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Working Analysis

Description:
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 MATLAB
codes are available on the author's webpage
Enhanced by an informal and lively writing style
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
Authors
Cooper, Jeffery
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Working Analysis

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