Solving Linear Equations.
This segment covers the solution of linear equations, balancing equations, isolation of the unknown, and moving terms from one side of the equation to the other. Removal of parentheses and simplification of terms is covered as well as collecting like terms. Equations covered are at the intermediate algebra level of difficulty. Also covered are literal equations or equations involving several different symbols in which one in particular is to be isolated.
3002 - Applications that Lead to Linear Equations.
This segment covers a variety of intermediate level word problems including problems involving distance, speed, and time as well as problems involving interest rates.
3003 - Solving Linear Inequalities.
This segment covers solving linear inequalities by isolating the unknown using methods similar to those for linear equations. The reversal of inequality symbol when multiplying both sides of an inequality by a negative number is also covered. The problems covered here are at the intermediate algebra level of difficulty.
3004 - Solving Absolute Value Equations.
This segment covers the solution of equations in which one or more terms contain the absolute value of a linear expression in the unknown . The method of isolation of the absolute value term is used.
3005 - Compound Inequalities.
This segment covers the method of solving and graphing compound inequalities and pairs of inequalities in one unknown.
3006 - Solving Absolute Value Inequalities.
This segment covers the method of solving absolute value inequalities by isolating the absolute value term and reducing to a system of compound inequalities.
3007 - Exponents.
This segment covers the laws of exponents in relation to the basic operations on real numbers as well as the use of the laws of exponents to simplify or rearrange algebraic expressions. Negative exponents are also covered.
3008 - Addition, Subtraction and Multiplication of Polynomials.
This segment covers addition and subtraction of polynomials as well as removal of parentheses. Multiplication of polynomials is also covered.
3009 - Greatest Common Factor and Factoring Trinomials.
This segment covers factoring of polynomials beginning with factoring out the greatest common factor. In the case of trinomials the method of arranging terms in descending degree and inspection of signs to locate signs in the factors is covered. In case of polynomials with four or more terms, the method of factoring by grouping is covered. The problems covered here are at the intermediate algebra level of difficulty.
3010 - Factoring Binomials.
This segment covers factoring binomials in the case of the difference of two perfect squares and in the case of the sum or difference of two cubes. The case of binomials which reduce to these cases after factorization of the greatest common factor is also covered. The problems covered here are at the intermediate algebra level of difficulty.
3011 - General Factoring.
This segment covers factoring polynomials in general. In the case of binomials the difference of two perfect squares and the sum or difference of two cubes as well as binomials which can be treated by these methods are covered. In the case of trinomials the method of arranging terms in order of decreasing degree in order to determine the signs of the terms in the factors is covered. For polynomials with more than three terms factoring by grouping is covered. Polynomials in more than one variable are also covered.
3012 - Solving Quadratic Equations by Factoring.
This segment covers the method of solving quadratic equations by first rearranging terms so as to force one side of the equation to be identically zero and then factoring the resulting trinomial or binomial. The factors are then used to obtain linear equations for the solutions. The problems covered are at the intermediate algebra level of difficulty.
3013 - Multiplication and Division of Rational Expressions.
This segment covers multiplication and division of rational expressions as well as reducing to lowest terms by factoring both numerator and denominator. In case of multiplication the use of cancellation before multiplication to simplify work is covered. The problems covered are at the intermediate algebra level.
3014 - Addition and Subtraction of Rational Expressions.
This segment covers addition and subtraction of rational expressions by finding the least common denominator after factoring all denominators. The problems covered here are at the intermediate algebra level of difficulty.
3015 - Complex Fractions.
This segment covers complex fractions and the short method of simplification by multiplying numerator and denominator by the least common denominator of all denominators in the terms of the numerator and denominator of the complex fraction. This segment also covers complex fractions in which negative exponents appear.
3016 - Division of Rational Expressions.
This segment covers the simplification of rational expressions by using long division of polynomials to divide the numerator by the denominator when the numerator has higher degree than the denominator.
3017 - Equations Involving Rational Expressions.
This segment covers methods for solving equations involving rational expressions which can be reduced to either linear or quadratic equations on multiplication of both sides of the equation by the least common denominator of all denominators in the equation. The notion of elimination of extraneous roots or solutions by checking all solutions in the original equation is also covered. The problems covered are at the level of intermediate algebra.
3018 - Applications that Lead to Rational Expressions.
This segment covers a variety of applications that arise which lead to equations involving rational expressions. In particular, problems involving distance, rate and time, as well as word problems are covered. Also covered are problems with literal equations.
3019 - Rational Exponents.
This segment covers the meaning and usage of rational exponents and the simplification of algebraic expressions using the laws of exponents when rational exponents are involved. The problems covered here are at the intermediate algebra level of difficulty.
3020 - Simplifying Radicals.
This segment covers the simplification of algebraic expressions involving radicals. This segment also covers the equivalence of radicals with fractional exponents as well as rationalizing denominators where these radicals are encountered in denominators.
3021 - Addition and Subtraction of Radical Expressions.
This segment covers the simplification of algebraic expressions with several terms involving radicals. The method of extraction of perfect roots from the various terms followed by collecting like terms is covered.
3022 - Multiplication and Division of Radical Expressions.
This segment covers multiplication and division of radical expressions and their simplification by extracting perfect roots. This segment also covers rationalizing radical expressions with binomial denominators by multiplying numerator and denominator by the appropriate conjugate of the denominator.
3023 - Radical Equations.
