#### Table of Contents - Volume 2

##### Chapter 5: The Integral

- 5.1
- Areas and integrals
- 5.2
- The area function
- 5.3
- The fundamental theorem of calculus
- 5.4
- Approximating sums: the integral as a limit
- 5.5
- Approximating sums: interpretations and applications
- 5.6
- Chapter summary

##### Chapter 6: Finding Antiderivatives

- 6.1
- Antiderivatives: the idea
- 6.2
- Antidifferentiation by substitution
- 6.3
- Integral aids: tables and computers

##### Chapter 7: Numerical Integration

- 7.1
- The idea of approximation
- 7.2
- More on error: left and right sums and the first derivative
- 7.3
- Trapezoid sums, midpoint sums, and the second derivative
- 7.4
- Simpson's rule
- 7.5
- Chapter summary

##### Chapter 8: Using the Definite Integral

- 8.1
- Introduction
- 8.2
- Finding volumes by integration
- 8.3
- Arclength
- 8.4
- Work
- 8.5
- Present value
- 8.6
- Fourier polynomials
- 8.7
- Chapter summary

##### Chapter 9: More Antidifferentiation Techniques

- 9.1
- Integration by parts
- 9.2
- Partial fractions
- 9.3
- Trigonometric antiderivatives
- 9.4
- Miscellaneous Exercises

##### Chapter 10: Improper Integrals

- 10.1
- When is an integral improper?
- 10.2
- Detecting convergence, estimating limits
- 10.3
- Improper integrals and probability
- 10.4
- l'H^[o]pital's rule: comparing rates
- 10.5
- Chapter summary

##### Chapter 11: Infinite Series

- 11.1
- Sequences and their limits
- 11.2
- Infinite series, convergence, and divergence
- 11.3
- Testing for convergence; estimating limits
- 11.4
- Absolute convergence; alternating series
- 11.5
- Power series
- 11.6
- Power series as functions
- 11.7
- Maclaurin and Taylor series
- 11.8
- Chapter summary

##### Chapter 12: Differential Equations

- 12.1
- Differential equations: the basics
- 12.2
- Slope fields: solving DE's graphically
- 12.3
- Euler's method: solving DE's numerically
- 12.4
- Separating variables: solving DE's symbolically
- 12.5
- Chapter summary

##### Chapter 13: Polar Coordinates

- 13.1
- Polar coordinates and polar curves
- 13.2
- Calculus in polar coordinates

##### Chapter 14: Multivariable Calculus: A First Look

- 14.1
- Three-dimensional space
- 14.2
- Functions of several variables
- 14.3
- Partial derivatives
- 14.4
- Optimization and partial derivatives: a first look
- 14.5
- Multiple integrals and approximating sums
- 14.6
- Calculating integrals by iteration
- 14.7
- Double integrals in polar coordinates

##### Selections from Volume I

- 3.8
- Inverse trigonometric functions and their derivatives
- 4.1
- Differential equations and their solutions
- 4.2
- More differential equations: modeling growth
- 4.3
- Linear and quadratic approximation; Taylor polynomials
- 4.9
- Parametric equations, parametric curves

*Paul Zorn *

Thu May 2 16:51:18 CDT 1996