**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

**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)

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