Unit 1: Linear Equations and Inequalities

Topic 1: Solving Linear Equations

• Introduction to Equations
• Solving Linear Equations
• Identities and Contradictions

Topic 2: Solving Linear Inequalities and Interval Notation

• Inequalities and Interval Notation
• Solving Inequalities

Topic 3: Solving Compound Inequalities

• Intersections
• Unions

Topic 4: Solving Absolute Value Equations and Inequalities

• Introduction to Absolute Value
• Absolute Value Equations
• Absolute Value Inequalities

Unit 2: Introduction to Functions and Graphs of Linear Equations, Equations of Lines, and Systems of Linear Equations

Topic 1: Plotting Points and Ordered Pair Solutions of Equations

• The Coordinate Plane
• Graphs of Equations

Topic 2: Introduction to Functions

• Introduction to Functions
• Graphs of Functions

Topic 3: Finding Domain and Range

• Domain and Range

Topic 4: Linear Functions: Graphs and Slope

• Linear Functions and y-Intercepts
• Linear Function and Slope

Topic 5: More on Graphing Linear Equations

• Graphing Methods
• Horizontal and Vertical Lines
• Parallel and Perpendicular Lines

Topic 6: Finding Equations of Lines

• Finding Equations of Lines
• Finding Equations of Parallel and Perpendicular Lines

Topic 7: Solving Systems of Equations in Two Variables

• Solving Systems of Equations
• Solving Systems by Substitution

Properties and Definitions of Exponents

• Introduction to Exponents
• Exponent Rules Part 1
• Exponent Rules Part 2

Unit 3: Operations with and Factoring Polynomials and Solving Polynomial Equations

Topic 1: Polynomials and Polynomial Functions

• Introduction to Polynomials
• Adding and Subtracting Polynomials

Topic 2: Multiplication of Polynomials

• Multiplying Polynomials
• Special Products
• Function Notation and Simplification

Topic 3: Greatest Common Factor and Factoring by Grouping

• Introduction to Factoring
• Factoring by Grouping

Topic 4: Factoring Trinomials

• Factoring Trinomials - Leading Coefficient 1
• Factoring Trinomials - Leading Coefficient Not 1

Topic 5: Factoring by Special Products

• Factoring Using Special Products

Topic 6: General Strategy for Factoring Polynomials

• General Strategy for Factoring Polynomials

Topic 7: Solving Equations by Factoring and Problem Solving

• Using the Zero Product Rule to Solve Equations
• Applications of Quadratic Equations

Unit 4: Rational Expressions and Functions

Topic 1: Rational Functions; Operations with Rational Expressions

• Rational Expressions and Functions
• Multiplying and Dividing Rational Expressions

Functions

• Function Basics
• Difference Quotient
• Domain Rules
• Domain: Multiple Restrictions
• Properties of Functions: Graphically
• Properties of Functions: Algebraically
• Transformations of Functions: The Rules
• Introduction to Rational Functions
• Asymptotes of Rational Functions
• Composition of Functions
• Introduction to Inverses
• Finding Inverses
• Inverses with Domain Restrictions
• Exponential Functions
• Introduction to Logarithms
• Logarithmic Functions
• Properties of Logarithms
• Solving Exponential/ Logarithmic Equations: Same Base
• Solving Exponential/ Logarithmic Equations: By Conversion
• Solving Other Types of Exponential Equations

Geometry and Trigonometry

• Introduction to Angles
• Trigonometric Functions
• Trig Function Values of Special Angles
• Basic Trig Identities
• General Angles in the Plane
• Reference Angles
• The Unit Circle and More Special Angles
• Graphing Sine and Cosine
• Transformations of Sine and Cosine
• Graphs of Other Trigonometric Functions
• Double Angle Identities
• Inverse Sine Function
• Inverse Cosine Function
• Inverse Tangent Function
• Composing Inverse Trigonometric Functions
• Solving Basic Trig Equations
• Solving More Trig Equations
• Polar Coordinates

