Problems in Mathematical Analysis III pdf epub mobi txt 電子書 下載2025

想要找書就要到 小美書屋

立刻按 ctrl+D收藏本頁

你會得到大驚喜!!

The best way to penetrate the subtleties of the theory of integration is by solving problems. This book, like its two predecessors, is a wonderful source of interesting and challenging problems. As a resource, it is unequaled. It offers a much richer selection than is found in any current textbook. Moreover, the book includes a complete set of solutions.

This is the third volume of Problems in Mathematical Analysis. The topic here is integration for real functions of one real variable. The first chapter is devoted to the Riemann and the Riemann-Stieltjes integrals. Chapter 2 deals with Lebesgue measure and integration.

The authors include some famous, and some not so famous, inequalities related to Riemann integration. Many of the problems for Lebesgue integration concern convergence theorems and the interchange of limits and integrals. The book closes with a section on Fourier series, with a concentration on Fourier coefficients of functions from particular classes and on basic theorems for convergence of Fourier series.

The book is mainly geared toward students studying the basic principles of analysis. However, given its selection of problems, organization, and level, it would be an ideal choice for tutorial or problem-solving seminars, particularly those geared toward the Putnam exam. It is also suitable for self-study. The presentation of the material is designed to help student comprehension, to encourage them to ask their own questions, and to start research. The collection of problems will also help teachers who wish to incorporate problems into their lectures. The problems are grouped into sections according to the methods of solution. Solutions for the problems are provided.

Problems in Mathematical Analysis I and II are available as Volumes 4 and 12 in the AMS series, Student Mathematical Library.

W. J. Kaczor: Marie Curie-Sklodowska University, Lublin, Poland,

M. T. Nowak: Marie Curie-Sklodowska University, Lublin, Poland

Cover 1
Title 4
Copyright 5
Contents 6
Preface 8
Part 1. Problems 12
Chapter 1. The Riemann-Stieltjes Integral 14
§1.1. Properties of the Riemann-Stieltjes Integral 14
§1.2. Functions of Bounded Variation 21
§1.3. Further Properties of the Riemann-Stieltjes Integral 26
§1.4. Proper Integrals 32
§1.5. Improper Integrals 39
§1.6. Integral Inequalities 53
§1.7. Jordan Measure 63
Chapter 2. The Lebesgue Integral 70
§2.1. Lebesgue Measure on the Real Line 70
§2.2. Lebesgue Measurable Functions 77
§2.3. Lebesgue Integration 82
§2.4. Absolute Continuity, Differentiation and Integration 90
§2.5. Fourier Series 95
Part 2. Solutions 106
Chapter 1. The Riemann-Stieltjes Integral 108
§1.1. Properties of the Riemann-Stieltjes Integral 108
§1.2. Functions of Bounded Variation 125
§1.3. Further Properties of the Riemann-Stieltjes Integral 137
§1.4. Proper Integrals 154
§1.5. Improper Integrals 175
§1.6. Integral Inequalities 218
§1.7. Jordan Measure 239
Chapter 2. The Lebesgue Integral 258
§2.1. Lebesgue Measure on the Real Line 258
§2.2. Lebesgue Measurable Functions 279
§2.3. Lebesgue Integration 292
§2.4. Absolute Continuity, Differentiation and Integration 307
§2.5. Fourier Series 327
Bibliography -Books 362
Index 366
A 366
B 366
C 366
D 366
E 366
F 366
H 366
I 366
J 366
L 366
M 367
O 367
P 367
R 367
S 367
T 367
U 367
V 367
W 367
Y 367
Back Cover 369
· · · · · · (收起)