Foundations of Mathematical AnalysisMathematical 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. |
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Contents
1 | |
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 |