Foundations of Mathematical Analysis

Front Cover
Springer Science & Business Media, Dec 17, 2011 - Mathematics - 570 pages
0 Reviews

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels.

This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts.

Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 The Real Number System
1
2 Sequences Convergence and Divergence
22
3 Limits Continuity and Differentiability
71
4 Applications of Differentiability
115
5 Series Convergence and Divergence
147
6 Definite and Indefinite Integrals
208
7 Improper Integrals and Applications of Riemann Integrals
271
8 Power Series
331
9 Uniform Convergence of Sequences of Functions
370
10 Fourier Series and Applications
429
11 Functions of Bounded Variation and RiemannStieltjes Integrals
468
References for Further Reading
506
Index of Notation
507
Appendix A Hints for Selected Questions and Exercises
513
Index
564
Copyright

Common terms and phrases

Bibliographic information