This segment covers the solution of equations with terms containing radicals via successive isolation of radicals and their removal by raising both sides of the equation to the appropriate power. The removal of extraneous solutions from the solution set by checking all solutions in the original equation is also covered.
3024 - Miscellaneous Quadratic Equations Solved by Factoring.
This segment covers a variety of equations, involving various previously studied algebraic expressions, which are reducible to quadratic equations which can then be solved by factoring. This segment also covers the method of solving equations by substituting new symbols for expressions which appear repeatedly in the same equation.
3025 - Solving Quadratic Equations by the Quadratic Formula.
This segment covers the solution of quadratic equations in which the unknowns can be collected into a single term which is the square of a binomial and then are solvable directly by roots. The technique of completing the square is covered to show that the preceding form can always be obtained.
3026 - Solving Quadratic Equations by the Quadratic Formula.
This segment covers the quadratic formula and its use in solving quadratic equations. This segment also covers the rearrangement of any quadratic into standard form to facilitate identification of appropriate coefficients as to their proper place in the quadratic formula for computation of solutions.
3027 - Applications that Lead to Quadratic Equations.
This segment covers various applications which lead to equations which after rearrangement and simplification become reduced to quadratic equations. This segment also covers the Pythagorean Theorem and applications to perimeter and area problems.
3028 - Intercepts, Distance and Slope.
This segment covers the rectangular coordinate system and intercept for linear equations in two unknowns. This segment also covers the calculation of the distance between pairs of points with given coordinates as well as the slope of the line segment connecting them.
3029 - Equations of Straight Lines.
This segment covers the slope-intercept and point-slope form for the equation of a line. The relationship of a slope to steepness and methods of calculating slope via rise over run as well as rearrangement into slope-intercept form is covered. Parallel and perpendicular lines are also covered. The problems covered are at the intermediate algebra level of difficulty.
3030 - Graphs of Linear Inequalities.
This segment covers graphing of linear inequalities by the technique of graphing the boundary lines and using test points off of the boundary lines to decide which regions to shade or include. This segment also covers intersection, union, and absolute value inequalities.
3031 - Simultaneous Equations.
This segment covers the solution of systems of linear equations using the elimination method as well as the substitution method. This segment also covers an application.
The College Algebra video series on DVD consists of 31 DVDs. Each DVD is approximately 25-30 minutes in length. Topics include factoring, rational expressions, radicals, rational exponents, complex numbers, linear equations and inequalities and applications, solving quadratic equations, absolute value equations and inequalities, polynomial and rational inequalities, circles, functions and graph sketching, rational root theorem, graphing rational functions, exponential and logarithmic functions, induction, and the Binomial Theorem.
This series is extremely helpful to students currently enrolled in a college algebra course, for review before enrolling in a trigonometry or calculus course, or for anyone wanting to review their college algebra skills.
4001 - Factoring.
This segment covers factoring in general for polynomials of several variables, reviewing the techniques for binomials, trinomials and factoring by grouping for polynomials with more than three terms. Also covered are examples where unknowns appear as exponents.
4002 - Operations on Rational Expressions.
This segment reviews addition, subtraction, multiplication, and division of rational expressions at the college algebra or precalculus level of difficulty.
4003 - Radical Expressions.
This segment reviews the properties of radicals and covers the simplification of algebraic expressions in several variables with radicals. Rationalizing denominators is also covered.
4004 - Rational Exponents.
This segment reviews the laws of exponents and covers simplification of algebraic expressions involving rational number exponents as well as factoring with negative and rational exponents.
4005 - Complex Numbers.
This segment covers addition, subtraction, multiplication, conjugation, and division of complex numbers and their use in solution of quadratic equations.
4006 - Solving Linear Equations.
This segment reviews strategies for solving linear equations of college algebra or precalculus level of difficulty which can be rearranged to linear form.
4007 - Word Problems.
This segment covers word problems of college algebra or precalculus level of difficulty including problems of mixtures, speed, distance and time, and interest rates.
4008 - Solving Quadratic Equations.
This segment covers solution of equations which can be rearranged to quadratic form. The methods of solution by factoring, by completing the square, and by quadratic formula are all covered.
4009 - Miscellaneous Equations.
This segment covers equations in general, some involving radicals which can be rearranged to linear or quadratic form. Only real roots are considered for this segment.
4010 - Inequalities.
This segment covers inequalities in one variable including examples with factored polynomials, with rational expressions, as well as compound inequalities.
4011 - Absolute Value Inequalities.
This segment reviews the definition and properties of absolute value and absolute value inequalities as well as solution of absolute value inequalities.
4012 - Polynomial and Rational Inequalities.
This segment covers polynomial and rational inequalities in general in one variable. The examples covered are at the college algebra or precalculus level of difficulty.
4013 - Circles, The Midpoint Formula, and The Distance Formula.
This segment covers analytic geometry problems involving distances between pairs of points, midpoints, and determination of radius and center for quadratic equations of two variables which describe circles.
4014 - Equations of Straight Lines.
This segment covers slope, its meaning, as well as methods for calculation. Perpendicular and parallel lines, point-slope form for equations of lines, and general form for linear equations in two variables are covered.
4015 - Functions.
This segment covers the mathematical definition of the word "function", the function notation, computation of values of given functions, problems of finding domains for functions specified by algebraic expressions, as well as the difference quotient.
4016 - Graph Sketching.
