Problems And Solutions In Real Analysis (Second Edition)

by Masayoshi Hata

Overview

This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces.Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references.Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive 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. This volume is also suitable for non-experts who wish to understand mathematical analysis.

Product Details

ISBN-13:	9789813142824
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	02/03/2017
Series:	Series On Number Theory And Its Applications , #14
Edition description:	Reprint
Pages:	376
Product dimensions:	6.00(w) x 8.90(h) x 0.60(d)

Table of Contents

Preface to the First Edition v

Preface to the Second Edition vii

Notations ix

1 Sequences and Limits 1

Solutions 6

2 Infinite Series 21

Solutions 26

3 Continuous Functions 39

Solutions 45

4 Differentiation 55

Solutions 62

5 Integration 75

Solutions 84

6 Improper Integrals 99

Solutions 104

7 Series of Functions 117

Solutions 125

8 Approximation by Polynomials 137

Solutions 141

9 Convex Functions 149

Solutions 153

10 Various Proofs of ζ(2) = π²/6 163

Solutions 169

11 Functions of Several Variables 181

Solutions 187

12 Uniform Distribution 197

Solutions 200

13 Rademacher Functions 207

Solutions 212

14 Legendre Polynomials 223

Solutions 228

15 Chebysbev Polynomials 239

Solutions 243

16 Gamma Function 253

Solutions 258

17 Prime Number Theorem 271

Solutions 278

18 Bernoulli Numbers 293

Solutions 300

19 Metric Spaces 313

Solutions 317

20 Differential Equations 325

Solutions 332

Bibliography 343

Index 355