A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis (A Course in Mathematical Analysis 3 Volume Set) 1st Edition by D. J. H. Garling (PDF)

Description

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 2 goes on to consider metric and topological spaces and functions of several variables. Volume 3 covers complex analysis and the theory of measure and integration.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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).)

⭐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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