Student Solutions Manual for Multivariable Calculus

Description

• NEW – Free CD—Shows animations of nearly all the text examples. It also has the entire book in Maple notebooks.

• NEW – An entire chapter devoted to calculus of transcendental functions—Combines parts of two previous chapters into the new Ch. 7.

  • Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter.

• NEW – Expanded treatment of differential equations (New Chapter 9).

  • Introduces students to both direction fields and Euler’s method together with the more symbolic elementary methods and applications for both first- and second-order equations.

• NEW – 1040 new True/False Questions—Available on the CD. They focus on theory and push the student to read.

• NEW – Reorganized content—Covers applied max-min problems in Ch.3 and defers related rates to Ch.4.

  • Offers students the opportunities to focus on and study these challenging topics in separate chapters—and test their knowledge of them in separate unit tests.

• Approximately 7000 total problems and interesting applications—Covers all ranges of difficulty, highly theoretical and computationally oriented problems.

  • Encourages students to learn by doing.

• Technology projects—Features icons that take users to Maple/ Mathematica/MATLAB/Calculator resources on the CD-ROM.

  • Gives students the opportunity to apply conceptually based technology following key sections of the text.

• 320 Section-ending Concepts: Questions & Discussion.

  • Serves students with a basis for either writing assignments or class discussion.

• Small optional section of matrix terminology and notation in the multivariable portion of the text.

• A lively and accessible writing style.

  • Helps students feel comfortable with the topics covered, and their ability to master them.

• Most visual text on the market.

  • Highlights are hundreds of Mathematica and MATLAB generated figures.

1. Functions, Graphs, and Models.

2. Prelude to Calculus.

3. The Derivative.

4. Additional Applications of the Derivative.

5. The Integral.

6. Applications of the Integral.

7. Calculus of Transcendental Functions.

8. Techniques of Integration.

9. Differential Equations.

10. Polar Coordinates and Parametric Curves.

11. Infinite Series.

12. Vectors, Curves, and Surfaces in Space.

13. Partial Differentiation.

14. Multiple Integrals.

15. Vector Calculus.

Appendices.

Answers.

Index.

• An entire chapter devoted to calculus of transcendental functions–Combines parts of two previous chapters into the new Ch. 7.

• • Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter.

• Expanded treatment of differential equations (New Chapter 9).

  • Introduces students to both direction fields and Euler’s method together with the more symbolic elementary methods and applications for both first- and second-order equations.

• Reorganized content–Covers applied max-min problems in Ch.3 and defers related rates to Ch.4.

  • Offers students the opportunities to focus on and study these challenging topics in separate chapters–and test their knowledge of them in separate unit tests.

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin, and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia’s honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution’s highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence. His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students.

David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 (under the direction of Prof. L. Bruce Treybig) while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran’s Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee’s research team’s primary focus was on the active transport of sodium ions by biological membranes. Penney’s primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms. Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous University-wide teaching awards as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author of research papers in number theory and topology and is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

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