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A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis, by D. J. H. Garling
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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.
- Sales Rank: #1126497 in Books
- Published on: 2013-06-10
- Released on: 2013-04-25
- Original language: English
- Number of items: 1
- Dimensions: 9.72" h x .67" w x 6.85" l, 1.20 pounds
- Binding: Paperback
- 318 pages
Review
"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
About the Author
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.
Most helpful customer reviews
2 of 2 people found the following review helpful.
Great Introduction for Undergraduates
By Emil Haugen
A really great introduction to real analysis which demands basically no prerequisites, something that fitted me very well. There is even a brief summary of set/number theory (in the Prologue) which is developed further in chapter two to deal with Abeilian groups,rings, fields, morphisms and some interesting -if not immedeately useful for this book- rudimentary number theory. For the better prepared student the author states clearly that the first section (chpts. 1,2 on set and number theory can be omitted but they're still nice to have in my opinion.) My only problem with that element of the book was that the first two chapters introduced a lot of new notation, sometimes without any clear explanation of what it meant. However, this is not vital to the understanding of the book and thus a pretty tiny drawback. The treatment of sequences and series and convergence and continuity to be particularly crisp and understandable. There is also a lot of "additional" material such as an introduction to Fourier series and a wide range of applications, for example the Gamma function and the Riemann Zeta function.
All in all a very concise book (even with the prologue), just shy of 300 pages but still comprehensive in its description of the fundamentals of real analysis. (And, for the undergraduate level, this is much better suited than Rudin, which to me seems like a better fit for more mature mathematicians (i.e. graduates).)
7 of 19 people found the following review helpful.
symbols problem
By Erroll
Mathematical symbols do not show correctly in kindle book.
I think it is a great book in Mathematical analysis, but the kindle book dose not work well.
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