This segment covers elementary graphing techniques for functions including definitions of even, odd, increasing, and decreasing functions.
4017 - Shifting and Reflecting Graphs.
This segment covers methods for vertical and/or horizontal shifting so as to reduce graphing problems for functions to simpler forms. Examples involving absolute value, radicals, and quadratic and cubic functions are included.
4018 - Algebra of Functions.
This segment covers This segment covers addition, subtraction, multiplication, division and composition of functions.
4019 - Inverse Functions.
This segment covers the definition of mutually inverse functions, one-to-oneness, problems of showing given pairs of functions to be mutually inverse, the horizontal line test for one-to-oneness and problems of finding inverses for given functions.
4020 - Quadratic functions.
This segment covers general quadratic functions and their graphs as well as methods for finding the vertex, horizontal and vertical intercepts, and axis of symmetry.
4021 - Polynomial Functions.
This segment covers graphing and finding horizontal and vertical intercepts for general polynomial functions.
4022 - Division of Polynomials, the Remainder Theorem and the Factor Theorem.
This segment covers long division for polynomials, synthetic division, the use of the remainder theorem for calculating function values by synthetic division, and the use of the factor theorem for finding roots of polynomials.
4023 - Rational Root Theorem.
This segment covers the use of the rational root theorem for factorization of polynomials.
4024 - Vertical and Horizontal Asymptotes.
This segment covers methods of finding vertical, horizo ntal, and oblique asymptotic lines to graphs of rational functions.
4025 - Graphing Rational Functions.
This segment covers the graphing of rational functions using techniques of shifting and reflecting, as well as intercepts and asymptotes.
4026 - Exponential Functions and Their Graphs.
This segment covers exponential functions, the number e, continuously compounded interest, growth and decay problems, as well as problems of graphing exponential functions.
4027 - Logarithms and Their Properties.
This segment covers the definition of logarithmic functions as inverse to exponential functions, properties of logarithms, and computations involving logarithms as well as logarithmic equations.
4028 - Logarithmic functions and Their Graphs.
This segment covers graphing of logarithmic functions, the change of base formula, and the use of logarithms to solve exponential equations.
4029 - Systems of Nonlinear Equations.
This segment covers substitution and elimination methods for solving two equations in two unknowns without linearity restrictions but with use of graphing to illustrate the solutions.
4030 - Induction.
This segment covers This segment covers the definition of proof by mathematical induction and the use of mathematical induction for proving certain identities.
4031 - Binomial Theorem.
This segment covers factorial notation, binomial coefficients and the use of the binomial theorem for expansion of a binomial raised to a power as well as determination of specific terms of the expansion in case of large powers.
The Trigonometry video series on DVD consists of 16 DVDs. Each DVD is approximately 25-30 minutes in length. Topics include angles, degrees and radians, trigonometric functions of general angles, graphing trigonometric functions, proving trigonometric identities, inverse trigonometric functions, right triangle applications, law of sines, law of cosines, polar coordinates, DeMoivre's Theorem, and nth roots of complex numbers.
This series is extremely helpful to students currently enrolled in a trigonometry course, for review before enrolling in a calculus course, or for anyone wanting to review their trigonometric skills.
5001 - Angles, Degrees and Radians.
This segment covers definitions for angles and their measures as well as the circular arc length formula and problems for conversion of angle measure for radians to degrees, degrees to minutes and vice-versa.
5002 - Introduction to Trigonometric functions.
This segment covers the definitions of the trigonometric functions of acute angles using right triangles, as well as special angles of 30, 60 and 45 degrees.
5003 - Trigonometric Functions of General Angles.
This segment covers the definitions of trig functions for general angles using rectangular coordinates, standard position and terminal side. The reciprocal, quotient and Pythagorean identities are covered.
5004 - Evaluating Trigonometric Functions.
This segment covers reference angles and their use in computation of trig functions of general angles.
5005 - Graphing Trigonometric Functions I.
This segment covers the reciprocal relations, the Pythagorean identities, evenness and oddness for trig functions and demonstrations of some simple trig identity problems.
5006 - Graphing Trigonometric Functions II.
This segment covers the formulas for trig functions of sum and difference of angles and their use for computing trig functions of certain angles which can be reduced to 30, 60, 45 degree angles using these formulas.
5007 - Trigonometric Identities I.
This segment covers the reciprocal relations, the Pythagorean identities, evenness and oddness for trig functions and demonstration of some simple trig identity problems.
5008 - Trigonometric Identities II.
This segment covers the formulas for trig functions of sum and difference of angles and their use for computing trig functions of certain angles which can be reduced to 30, 60, 45 degree angles using these formulas./dd>
5009 - Trigonometric Identities III.
This segment covers the double-angle and half-angle formulas and their use in calculations as well as in solution of trig identities.
5010 - Inverse Trigonometric Functions.
This segment covers inverse functions for sine, cosine, and tangent functions as well as computations involving trig functions of an expression containing an inverse trig function.
5011 - Trigonometric Equations.
This segment covers the use of trig identities for solving trigonometric equations.
5012 - Right Triangle Applications.
This segment covers the use of trig functions to solve right triangles from partial information, and applications.
5013 - Law of Sines.
This segment covers the use of the law of sines to solve triangles from partial information.
5014 - Law of Cosines.
This segment covers the use of the law of cosines to solve general triangles from partial information, as well as applications.
5015 - Polar Coordinates.
