Calculus Videos

Here you can find links to all the videos that I’ve created for my Calculus I course.

Unit 1: Precalculus Review

Unit 1 Playlist

1.1.1 Basics of Functions

1.1.2 Representations of Functions

1.1.3 Piecewise Defined Functions

1.1.4 Symmetry

1.2.1 Linear Models

1.2.2 Other Types of Functions

1.3.2 Combinations of Functions

A.D.1 Trigonometric Functions

A.D.2 Trigonometric Identities

A.D.3 Graphs of Trigonometric Functions

1.4.1 Exponential Functions

1.5.1 Inverse Functions

1.5.2 Logarithmic Functions

1.5.3 Inverse Trigonometric Functions

Unit 2: The Basics of Limits

Unit 2 Playlist

2.2.1 The Idea of a Limit

2.2.2 One-Sided Limits

2.2.3 Infinite Limits

2.3.1 Limit Laws

2.3.2 Direct Substitution Property

2.3.3 What to do with 0/0

2.3.4 Other Limit Techniques

2.3.5 The Squeeze Theorem

Unit 3: More on Limits

Unit 3 Playlist

2.5.1 Idea of Continuity

2.5.2 Continuity of Elementary Functions

2.5.3 Intermediate Value Theorem

2.6.1 Idea of a Limit at Infinity

2.6.2 Techniques for Evaluating Limits at Infinity

2.6.3 Horizontal Asymptotes

Unit 4: The Definition of the Derivative

Unit 4 Playlist

2.1.1 The Tangent Problem

2.1.2 The Velocity Problem

2.7.1 The Definition of the Derivative

2.7.2 Tangents and Velocities

2.7.3 Rates of Change

2.8.1 The Derivative Function

2.8.2 Differentiability

2.8.3 Higher Derivatives

Unit 5: Basic Differentiation Rules

Unit 5 Playlist

3.1.1 Power Functions

3.1.2 New Derivatives from Old

3.1.3 Different Types of Derivative Problems

3.1.4 Exponential Functions

3.2.1 The Product Rule

3.2.2 The Quotient Rule

3.3.1 Derivatives of sin and cos

3.3.2 Derivatives of other Trigonometric Functions

Unit 6: The Chain Rule

Unit 6 playlist

3.4.1 The Chain Rule

3.4.2 The Chain Rule Together with Other Rules

3.4.3 Other Types of Chain Rule Problems

3.4.4 The Derivative of a^x

3.5.1 Implicit Differentiation

3.5.2 Applications of Implicit Differentiation

3.5.3 Derivatives of Inverse Trigonometric Functions

3.6.1 Derivative of ln x

3.6.2 Derivative of log_a x

3.6.3 Logarithmic Differentiation

Unit 7: Rates of Change

Unit 7 Playlist

3.7.1 Rates of Change in General

3.7.2 Rates of Change in Physics

3.7.3 Rates of Change in Social Sciences

3.9.1 Dealing with two Dependent Variables

3.9.2 Distance and Similar Triangle Problems

3.9.3 More Complicated Related Rates Problems

Unit 8: Basic Applications

Unit 8 playlist

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