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 1 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
3 covers complex analysis and the theory of measure and
integration.
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