This segment covers polar coordinates as well as the use of sine and cosine to transform from polar to rectangular coordinates and the tangent function for converting from rectangular to polar coordinates.
5016 - Trigonometric Form, DeMoivre's Theorem and Nth Roots of Complex Numbers.
This segment covers the trigonometric or polar form for complex numbers and DeMoivre's theorem for computation of roots of complex numbers.
The Geometry video series on DVD consists of 16 DVDs. Each DVD is approximately 25-30 minutes in length. Topics include postulates, proof, triangles, congruence and similarity, parallel lines, quadrilaterals, right triangles, circles, area, coordinate geometry, solids, constructions and introduction to Non-Euclidean geometries.
This series is extremely helpful to students currently enrolled in a freshman or sophomore level college geometry course or for anyone wanting to review their advanced plane geometry skills.
7001 - Postulates and Basic Terms. This segment covers basic postulates and terms of Euclidean geometry including between, line segment, ray, angle, straight angle, vertical angles, linear pair, and degrees. Also covered are acute, right, and obtuse angles as well as supplementary and complementary angles.
7002 - Introduction to Proofs. This segment covers the parts of a direct proof and an indirect proof. Theorems are proven by direct proofs using a statement-reason form. "If then" statements are introduced as well as the converse and the contrapositive of these statements.
7003 - Triangles, Part I. This segment covers congruent triangles as well as scalene, isosceles, equilateral, right and equiangular triangles. SAS, ASA, and SSS congruencies for triangles are also presented and a few theorems about triangles are proved using direct proofs.
7004 - Triangles, Part II. This segment covers exterior angles, concurrent lines, centroid, altitude, and orthocenter. Direct proofs of theorems involving triangles are included.
7005 - Parallel Lines. This segment covers parallel lines, transversals, corresponding angles and alternate interior angles. Euclid's Parallel Postulate is also covered. An example of an indirect proof is included as well as direct proofs. Direct proofs include "The sum of the measures of the angles of a triangle is 180 degrees" and "An exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.".
7006 - Constructions, Part I. This segment covers basic geometric constructions with a compass and straightedge. Constructions shown include constructing congruent line segments and angles, bisecting an angle, constructing the perpendicular bisector of a segment, the perpendicular to a line and the medians and altitudes of a triangle.
7007 - Quadrilaterals. This segment covers convex and concave polygons, regular polygons, the diagonals of a polygon as well as special quadrilaterals including parallelogram, trapezoid, rhombus, rectangle, square and isosceles trapezoid. A direct proof of "The opposite sides and opposite angles in a parallelogram are congruent" is shown.
7008 - Similarity. This segment covers similar polygons and triangles as well as AA, SAS, and SSS similarities for triangles. Exercises are included placing emphasis on the understanding of proportional sides of similar triangles. Direct proofs involving similar triangles are also included.
7009 - Right Triangles. This segment covers right triangles, the hypotenuse and the legs of a right triangle, HL congruency theorem, geometric mean, the Pythagorean theorem and 30-60-90 degree and 45-45-90 degree triangles as well as the relationships that exist between the sides of these special triangles. A proof of "The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original right triangle" is included.
7010 - Circles, Part I. This segment covers circles, center, radius, secant, chord, diameter, concentric circles, tangent, point of tangency, semicircle, central angles, minor and major arcs and how they are measured. Direct and indirect proofs are included.
7011 - Circles, Part II. This segment covers This segment covers inscribed angles and secant angles and their measure. Also covered are the relationships of the lengths of the sides of two chords intersecting in a circle, two secant segments drawn from an external point, and an intersecting tangent segment and secant segment. An example of a direct proof is also included as well as exercises.
7012 - Constructions, Part II. This segment covers geometric constructions with a compass and a straightedge. Constructions shown include dividing a line segment into a given number of congruent segments, constructing the fourth proportional to three given segments, constructing a circle given three points that are not collinear, constructing the tangent to a circle from a point on the circle, constructing the tangents to a circle from an external point, and constructing an equilateral triangle given a side.
7013 - Area. This segment includes the concepts of perimeter and area. Circumference of a circle is presented as well as area formulas of a rectangle, triangle, parallelogram, circle, trapezoid, and square. Exercises finding perimeters and areas are also included.
7014 - Coordinate Geometry. This segment covers the Cartesian or rectangular coordinate system as well as the midpoint formula and the distance formula. Slope is covered as well as parallel lines, perpendicular lines, and slope-intercept and point-slope forms of lines. The standard form of a circle is also included.
7015 - Solids. This segment covers convex solids and polyhedrons as well as face, vertex, and side of a polyhedron. Regular polyhedrons, prisms, parallelepipeds, pyramids, sphere, cones and cylinders are also included. The concept of surface area and volume is covered as well as formulas for some convex solids.
7016 - Introduction to Non-Euclidean Geometry. This segment covers a comparison of Euclid's Parallel Postulate to the Riemann Postulate and the Gauss-Lobachevski-Bolyai Postulate. Interesting facts about Elliptic geometry are presented by looking at a spherical model. Also some properties of Hyperbolic geometry are covered.
Calculus video series on DVD consists of 56 DVDs. Each DVD is approximately 25 to 30 minutes in length. The DVDs cover the material in a standard college freshman year calculus course, and suitable for science and engineering majors. Topics covered include limits, continuity, differentiation, applications of differential calculus to graphing and optimizing functions, transcendental functions and their derivatives, integral calculus and applications to areas and volumes, L'Hopital's Rule, sequences and series, elementary vector algebra with dot products and cross-products.
