Surprises and counterexamples in real function theory
著者
書誌事項
Surprises and counterexamples in real function theory
（Texts and readings in mathematics, 42）
Hindustan Book Agency, c2007
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内容説明・目次
内容説明
This book presents a variety of intriguing, surprising and appealing topics and nonroutine theorems in real function theory. It is a reference book to which one can turn for finding that arise while studying or teaching analysis.Chapter 1 is an introduction to algebraic, irrational and transcendental numbers and contains the Cantor ternary set. Chapter 2 contains functions with extraordinary properties; functions that are continuous at each point but differentiable at no point. Chapters 4 and intermediate value property, periodic functions, Rolle's theorem, Taylor's theorem, points of tangents. Chapter 6 discusses sequences and series. It includes the restricted harmonic series, of alternating harmonic series and some number theoretic aspects. In Chapter 7, the infinite peculiar range of convergence is studied. Appendix I deal with some specialized topics. Exercises at the end of chapters and their solutions are provided in Appendix II.This book will be useful for students and teachers alike.
目次
- 1: Introduction to the real line R and some of its subsets
- 2: Functions: Pathological, peculiar and extraordinary
- 3: Famous everywhere continuous, nowhere differentiable functions: van der Waerden's and other
- 4: Functions: Continuous, periodic, locally recurrent and others
- 5: The derivative and higher derivatives
- 6: Sequences, Harmonic Series, Alternating Series and related result
- 7: The infinite exponential and related results. A.1. Stirling's formula and the trapezoidal rule
- A.2. Schwarz differentiability
- A.3. Cauchy's functional equation f(x + y) = f(x) + f(y)
- Appendix II: Hints and solutions to exercises.
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