Working Analysis

ISBN-13: 9780121876043 / Angielski / Twarda / 2004 / 688 str.

Jeffery Cooper

Opis

Working Analysis is for a two semester course in advanced calculus. It develops the basic ideas of calculus rigorously but with an eye to showing how mathematics connects with other areas of science and engineering. In particular, effective numerical computation is developed as an important aspect of mathematical analysis.

• Maintains a rigorous presentation of the main ideas of advanced calculus, interspersed with applications that show how to analyze real problems
• Includes a wide range of examples and exercises drawn from mechanics, biology, chemical engineering and economics
• Describes links to numerical analysis and provides opportunities for computation; some MATLAB codes are available on the author's webpage
• Enhanced by an informal and lively writing style

Recenzje

"This is a solid, well-written advanced calculus book that deserves to be on the shelves of mathematics department offices when faculty are selecting course resources." --J. Feroe, Vassar College, in CHOICE, JUNE 2005

"In my opinion the book by Cooper is a viable competitor to Strichartz...To summarize, this textbook is based on a very healthy philosophy that it is easier to learn mathematical analysis when it is intertwined with meaningful applications. The book is fun to read and, I am sure, will be fun to learn from.” --Victor Roytburd, Rensselaer Polytechnic Institute, in SIAM REVIEW

Spis treści

Preface
Part I: 1. Foundations
2. Sequences of Real Numbers
3. Continuity
4. The Derivative
5. Higher Derivatives and Polynomial Approximation
6. Solving Equations in One Dimension
7. Integration
8. Series
Appendix I
Part II: 9. Convergence and Continuity in Rn
10. The Derivative in Rn
11. Solving Systems of Equations
12. Quadratic Approximation and Optimization
13. Constrained Optimization
14. Integration in Rn
15. Applications of Integration to Differential Equations
Appendix II
Solutions to Selected Exercises
References
Index