The first 32 segments can also be used to supplement the typical one-semester elementary or basic calculus course, suitable for business majors and students of the liberal arts.
6001 - Rectangular Coordinates and Graphing.
This segment covers the rectangular coordinate system and representation of ordered pairs of real numbers as points in the plane as well as the representation of points in the plane by ordered pairs of real numbers.
6002 - Functions and Their Graphs.
This segment covers the mathematical definition of the word "function", the function notation, graphing of functions, and some simple examples of functions and their graphs.
6003 - Average Rate of Change and Slope of Lines.
This segment covers average rate of change for a function between two points, slope of lines, the relation between slope, average rate of change, and velocity.
6004 - Formulas for Lines.
This segment covers the point-slope and slope-intercept forms for equations of lines as well as problems involving equations for parallel and perpendicular lines.
6005 - Limits and Continuity.
This segment covers computations of limits using limit rules, the definition of continuity, and the use of continuity in computations of limits.
6006 - The Delta-Process and Instantaneous Rates of Change.
This segment covers the computation of derivatives or instantaneous rates of change as limits of difference quotients or limits of average rates of change.
6007 - Tangent Lines.
This segment covers the computation of equations of tangent lines to graphs of functions using the differentiation rules and point-slope form for equations of lines.
6008 - Differentiation Rules (Powers and Sums).
This segment covers the power, sum, difference, and scalar multiplication rules for differentiation.
6009 - The Product and Quotient Rules.
This segment covers the product and quotient rules for differentiation including examples showing the power rule for positive integer powers as a consequence of the product rule.
6010 - Composite Functions and the Chain Rule.
This segment covers the definition of the composition operation for functions as well as examples of computations with composite functions. The chain rule for differentiation of composite functions is covered and examples are covered illustrating how and when to apply the chain rule.
6011 - Optimization Using Differentiation: Critical Points.
This segment covers the technique of optimization of a function by finding all zeroes of the derivative.
6012 - Second Derivative, Inflection Points and Concavity.
This segment covers higher derivatives, inflection points, concavity, and examples illustrating the use of these concepts in graphing and in optimization.
6013 - Implicit Differentiation.
This segment covers implicit differentiation and its use in finding slopes of tangent lines to curves at specific points when the curves are defined implicitly by equations.
6014 - Inverse Functions and Their Derivatives.
This segment covers inverse functions and their graphical relationships as well as methods for finding inverses of invertible functions and for finding derivatives of the inverses.
6015 - Exp, Log and Differentiation.
This segment covers the exponential and logarithmic functions as well as their derivatives, and techniques for differentiation of functions involving the exponential and logarithmic functions using differentiation rules.
6016 - Logarithmic Differentiation.
This segment covers logarithmic differentiation and its use in differentiating products with many factors as well as complicated exponential expressions.
6017 - Applications to Growth and Decay.
This segment covers the use of exponential and logarithmic functions in solving problems where rate of change of a quantity is proportional to the amount of that quantity. Applications include population growth, radioactive decay, and continuously compounded interest.
6018 - Trig Functions.
This segment reviews the trig functions and covers their derivatives and the use of differentiation rules to differentiate functions involving trig functions.
6019 - Related Rates.
This segment covers applications involving related rates using differentiation rules to differentiate equations relating various quantities to obtain equations relating rates of change.
6020 - Differentiation and Approximation.
This segment covers the use of differentiation to obtain linear approximations to function values at points near points where values and derivatives are computable.
6021 - Taylor's Formula.
This segment covers Taylor's formula and its use in approximating function values as well as problems of finding Taylor polynomials for functions.
6022 - Areas, Antidifferentiation and the Fundamental Theorem of Calculus.
This segment is an introduction to the ideas of integral calculus and the use of antidifferentiation and the fundamental theorem of calculus in the computation of area.
6023 - Integration Formulas.
This segment covers the power, sum, difference, and scalar multiplication rules for integration and techniques for reducing antidifferentiation of certain types of functions to application of these rules.
6024 - Substitution.
This segment covers the power, sum, difference, and scalar multiplication rules for integration and techniques for reducing antidifferentiation of certain types of functions to application of these rules.
6025 - Integration by Parts.
This segment covers integration by parts and techniques for using integration by parts to antidifferentiate certain classes of functions.
6026 - Definite Integrals and Areas.
This segment covers the computation of areas for regions bounded by curves using the definite integral.
6027 - Definite Integrals, Substitution, and Integration by Parts.
This segment covers definite integrals which can be computed by substitution and/or integration by parts.
6028 - Advanced Area Problems.
This segment covers more difficult examples of area where boundaries may involve several curves and computations involve more than one definite integral.
6029 - Volume Problems.
This segment covers volumes for solids of revolution as well as Cavallieri's principle for finding volumes from cross-sectional area functions by integration.
6030 - Advanced Volume Problems.
This segment covers problems of finding volumes of more complicated geometric solids including the torus, the ball with a hole drilling through, and the intersection of two solid cylinders.
6031 - Applications to Physics.
This segment covers applications to calculus to Newtonian mechanics, the laws of motion for an object with one degree of freedom of movement, the concepts of potential and kinetic energy, conservation of energy and gravitation.
6032 - Applications to Business.
