CONTENTS
Part I Single Variable Calculus
Chapter 1. Functions
1.1 Functions and Graph Solution
1.4 Translation, Stretching and Rotation of Functions Solution
Chapter 2. Limits and Continuity
Chapter 3. Derivatives
3.1 Definition of Derivatives, Differentiation
3.2 Derivatives of Basic Functions, The Product and Quotient Rule
3.3 The Chain Rule and Inverse Functions
*3.4 Approximation and Related Rates
Chapter 4. Applications of Derivatives
4.1 Extreme values of a function
4.3 The Limit of Indeterminate Forms and L’Hospital’s Rule
Chapter 5. Integrals
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.6 The Logarithm Defined as an Integral
Chapter 6. Applications of Integration
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function
Chapter 7. Techniques of Integration
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions and CAS
*7.7 Approximate Integration and CAS
Chapter 8. Further Applications of Integration
8.2 Area of a Surface of Revolution
Chapter 9. Infinite Sequences and Infinite Series
9.2 Tests for convergence of series with positive terms
9.3 Alternating Series and Absolute Convergence
9.5 Taylor, Maclaurin, and Binomial Series
Chapter 10. Parametric Equations and Polar Coordinates
10.2 Calculus with Parametric Curves
10.4 Areas and Lengths in Polar Coordinates