A Course in Mathematical Analysis: Volume 2, Metric and Topological Spaces, Functions of a Vector Variable 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 teachers. Volume I focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume III covers complex analysis and the theory of measure and integration.

User’s Reviews

Editorial Reviews: Book Description The second volume of three providing a full and detailed account of undergraduate mathematical analysis. About the Author D. J. H. Garling is 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.

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

⭐I know metric spaces (Have read Rudin C2 for multiple times) and try to attack topological spaces (C13) and fails miserably…This book is probably for reference only, not for learning. You won’t be able to infer which theorem is a must-read because the author simply packing every theorem together. No motivational examples, etc.I do appreciate the effort to finish Analysis I, II, topology, complex analysis and modern integration in 900 pages or so.The book is probably good to check your understanding after finishing all things.

⭐The best comprehensive work by far.

⭐

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