The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This first volume focuses on the analysis of real-valued functions of a real variable. Besides developing the basic theory it describes many applications, including a chapter on Fourier series. It also includes a Prologue in which the author introduces the axioms of set theory and uses them to construct the real number system. Volume II goes on to consider metric and topological spaces and functions of several variables. Volume III covers complex analysis and the theory of measure and integration.
- Developed from the author's own undergraduate courses taught at the University of Cambridge
- Over 300 exercises challenge the reader to learn through practice
- Useful background reading for a wide range of courses in mathematics
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Reviews & endorsements
"Garling is a gifted expositor and the book under review really conveys the beauty of the subject, not an easy task. [It] comes with appropriate examples when needed and has plenty of well-chosen exercises as may be expected from a textbook. As the author points out in the introduction, a newcomer may be advised, on a first reading, to skip part one and take the required properties of the ordered real field as axioms; later on, as the student matures, he/she may go back to a detailed reading of the skipped part. This is good advice."
Felipe Zaldivar, MAA Reviews
"This work is the first in a three-volume set dedicated to real and complex analysis that "mathematical undergraduates may expect to meet in the first two years or so … of analysis" … The exposition is superb: open and nontelegraphic. Highly recommended. Upper-division undergraduates and graduate students."
D. Robbins, Choice
"These three volumes cover very thoroughly the whole of undergraduate analysis and much more besides."
John Baylis, The Mathematical Gazette
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Product details
- Date Published: June 2013
- format: Paperback
- isbn: 9781107614185
- length: 318 pages
- dimensions: 244 x 173 x 18 mm
- weight: 0.51kg
- contains: 21 b/w illus. 340 exercises
- availability: Available
Table of Contents
Introduction
Part I. Prologue: The Foundations of Analysis:
1. The axioms of set theory
2. Number systems
Part II. Functions of a Real Variable:
3. Convergent sequences
4. Infinite series
5. The topology of R
6. Continuity
7. Differentiation
8. Integration
9. Introduction to Fourier series
10. Some applications
Appendix: Zorn's lemma and the well-ordering principle
Index.
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Author
D. J. H. Garling, University of Cambridge
D. J. H. Garling is an Emeritus Reader in Mathematical Analysis at the University of Cambridge. He has 50 years' experience of teaching undergraduate students in most areas of pure mathematics, but particularly in analysis.