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El. knyga: Problems And Solutions In Real Analysis

(Kyoto Univ, Japan)
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This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.
Preface v
Sequences and Limits
1(14)
Solutions
5(10)
Infinite Series
15(16)
Solutions
20(11)
Continuous Functions
31(12)
Solutions
35(8)
Differentiation
43(16)
Solutions
49(10)
Integration
59(18)
Solutions
66(11)
Improper Integrals
77(16)
Solutions
81(12)
Series of Functions
93(20)
Solutions
100(13)
Approximation by Polynomials
113(12)
Solutions
117(8)
Convex Functions
125(14)
Solutions
129(10)
Various proofs of ζ(2) = π2/6
139(18)
Solutions
146(11)
Functions of Several Variables
157(14)
Solutions
161(10)
Uniform Distribution
171(10)
Solutions
174(7)
Rademacher Functions
181(10)
Solutions
185(6)
Legendre Polynomials
191(14)
Solutions
195(10)
Chebyshev Polynomials
205(14)
Solutions
209(10)
Gamma Function
219(20)
Solutions
225(14)
Prime Number Theorem
239(18)
Solutions
245(12)
Miscellanies
257(16)
Solutions
263(10)
Bibliography 273(12)
Index 285