This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind the mathematics and enabling them to construct their own proofs.
Features
1.Flexible presentation, with uniform writing style and notation, covers the material in small sections, allowing instructors to adapt this book to their syllabus.
2.The practical focus explains assumptions so that students learn the motivation behind the mathematics and are able to construct their own proofs.
3.Early introduction of the fundamental goals of analysis Refers and examines how a limit operation interacts with algebraic operation.
4.Optional appendices and enrichment sections enables students to understand the material and allows instructors to tailor their courses.
5.An alternate chapter on metric spaces allows instructors to cover either chapter independently without mentioning the other.
6.More than 200 worked examples and 600 exercises encourage students to test comprehension of concepts, while using techniques in other contexts.
7.Separate coverage of topology and analysis presents purely computational material first, followed by topological material in alternate chapters.
8.Rigorous presentation of integers provides shorter presentations while focusing on analysis.
9.Reorganized coverage of series separates series of constants and series of functions into separate chapters.
10.Consecutive numbering of theorems, definitions and remarks allows students and instructors to find citations easily.
About the Author
William Wade received his PhD in harmonic analysis from the University of California—Riverside. He has been a professor of the Department of Mathematics at the University of Tennessee for more than forty years. During that time, he has received multiple awards including two Fulbright Scholarships, the Chancellor's Award for Research and Creative Achievements, the Dean's Award for Extraordinary Service, and the National Alumni Association Outstanding Teaching Award.
Table of Contents:
Part I. ONE-DIMENSIONAL THEORY
Chapter 1. The Real Number System
Chapter 2. Sequences in R
Chapter 3. Continuity on R
Chapter 4. Differentiability on R
Chapter 5 Integrability on R
Chapter 6. Infinite Series of Real Numbers
Chapter 7. Infinite Series of Functions
Part II. MULTIDIMENSIONAL THEORY
Chapter 8. Euclidean Spaces
Chapter 9. Convergence in Rn
Chapter 10. Metric Spaces
Chapter 11. Differentiability on Rn
Chapter 12. Integration on Rn
Chapter 13. Fundamental Theorems of Vector Calculus
Chapter 14. Fourier Series
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