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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



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Paul Zorn
Thu May 2 16:51:18 CDT 1996

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