This segment covers applications of calculus to business problems, the calculus interpretation of the word "marginal" as used in business, marginal cost, marginal profit, marginal revenue, and optimization problems arising in business.
6033 - Special Trigonometric Limits.
The special trigonometric limits of sin(x) over x and (1-cos(x)) over x as x approaches zero are reviewed and examples are worked involving limits of algebraic expressions involving trigonometric functions which can be evaluated by reduction to one of the former cases.
6034 - General Limits.
The basic theorems on limits are reviewed including the composition or substitution theorem, the squeeze theorem, and its corollary, the fact that a product of a bounded function by a function with limit zero must also have limit zero. Examples of limits of a more advanced nature are worked which illustrate the use of these theorems.
6035 - One-Sided Limits.
The definition of one-sided limit is given and visually illustrated. The theorem on the relation between one-sided limits and two-sided (ordinary) limits is reviewed, and examples worked both for the computation of one-sided limits and the use of one-sided limits to show non-existence of certain two-sided limits.
6036 - Limits Using Continuity.
The elementary examples of limits are worked out using the idea of extending a continuous function to include the limit point in the domain as in the removal of a singularity.
6037 - Hyperbolic Functions.
The hyperbolic trigonometric functions are defined, their basic identities are reviewed as well as their derivatives. Examples of differentiation involving hyperbolic functions are worked.
6038 - L'Hopital's rule.
L'Hopital's rule for computation of limits of indeterminate form is reviewed and examples of limit problems requiring L'Hopital's rule are worked.
6039 - Trigonometric Integrals.
Techniques and reduction formulas for integrating products of trigonometric functions are reviewed. Examples are worked illustrating the various cases.
6040 - Trigonometric Substitutions.
Techniques of using trigonometric substitution to simplify integrands are reviewed and examples are worked showing how to integrate functions containing quadratic expressions by trigonometric substitution.
6041 - Partial Fractions.
The technique of integrating a rational function by expressing it as a sum of partial fractions is reviewed and illustrated in worked examples.
6042 - Improper Integrals.
The definition of an improper integral as a limit of proper integrals is reviewed and examples of improper integrals are worked.
6043 - Area in Polar Coordinates.
The technique and formula for area in polar coordinates is reviewed. Examples are worked using the integration formula for area in polar coordinates to compute areas of regions bounded by curves expressed in polar coordinates.
6044 - Sequences and Convergence.
The basic definitions of sequences, convergence, and divergence are reviewed. The theorem on use of computing limits of sequences in terms of limits of continuous functions is discussed, and examples are worked for illustration.
6045 - Summation Notation.
The sigma notation for summation is reviewed, examples are worked showing how to compute sums expressed in sigma notation. The concept of dummy index is discussed and examples are worked showing how to change indices in the sigma notation via substitution.
6046 - Infinite Series.
The basic definitions of infinite series and partial sums are reviewed, the definitions of convergence and divergence for infinite series are reviewed and the nth term test for divergence of an infinite series is reviewed. Examples of telescoping series and geometric series are worked as well as examples showing the use of the nth term test to prove divergence of certain series.
6047 - Comparison Test.
The comparison test and limit comparison tests are reviewed and discussed for infinite series and examples are worked illustrating their use in determining convergence or divergence of certain infinite series.
6048 - Integral Test.
The comparison test and limit comparison tests are reviewed and discussed for infinite series and examples are worked illustrating their use in determining convergence or divergence of certain infinite series.
6049 - Absolute Convergence and Alternating Series.
Absolute convergence is reviewed as well as forms of the comparison test and limit comparison for series with negative as well as positive terms in the determination of absolute convergence. Conditional convergence is reviewed. Alternating series are defined and the nth term test for convergence of an alternating series is reviewed. Examples illustrating the concepts are worked as well as examples using the nth term to estimate the error in a partial sum and examples of finding the proper partial sum for estimating an alternating series sum to within predetermined error tolerance.
6050 - Ratio Test and Root Test.
The ratio test and the root test for determining convergence or divergence of infinite series are reviewed and discussed. Examples are worked illustrating both tests as well as how to choose between the two n tests from the form of the nth term.
6051 - Power Series.
Power series, radius of convergence, and interval of convergence are defined and discussed as well as the theorems on termwise differentiation and integration of power series. The ratio and root test forms for determining radius of convergence are reviewed and examples are worked illustrating their use.
6052 - Taylor Series.
The Taylor series of a function is defined and the Lagrange form of the Taylor remainder is reviewed and used to show certain functions equal their Taylor series. Examples are also worked illustrating techniques of algebra combined with termwise differentiation and integration to obtain Taylor series of certain functions from the formula for the sum of the geometric series.
6053 - Vectors.
Vectors are defined as arrows in space and the basic rules of vector addition and scalar multiplication are discussed visually. The commutative and associative laws are visually demonstrated for vector addition and the distributive law for scalar multiplication is demonstrated visually. The notion of a space of vectors is discussed and the definition of a frame of vectors is given in cases of all vectors in a line, a plane, or 3-dimensional space. The formulas for computing the addition and scalar multiplication in coordinates relative to a frame are demonstrated in one and two dimensions and reviewed for three dimensions.
6054 - Dot Product and Length.
