Supplementary Videos
Intermediate Algebra
Unit 1: Linear Equations and Inequalities
Topic 1: Solving Linear Equations
Topic 2: Solving Linear Inequalities and Interval Notation
Topic 3: Solving Compound Inequalities
Topic 4: Solving Absolute Value Equations and 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
Topic 2: Introduction to Functions
Topic 3: Finding Domain and Range
Topic 4: Linear Functions: Graphs and Slope
Topic 5: More on Graphing Linear Equations
Topic 6: Finding Equations of Lines
Topic 7: Solving Systems of Equations in Two Variables
Properties and Definitions of Exponents
Unit 3: Operations with and Factoring Polynomials and Solving Polynomial Equations
Topic 1: Polynomials and Polynomial Functions
Topic 2: Multiplication of Polynomials
Topic 3: Greatest Common Factor and Factoring by Grouping
Topic 4: Factoring Trinomials
Topic 5: Factoring by Special Products
Topic 6: General Strategy for Factoring Polynomials
Topic 7: Solving Equations by Factoring and Problem Solving
Unit 4: Rational Expressions and Functions
Topic 1: Rational Functions; Operations with Rational Expressions
Precalculus
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
Calculus I
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
Calculus II
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
Calculus III
A Demo of Arclength Calculations
The Code Used
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
Chapter 14
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