D. J. H. GarlingCambridge University Press, 4/25/2013EAN 9781107032026, ISBN10: 1107032024Hardcover, 318 pages, 24.9 x 18 x 2.3 cmLanguage: EnglishThe 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.IntroductionPart I. PrologueThe Foundations of Analysis1. The axioms of set theory2. Number systemsPart II. Functions of a Real Variable3. Convergent sequences4. Infinite series5. The topology of R6. Continuity7. Differentiation8. Integration9. Introduction to Fourier series10. Some applicationsAppendixZorn's lemma and the well-ordering principleIndex.
