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Klappentext The text 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 MATLABcodes are available on the author's webpage* Enhanced by an informal and lively writing style Zusammenfassung Suitable for a two semester course in advanced calculus! this work develops the basic ideas of calculus with an eye to showing how mathematics connects with other areas of science and engineering. It includes a range of examples and exercises drawn from mechanics! biology! chemical engineering and economics. Inhaltsverzeichnis 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
List of contents
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
Report
"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