The geometric definition of dot product for vectors as arrows in space is given and the commutative and distributive laws are demonstrated visually. The formulas for computing the dot product in coordinates relative to a frame are demonstrated as well as the utility of an orthonormal frame for simplifying the formulas. The relation of dot product to length is reviewed and demonstrated. The importance of understanding the geometry of the vector operations is emphasized throughout in order to facilitate the use of vector techniques in applications.
6055 - Vector Component Computations.
The formulas for computing vector addition, scalar multiplication, and dot product are reviewed and used together with their geometric properties to derive geometric formulas and equations. The coordinate formulas for the distance between a pair of points in space, the normalization of a vector, the equation of a sphere, and the distance from a point to a plane are demonstrated using vectors.
6056 - Vector Cross Product.
The geometric definition of the cross product and the right hand rule are given and demonstrated visually. the relation between lengths of the cross product are reviewed. The anticommutative and distributive laws for the cross product are geometrically and visually demonstrated and consequences examined. The coordinate formula for the cross product using coordinates relative to the standard right hand coordinate system is derived and the technique for each calculation using two by two determinants are demonstrated and illustrated by example.
Probability & Statistics Video Series
This DVD video series consists of 60 DVDs. Each DVD is approximately 25 to 30 minutes in length. The objective of this series is to give the student a resource in probability and statistics. The approach we used is to cover all the topics of the standard two semester course in Probability and Statistics, one topic per segment. For each segment, the basic set-up and theoretical framework is reviewed and then examples are worked illustrating the theory. Word problems of a realistic nature are emphasized throughout.
The topics covered include frequency distributions, measures of central tendency of data such as the mean, and standard deviation, probability and conditional probability, random variables and expectations, binomial, normal, and Poisson distributions, confidence intervals, hypothesis tests, regression and correlation, goodness of fit, testing for normality, and analysis of variance.
8001 - Populations and Data.
This segment is an introductory discussion about what problems statisticians deal with, and the notion of population as distinct from data.
8002 - Frequency distributions.
This segment is about grouping numerical data into classes, frequency, relative frequency, density, real class intervals, real class boundaries, real class midpoints, guidelines for choosing classes.
8003 - Visual Display of Data.
This segment covers histograms, frequency polygons, cumulative distributions and ogives, and pie graphs.
8004 - Mean.
This segment covers the formulas for the mean of a sample and of a population and examples illustrating their computation.
8005 - Mode, Median, and Midrange.
This segment covers the definition and computation of modes, medians, and midranges for data and for populations.
8006 - Means, Medians, and Modes of Grouped Data.
This segment covers the estimation and computation of means, medians, and modes of grouped data such as from frequency, relative frequency, and density histograms for data and for populations.
8007 - Variance and Standard Deviation.
This segment covers the formulas and computations of variance and standard deviation of populations, samples, and grouped data, emphasizing mean of square minus square of mean.
8008 - Sample Spaces and Events.
This segment covers the basic notions for setting up probability theory, the notions of outcome, sample space, and event.
8009 - Probability Laws and Gambling Odds.
This segment covers the basic laws of probability, the relationship between mathematical probability and gambling odds, and elementary computations with laws of n probability, as well as the notion of mutually exclusive events.
8010 - Model of Equally Likely Outcomes.
This segment covers the definition and basic examples and applications of the model of equally likely outcomes for computing probability.
8011 - Conditional Probability.
This segment covers the definition and applications of conditional probability.
8012 - Independent Events.
This segment covers the definition of independence for events, equivalent formulations for detecting independence and comparison with notion of mutual exclusivity.
8013 - Bayes Theorem.
This segment covers the result known as Bayes Theorem for computation of certain conditional probabilities using a partition of the sample space, as well as applications.
8014 - Multiplication Principle for Counting.
This segment covers the multiplication principle for counting the outcomes for multi-stage processes where the number of outcomes at each stage is independent of the particular history of outcomes of previous stages. Applications of the multiplication principle to typical counting problems are given.
8015 - Permutations and Factorials.
This segment covers computations with permutations and factorial notation for counting permutations as well as applications to probability.
8016 - Combinations.
This segment covers This segment covers the definitions of combinations, binomial coefficients, Pascal's triangle, and applications to probability.
8017 - Random Variables and Distributions.
This segment covers the basic definitions of function, of random variable as real-valued function on sample space, of distribution of a random variable and examples.
8018 - Continuous Random Variables and Densities.
This segment covers the notion of continuous random variable and the use of density to describe its distribution, as well as illustrative examples.
8019 - Expectations of Random Variables.
This segment covers the definition and computation of the expected value of a random variable as well as the rules for computation of expected values of sums and constant multiples of random variables, the linearity of expectation.
8020 - Variance of Random Variables.
This segment covers the definition of the variance of a random variable as the expected value of the squared deviation from the mean and the equivalence with the expected value of the square minus the square of the expected value as well as the use of the latter in computations.
8021 - Independent Random Variables.
This segment covers the definition and basic rules for the computation of expected value of a product of independent random variables, the variance of the sum of independent random variables, and applications.
8022 - Binomial Distribution.
This segment covers the definition and the basic applications of the binomial distribution to problems of repeated independent trials of a two-outcome experiment.
8023 - Poisson distribution.
This segment covers the definition and applications of the Poisson distribution.
8024 - Tchebychev's Approximation.
This segment covers the inequality known as Tchebychev's approximation and applications to random variables with unknown distribution.
8025 - Central Limit Theorem.
This segment covers the definition of the normal distribution, the method of standardization of a normal random variable for determining its distribution from the tabulated Z-distribution, the standard normal random variable.
