# The Teacher's Guide to Calculus, v0.3

## Metropolitan State College of Denver

#### Chapter 1: Limits

§1.1 The Main Definition
§1.2 One-Sided Limits
§1.3 Existence
§1.4 Conventions Regarding The "Infinity" Symbol
§1.5 Limit Theorems
§1.6 Applications
§1.7 Some Warnings

#### Chapter 2: Continuity

§2.1 Definitions
§2.2 Continuity on Intervals and Other Sets
§2.3 The Continuity Theorems
§2.4 Sequences & Continuity
§2.5 Some Topological Considerations
§2.6 More on Continuity
§2.7 Uniform Continuity
§2.8 Continuity & Inverse Functions

#### Chapter 3: Transcendental Functions I

§3.1 The Trigonometric Functions
§3.2 Continuity of the Trigonometric Functions
§3.3 Exponential Functions
§3.4 Inverse Trigonometric Functions
§3.5 Inverse Exponentials; Logarithms

#### Chapter 4: Derivatives & Differentiability

§4.1 Definitions
§4.2 The Chain Rule
§4.3 The Inverse Function Rule
§4.4 Functions of Two Variables
§4.5 Implicit Differentiation
§4.6 Derivatives of Transcendental Functions
§4.7 Uniform Differentiability
§4.8 Mean & Intermediate Values for Derivatives

#### Chapter 5: Measuring & Estimating

§5.1 The Racetrack Principal & Monotonicity
§5.2 Concavity
§5.3 Linearization
§5.4 Newton's Method
§5.5 Euler's Method

#### Chapter 6: Integrals

§6.1 Definitions and Existence
§6.2 Basic Properties
§6.3 The Fundamental Theorem of Calculus
§6.4 Approximation of Definite Integrals
§6.5 Some Applications

#### Chapter 7: Transcendental Functions II

§7.1 The Trigonometric Functions
§7.2 Logarithmic and Exponential Functions