Chapter 2 - Limits and Derivatives

• §1: 1. The Tangent Problem
• §1: 2. The Velocity Problem
• §2: 1. Limits: Introduction
• §2: 2. Limits: Infinite Limits
• §2: 3. Limits: Example Calculations
• §2: 4. Limits: Vertical Asymptotes
• §3: 1. The Limit Laws: Introduction Laws
• §3: 2. The Limit Laws, Worked Examples
• §3: 3. The Limit Laws, Further Examples
• §3: 4. The Limit Laws, Conclusions
• §5: 1. Continuity: Introduction
• §5: 2. Continuity Exercises: Making A Function Continuous
• §6: 1. Limits at Infinity: Introduction
• §6: 2. Limits at Infinity: Worked Examples
• §6: 3. Limits at Infinity: Further Examples
• §6: 4. Limits at Infinity: Horizontal Asymptotes
• §7: 1. Derivatives: Definition
• §7: 2. Derivatives: Example Calculations
• §7: 3. Derivatives: Velocity
• §8: 1. Derivative as a Function: Introduction
• §8: 2. Derivative as a Function: Example Calculations
• §8: 2. Derivative as a Function: Non-Differentiability

Chapter 3 - Differentiation Rules

• §1: 1. Derivatives of Polynomials
• §1: 2. The Derivative of the Exponential Function
• §1: 3. Derivatives of Polynomials and the Natural Exponential Function
• §2: 1. The Product and Quotient Rules: Introduction
• §2: 2. The Product and Quotient Rules: Examples, Part 1
• §2: 3. The Product and Quotient Rules: Examples, Part 2
• §3: 1. Derivatives of Trigonometric Functions: Introducton
• §3: 2. Exercises with the Derivatives of Sine and Cosine
• §3: 3. The Derivative of Tangent and Other Trig Functions
• §4: 1. The Chain Rule: Introduction
• §4: 2. The Chain Rule: Examples
• §4: 3. The Chain Rule: Iteration
• §4: 4. The Chain Rule: Other Exponentials
• §5: 1. Implicit Differentiation: First Example
• §5: 2. Implicit Differentiation: An Involved Example
• §6: 1. Derivative of Logarithms: Introduction
• §6: 2. Derivatives of Logarithms: Intermediate Examples
• §6: 3. Derivatives of Logarithms: A New Technique
• §6: 4. Derivatives of Inverse Trigonometric Functions
• §7: 1. Applications of Differentiation: Velocity
• §7: 2. Applications of Differentiation: More on Motion
• §7: 3. Applications of Differentiation: Distance Traveled
• §9: 1. Related Rates: Introduction
• §9: 2. Related Rates: Lamp Post Example
• §9: 3. Related Rates: Trigonometric Example
• §10: 1. Linearization: Introduction
• §10: 2. Linearization: Worked Example

Chapter 4 - Applications of Differentiation

• §1: 1. Maximum and Minimum Values: Introduction
• §1: 2. Maximum and Minimum Values: Critical Numbers
• §1: 3. Maximum and Minimum Values: Exercises
• §2: 1. The Mean Value Theorem: Introduction
• §2: 2. The Mean Value Theorem: An Example
• §2: 3. The Mean Value Theorem: A Second Example
• §2: 4. The Mean Value Theorem: Optional
• §3: 1. Derivatives and the Shape of a Graph: Increasing and Decreasing
• §3: 2. Derivatives and the Shape of a Graph: Concavity and Points of Inflection
• §3: 3. Interpreting the Graph of the Derivative
• §4: 1. L'Hospital's Rule: Introduction and First Examples
• §4: 2. L'Hospital's Rule: Intermediate Examples
• §4: 3. L'Hospital's Rule: Limits as x Approaches Infinity
• §7: 1. Optimization: 
• §7: 2. Optimization: 
• §7: 3. Optimization: 
• §9: 1. Antiderivatives: Introduction
• §9: 2. Antiderivatives: Examples