8026 - Central Limit Theorem.
This segment covers the central limit theorem on limit in mean of a sequence of identically distributed random variables being normally distributed as well as generally accepted criterion for using the normal approximation in applications.
8027 - Normal Approximation to Binomial.
This segment covers the criterion and applications for approximating the binomial distribution by the normal distribution.
8028 - Sampling Distribution of Mean.
This segment covers the notion of the sample mean as a random variable and its expected value.
8029 - Standard Error of Mean.
This segment covers the standard error of the mean as the variance of the sample mean as a random variable, as well as computational examples.
8030 - Confidence Intervals with Variance Known.
This segment covers the construction of confidence intervals for the mean of a random variable in cases where the variance of the random variable is known, and where a sample mean and the standard Z-distribution can be applied.
8031 - T-Distribution and Confidence Intervals.
This segment covers the construction of confidence intervals for the mean of a normal random variable in cases where the sample mean, the sample variance, and the T-distribution are required.
8032 - Confidence Intervals for Proportions.
This segment covers the use of the normal approximation to the binomial for constructing confidence intervals for a proportion using sample data and the standard Z-distribution.
8033 - Confidence Intervals for Variance and Chi-Square.
This segment covers sample variance as a random variable, standardization of sample variance, the chi-square distribution and applications to confidence intervals for variance and standard deviation.
8034 - Hypothesis Testing.
This segment covers the basic notions of a hypothesis test, the Type I and Type II errors, the notion of level of significance and null hypothesis,and power, as well as comparison with scientific method and legal trial. Emphasis here is on developing understanding of the basic logical set up and framework for hypothesis testing in general, and use the fact that the alternate hypothesis is the only hypothesis which can be proved as a guide to setting up hypothesis tests..
8035 - Hypothesis Tests About Mean.
This segment covers the basic maximum power tests for null hypotheses which are inequalities or equalities involving the mean of an unknown population, when to use the Z-distribution.
8036 - Hypothesis Tests With Variance Unknown.
This segment covers hypothesis tests of inequalities or equalities involving the mean using the T-distribution in the case the population variance is unknown.
8037 - Hypothesis Tests of Proportions.
This segment covers hypothesis tests of inequalities or equalities involving variance of standard deviation using sample data and the chi-square distribution.
8038 - Hypothesis Tests of Variance.
This segment covers hypothesis tests of inequalities or equalities involving variance of standard deviation using sample data and the chi-square distribution.
8039 - Confidence Intervals for Difference of Means.
This segment covers the methods for constructing a confidence interval for the difference of means of two different populations.
8040 - Hypothesis Tests for Difference of Means.
This segment covers the hypothesis tests and methods of dealing with equalities and inequalities of means of two different populations.
8041 - Confidence Intervals & Hypothesis Tests I.
This segment covers tests and confidence intervals for the difference of two means in case the variances are unknown, using pooled variance in cases the variances can be assumed equal and the formula for degrees of freedom to compensate if variances cannot be assumed equal.
8042 - Confidence Intervals & Hypothesis Tests II.
This segment covers confidence intervals and hypothesis tests for the difference of two proportions.
8043 - Confidence Intervals & Hypothesis Tests III.
This segment covers confidence intervals and hypothesis tests concerning the difference in two related populations.
8044 - Confidence Intervals & Hypothesis Tests IV.
This segment covers hypothesis tests and confidence intervals for comparing variances of two independent normal populations using the F-distribution.
8045 - Linear Regression.
This segment covers scatter diagrams and the least-squares best fitting straight line relating two variables.
8046 - Coefficient of Correlation.
This segment covers the computation of the sample correlation coefficient and its use in the hypothesis test for independence of two random variables.
8047 - Standard Error of Regression.
This segment covers the standard error of the regression line and the confidence intervals for the regression slope and vertical intercept, as well as the confidence interval for the variance in the regression error.
8048 - Prediction Intervals.
This segment covers the confidence intervals for single observation on the regression line.
8049 - Goodness of Fit.
This segment covers the Pearson chi-squared statistic and its use in testing hypothetical categorical models.
8050 - Normality Test.
This segment covers the goodness of fit test as applied to testing for normality in a population.
8051 - Two Variance Goodness of Fit and Independence.
This segment covers the goodness of fit test as applied to testing for independence of two classifications.
8052 - Index of Predictive Association.
This segment covers the use of the index of predictive association as a measure of dependence of two attributes.
8053 - One-Way Analysis of Variance.
This segment covers one-way analysis of variance of normal populations and the related hypothesis test for equality of means using the F-distribution.
8054 - Two-Way Analysis of Variance I.
This segment covers the simultaneous hypothesis tests for two-way classification using one observation per cell.
8055 - Two-Way Analysis of Variance II.
This segment covers two-way analysis of variance in the case of multiple observations per cell.
8056 - Sign Test.
This segment covers the one-sample sign test for hypothesis about the median of a possibly non-normal population.
8057 - Two-Sample Sign Test.
This segment covers the two-sample sign test for differences.
8058 - Runs Test.
This segment covers the runs test for randomness and its applications.
8059 - Rank Tests.
This segment covers the Mann-Whitney rank test and the Wilcoxon signed rank test.
8060 - Spearman Rank Correlation.
This segment covers the computation of the Spearman rank correlation and the Spearman rank correlation test.
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