Problems And Solutions In Real Analysis, 2nd Edition
by Masayoshi Hata  (Author)

About this book
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.

Brief Contents
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
    Solutions104
7. Series of Functions 117
    Solutions125
8. Approximation by Polynomials 137
    Solutions141
9. Convex Functions 149
    Solutions153
10. Various Proofs of ￡(2) = 7r2/6 163
    Solutions169
11. Functions of Several Variables 181
    Solutions187
12. Uniform Distribution 197
    Solutions200
13. Rademacher Functions 207
    Solutions212
14. Legendre Polynomials 223
    Solutions228
15. Cheby shev Polynomials 239
    Solutions243
16. Gamma Function 253
    Solutions258
17. Prime Number Theorem 271
    Solutions278
18. Bernoulli Numbers 293
    Solutions300
19. Metric Spaces 313
    Solutions317
20. Differential Equations 325
    Solutions332
Bibliography 343
Index 355

Series: Number Theory and Its Applications (Book 14)
Pages: 376 pages
Publisher: WSPC; 2 edition (December 12, 2016)
Language: English
ISBN-10: 9813142820
ISBN-13: 978-9813142824