Working Analysis

Front Cover
Gulf Professional Publishing, 2005 - Mathematics - 663 pages
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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
 

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Contents

Foundations
3
Sequences of Real Numbers
29
Continuity
57
The Derivative
85
Higher Derivatives and Polynomial
121
Solving Equations in One Dimension
151
Integration
171
i
261
The Derivative in Rn
295
Solving Systems of Equations
323
Quadratic Approximation and Optimization
385
Constrained Optimization
439
Integration in
489
Applications of Integration to Differential
555
Appendix II
599
References
631

Convergence and Continuity in
271

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