## Thursday, July 5, 2012

### Calculus Tutorials

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
6.5 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