 
Calculus: Single and Multivariable, Fourth Edition
December 2004, ©2005
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CALCULUS 4/e exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology. The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
2. Key Concept: The Derivative.
3. Short-Cuts to Differentiation.
4. Using the Derivative.
5. Key Concept: The Definite Integral.
6. Constructing Antiderivatives.
7. Integration.
8. Using the Definite Integral.
9. Series.
10. Approximating Functions.
11. Differential Equations.
12. Functions of Several Variables.
13. A Fundamental Tool: Vectors.
14. Differentiating Functions of Many Variables.
15. Optimization: Local and Global Extrema.
16. Integrating Functions of Many Variables.
17. Parameterized Curves and Vector Fields.
18. Line Integrals.
19. Flux Integrals.
20. Calculus of Vector Fields.
Appendix A: Roots, Accuracy, and Bounds.
Appendix B: Complex Numbers.
Appendix C: Newton's Method.
Appendix D: Determinants.
Ready Reference.
Answers to Odd Numbered Problems.
Index.
More problems using the Fundamental Theorem have been added to Section 5.4.
A new section in chaper 4 is devoted to related rates, with more thorough coverage, and more problems and examples.
The problem set for L'Hôpital's rule includes more challenging and different types of problems.
The coverage of the chain rule has been revised, and includes more multi-step chain rule problems and examples, including more on doing chain rule without intermediate variables. The chain rule section appears in chapter 3 and is followed by a new section applying the chain rule to finding the derivatives of inverse functions.
Chapter 9 on series has been has been extensively expanded and rewritten. There is a new section at the beginning on sequences, including recursively defined sequences. The chapter now includes p-series and the limit comparison test, with numerous examples, and a discussion of conditional convergence. The chapter discusses in more detail interval of convergence versus radius of convergence (with more attention to convergence at the end points). There are many, many new problems and exercises (well over a hundred).
In chapter 10 the section on the Lagrange form of the error bound for Taylor polynomials has been revised.
Estimation of error has been added to Section 3.9 to foreshadow Taylor polynomials. There is now an example and box in 3.9 examining an error formula for local linearization, along with a sequence of calculator exercises exploring this formula, with forward reference to Taylor polynomials.
The discussion of concavity in section 2.6 has been revised and now has a box that says explicitly "that if the graph of f is concave up, we can only conclude that f" is nonnegative."
More optimization problems were added.
Hyperbolic functions are now treated at the end of chapter 3; many problems involving hyperbolic functions have been added here, and elsewhere in the text.
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