**Calculus**

Numbering approximately corresponds to James Stewart,

*Calculus*, 6th ed. (Belmont, CA: Thompson, 2008).

**Chapter 1: Functions**

1.1 What is a function?

1.2 Types of functions

1.3 Transforming functions

**Chapter 2: Limits**

2.1 The Tangent Problem (the beginning of Differential Calculus)

2.2a What is a Limit?

2.2b Right and Left Hand Limits

2.3a Limit Laws

2.3b The Squeeze Theorem

2.4 The Precise Definition of a Limit

2.5 Limits and Continuity

**Chapter 3: Derivatives**

3.1 What is a Derivative?

3.2 The Power Rule (also Constant Rule, Sum Rule, Difference Rule)

3.3 The Product and Quotient Rule

3.4 Derivatives of Trig Functions

3.5 The Chain Rule

3.6 Implicit Differentiation

**Chapter 4: Applications of Differentiation**

4.1 Maximum and Minimum Values

4.2 The Mean Value Theorem

4.3 Derivative Tests

4.4 Infinite Limits

4.5 Summary of Sketching Graphs

4.6 Optimization Problems (including First Derivative Test, business functions)

4.7 Newton's Method

4.8 Antiderivatives

**Chapter 5: Integral Calculus**

5.1 The Area Problem (beginning of Integral Calculus)

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4a Indefinite Integrals

5.4b Some Basic Indefinite Integral Formulas

5.4c Net Change Theorem

5.5a The Substitution Method (for indefinite integrals)

5.5b The Substitution Method (for definite integrals)

**Chapter 6: Applications of Integration**

6.1 Areas Between Curves

6.2 Volumes

6.3 Volume by Cylindrical Shell

6.4 Work (see also the physics video on work)

6.5 Average Value of a Function

**Chapter 7: Inverse Functions**

7.1 Introduction to Inverse Functions

**Chapter 10: Differential Equations**

10.1 Modeling with Differential Equations

10.2a Slope and Distance Fields

10.2b Euler's Method

**Chapter 11: Parametric Equations and Polar Coordinates**

11.1 Curves Defined by Parametric Equations

**Chapter 13: Vectors and the Geometry of Space**

13.1 Three Dimensional Coordinate Systems

13.2 Vectors

13.3 The Dot Product (see also this physics version)

13.4 The Cross Product (see also this physics version)

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