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College Algebra Video Lectures,
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Chapter R (review): Basic Concepts of Algebra
Chapter 1: Graphs, Functions, and Models
Chapter 2: Functions, Equations, and Inequalities
Chapter 3: Polynomial and Rational Functions
Chapter 4: Exponential and Logarithmic Functions
Chapter 5: Systems of Equations and Matrices
Chapter 6: Conic Sections: Circles, Ellipses, Parabolas, & Hyperbolas
Chapter 7: Sequences, Series, Combinatorics, Combinations, & Permutations


Chapter R(review): Basic Concepts of Algebra

Animation

Laws of Exponents

Reading Scientific Numbers, Activity 2

Writing numbers scientifically

Writing numbers scientifically

Adding polynomials

Finding the degree of a polynomial

Multiply Polynomials

The FOIL method

Factoring a difference of squares

Factoring a trinomial

Factoring a trinomial

Factoring a Trinomial with a Common Factor

Factoring a Trinomial with a Common Factor

Factoring by grouping

Factoring out a common factor

Factoring trinomial squares

Multiplying rational expressions

Simplifying a Complex Fraction

Subtracting rational expressions

Applying the Rules for Rational Exponents

Multiplying radical expressions

Simplifying a Radical Quotient

Solving Right Triangles

Understand the Process of Simplifying Radical Expressions

Solving linear equations

The principle of zero products

Section Video Lectures

R.1 Video: The Real-Number System

R.2 Video: Integer Exponents, Scientific Notation, and Order of Operations

R.3 Video: Addition, Subtraction, and Multiplication of Polynomials

R.4 Video: Factoring

R.5 Video: Rational Expressions

R.6 Video: Radical Notation and Rational Exponents

R.7 Video: The Basics of Equation Solving

PowerPoint

Chapter R Lecture

 

Chapter 1. Graphs, Functions, and Models

Animation

Determine the Distance Between Two Points

Equations of circles

Finding intercepts

Plotting Ordered Pairs

Using Function Notation

Graphing Linear Functions

Linear Functions

Finding the slope and y-intercept from the equation

Point-Slope Form

Regression lines

Slope-intercept equation of a line

Exploring Increasing, Descreasing, & Constant Functions

Graphs of basic functions

Evaluating compositions

PowerPoint

Chapter One Lecture

Section Video Lectures

1.1 Video: Introduction to Graphing

1.2 Video: Functions and Graphs

1.3 Video: Linear Functions, Slope, and Application

1.4 Video: Equations of Lines and Modeling

1.5 Video: More on Functions

1.6 Video: The Algebra of Functions

1.7 Video: Symmetry and Transformations

 

Chapter 2. Functions, Equations, and Inequalities

Animation

Zeroes of Linear Functions

Formulas

Solving for a specified variable

Solving Two-Step Equations

The addition principle

Multiplying complex numbers

Subtracting complex numbers

Solving a quadratic equation with complex solutions

Solving equations that are quadratic in form

Solving Quadratic Equations by Completing the Square

Solving using the quadratic formula

Graphing quadratic functions

Graphing quadratic functions

Solving a Problem Involving a Rectangular Region

Equations involving absolute value

Solving radical equations

Solving rational equations

Using the squaring property when one side has two terms

Compound inequalites

Solving absolute value inequalites

Solving inequalities

Solving linear inequalities

Section Video Lectures

2.1 Video: Linear Equations, Functions, and Models

2.2 Video: The Complex Numbers

2.3 Video: Quadratic Equations, Functions, and Models

2.4 Video: Analyzing Graphs of Quadratic Equations

2.5 Video: More Equation Solving

2.6 Video: Solving Linear Inequalities

PowerPoint

Chapter Two Lecture

 

Chapter 3. Polynomial and Rational Functions

Animation

Exploring Zeros of Polynomial Functions

Synthetic Division

Finding all zeros of a polynomial function

Graphing Rational Functions and their Asymptotes

Solving Polynomial Inequalities

Solving nonlinear inequalities

Section Video Lectures

3.1 Video: Polynomial Functions and Modeling

3.2 Video: Graphing Polynomial Functions

3.3 Video: Polynomial Division; The Remainder and Factor Theorems

3.4 Video: Theorems about Zeros of Polynomial Functions

3.5 Video: Rational Functions

3.6 Video: Polynomial and Rational Inequalities

3.7 Video: Variation and Applications

PowerPoint

Chapter Three Lecture

 

Chapter 4. Exponential and Logarithmic Functions

Animation

Finding the equation of an inverse

Identifying one to one functions

Graphing exponential functions

Graphing the natural exponential function

Changing logarithmic bases

Converting between exponential and logarithmic form

Graphing logarithmic functions

Using the Power Rule

Exponential and Logarithmic Equations

Logarithmic functions

Solving exponential equations

PowerPoint

Chapter Four Lecture

Section Video Lectures

4.1 Video: Inverse Functions

4.2 Video: Exponential Functions and Graphs

4.3 Video: Logarithmic Functions and Graphs

4.4 Video: Properties of Logarithmic Functions

4.5 Video: Solving Exponential and Logarithmic Equations

4.6 Video: Applications and Models; Growth and Decay, and Compound Interest

 

Chapter 5. Systems of Equations and Matrices

Animation

Applications of systems of equations

Solve a system by elimination

Solve a system by substitution

Solving systems graphically

Traveling boat

Solving a System in Three Variables

Matrix Solution of Linear Systems

Solving systems of linear equations using matrices

Finding the Product of Matrices

Using Inverse Matrices to Solve Systems of Equations

Cramer's Rule

Graphing two-variable inequalities

Graphing two-variable inequalities

Linear programming

Solving systems of linear inequalites

Solving systems of linear inequalities

Partial Fractions

PowerPoint

Chapter Five Lecture

Section Video Lectures

5.1 Video: Systems of Equations in Two Variables

5.2 Video: Systems of Equations in Three Variables

5.3 Video: Matrices and Systems of Equations

5.4 Video: Matrix Operations

5.5 Video: Inverses of Matrices

5.6 Video: Determinants and Cramer's Rule

5.7 Video: Systemsof Inequalities and Linear Programming

5.8 Video: Partial Fractions

 

Chapter 6. Conic Sections

Animation

Graphing Parabolas

Summary of Conic Sections

Graphing Ellipses

Equations of ellipses

Graphing Ellipses

Graphing Hyperbolas

Graphing hyperbolas

Solving non-linear systems of equations

Solving nonlinear systems of equations

Solving nonlinear systems of equations

PowerPoint

Chapter Six Lecture

Section Video Lectures

6.1 Video: The Parabola

6.2 Video: The Circle and the Ellipse

6.3 Video: The Hyperbola

6.4 Video: Nonlinear Systems of Equations and Inequalities

 

Chapter 7. Sequences, Series, and Combinatorics

Animation

Finding terms in a sequence

Geometric Sequences

Geometric sequences and series

Using Mathematical Induction

Mathematical Induction

Use of Multiplication and Exponentiation to Solve a Word Problem

Applying the Binomial Theorem

Probability with Combinatorics

Section Video Lectures

7.1 Video: Sequences and Series

7.2 Video: Arithmetic Sequences and Series

7.3 Video: Geometric Sequences and Series

7.4 Video: Mathematical Induction

7.5 Video: Combinatorics: Permutations

7.6 Video: Combinatorics: Combinations

7.7 Video: The Binomial Theorem

7.8 Video: Probability

PowerPoint

Chapter Seven Lecture


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