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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