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Working Analysis - Jeffery Cooper

Working Analysis

By: Jeffery Cooper

Hardcover | 21 September 2004

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Hardcover


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Preface
Part I:
1. Foundations
1. 1 Ordered Fields
1.2 Completeness
1.3 Using In equalities
1.4 Induction
1.5 Sets and Function s

2. Sequences of Real Numbers
2 .1 Limits of Sequences
2.2 Criteria for Convergence
2.3 Cauchy Sequences

3. Continuity
3.1 Limits of Functions
3.2 Continuous Functions3.3 Further Properties of Continuous Functions
3.4 Golden-Section Search
3.5 The Intermediate Value Theore m

4. The Derivative
4.1 The Deri vative and Approximation
4.2 The Mean Value Theorem
4.3 The Cauchy Mean Value Theorem and lÈHopitalÈs Rule
4.4 The Second Derivative Test

5. Higher De rivatives and Polynomial Approximation
5.1 Taylor Polynomia ls
5.2 Numerical Differentiation
5.3 Polynomia l Inerpolation
5.4 Convex Funtions
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Industry Reviews
"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 "...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 "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

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