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

Unit 1: Precalculus Review

1.1.2 Representations of Functions

1.1.3 Piecewise Defined Functions

1.2.2 Other Types of Functions

1.3.2 Combinations of Functions

A.D.2 Trigonometric Identities

A.D.3 Graphs of Trigonometric Functions

1.5.3 Inverse Trigonometric Functions

Unit 2: The Basics of Limits

2.3.2 Direct Substitution Property

Unit 3: More on Limits

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

Unit 4: The Definition of the Derivative

2.7.1 The Definition of the Derivative

Unit 5: Basic Differentiation Rules

3.1.2 New Derivatives from Old

3.1.3 Different Types of Derivative Problems

3.3.1 Derivatives of sin and cos

3.3.2 Derivatives of other Trigonometric Functions

Unit 6: The Chain Rule

3.4.2 The Chain Rule Together with Other Rules

3.4.3 Other Types of Chain Rule Problems

3.5.1 Implicit Differentiation

3.5.2 Applications of Implicit Differentiation

3.5.3 Derivatives of Inverse Trigonometric Functions

3.6.3 Logarithmic Differentiation

Unit 7: Rates of Change

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

3.10.3 Approximating Values of Functions

Unit 9: Derivatives, Limits, and the Mean Value Theorem

Unit 10: Derivatives and Graphs

4.1.1 Absolute and Local Maxima and Minima

4.1.2 Fermat’s Theorem and Critical Numbers

4.1.3 The Extreme Value Theorem and the Closed Interval Method

4.3.1 What f′ says about the graph of f

4.3.2 What f′′ says about the graph of f

4.3.3 The Basics of Curve Sketching

4.5.1 Guidelines for Sketching a Curve

Unit 11: Applied Optimization

4.7.1 Using a Formula to Optimize a Function

4.7.2 Distance, Area, Volume Problems

Unit 12: Additional Applications