Chapter 5 - Integration

• §2: 1. The Definite Integral: Introduction
• §2: 2. The Definite Integral: Exercises
• §3: 1. The Fundamental Theorem of Calculus: Introduction
• §3: 2. The Fundamental Theorem of Calculus: Exercises
• §3: 3. The Fundamental Theorem of Calculus: Further Examples
• §4: 1. Indefinite Integrals: Introduction
• §4: 2. Indefinite Integrals: Worked Examples
• §4: 3. Indefinite Integrals: A Step in Evaluating Definite Integrals
• §5: 1. Integration by Substitution: Introduction
• §5: 2. Integration by Substitution: Worked Examples
• §5: 3. Integration by Substitution: Further Examples

Chapter 5 - Integrals

• §5.2: The Definite Integral 
• §5.3: The Fundamental Theorem of Calculus, Part 1
• §5.3: The Fundamental Theorem of Calculus, Part 2
• §5.4: Indefinite Integrals
• §5.4: Displacement vs Distance
• §5.5: The Substitution Rule

Chapter 6 - Applications of Integration

• §6.1: The Area Between f(x) and g(x)
• §6.1: The Area Between f(y) and g(y)
• §6.2: Volumes
• §6.2: Volumes Rotated Around the Axes
• §6.2: Volumes Rotated About Other Lines

Chapter 7 - Techniques of Integration

• §7.1: Integration by Parts
• §7.2: Trigonomatric Integrals with Sine and Cosine
• §7.2: Trigonometric Integrals with Secant and Tangent
• §7.3: Trigonometric Substitution with Sine
• §7.3: Trigonometric Substitution with Tangent
• §7.3: Trigonometric Substitution with Secant
• §7.4: Long Division of Polynomials
• §7.4: Partial Fractions with Linear Factors
• §7.4: Partial Fractions with Irreducible Quadratic Factors
• An Additional Video Reviewing 7.3 and 7.4
• §7.8: Improper Integrals, Type 1
• §7.8: Improper Integrals, Type 2
• §7.8: The Comparison Theorem

Chapter 11 - Infinite Sequences and Series

• §11.1: Sequences and Limits
• §11.1: Some Special Sequences
• An Additional Video Reviewing Sequences
• §11.2: Introduction to Series
• §11.2: Geometric and Telescoping Series
• §11.2: The Test for Divergence
• §11.3: The Integral Test
• §11.4: The Limit Comparison Tets
• §11.4: Direct Comparison
• §11.5: Alternating Series
• §11.5: Absolute and Conditional Convergence
• §11.6: The Ratio and Root Tests
• A Series Review Video by Elie Abdo 
• §11.8: Power Series
• §11.9: Differentiation and Integration of Power Series
• §11.9: Representations of Functions as Power Series
• §11.10: Introduction to Taylor and MacLaurin Series
• §11.10: Taylor Series from Known Series
• §11.11: Taylor Polynomials

Chapter 10

Chapter 12

• 2: 4
• 2: 8
• 2: 26
• 3: 5-9-19
• 3: 11
• 3: 12
• 3: 26
• 3: 64
• 4: 3-14
• 4: 15
• 5: 9
• 5: 26
• 5: 35
• A: 1
• A: 2
• A: 3
• A: 7
• A: 8
• A: 9
• Review: 11

Chapter 13

• 2: 18
• 2: 20
• 3: 3
• 3: 5
• 4: 4

Chapter 14

• 3: 61
• 3: 69
• 5: 35
• 6: 15
• 6: 25
• Review: 36
• Review: 44
• Review: 46
• Review: 48

Chapter 15

• 1: 32
• 1: 33
• 2: 23
• 2: 25
• 3: 24
• 3: 31
• 5: 7
• 5: 8
• 6: 12
• 7: 21
• 7: 25a
• 8: 5, 7, and 10
• 8: 26
• 8: 29a
• A: 1
• Review: 20
• Review: 27

Chapter 16

• 2: 9
• 2: 20
• 2: 21
• 2: 34
• 3: 17
• 4: 11
• 7: 23
• 9: 5

Chapter 4

• §6: Lecture 1
• §6: Lecture 2
• §6: Lecture 3

Chapter 5

• §1: Free undamped motion 
• §1: Example 1
• §2: Free damped motion
• §2: Example 2
• §3: Examples