(Ebook) A Course in Mathematical Analysis. Volume II: Metric and Topological Spaces, Functions of a Vector Variable by D.J.H. Garling ISBN 9781107032033, 9781107352926, 9781107675322, 1107032032, 1107352924, 1107675324, B00BM4TII8

(Ebook) A Course in Mathematical Analysis. Volume II: Metric and Topological Spaces, Functions of a Vector Variable by D.J.H. Garling ISBN 9781107032033, 9781107352926, 9781107675322, 1107032032, 1107352924, 1107675324, B00BM4TII8

Main subject categories: • Real analysis • Topology • Metric spaces • Convergence • Continuity • Completeness • Compactness • Connectedness • Functions of a vector variable • Differentiating functions of a vector variable • Integrating functions of several variables • Differential manifolds in Euclidean spaceThe 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.