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Multivariable analysis. (English)
London: Springer (ISBN 978-0-85729-191-2/pbk; 978-0-85729-192-9/ebook). x, 394~p. EUR~59.95/net; \sterling~53.99; SFR~86.00 (2011).
The background assumed for studying this book is calculus of one and several variables, linear algebra, and real analysis in one variable. Thus, e.g., the Bolzano-Weierstrass theorem and the Heine-Borel theorem in \$\Bbb R\$ are assumed known, but these theorems in \$\Bbb R^n\$ are part of the material of the book. The first chapter, Preliminaries, gives a summary of what is assumed known. No proofs nor exercises are given. The remaining chapters are (2) Functions Between Euclidean Spaces, (3) Differentiation, (4) Inverse and Implicit Function Theorems, (5) Extrema, (6) Riemann Integration in Euclidean Space, (7) Transformation of Integrals, (8) The General Stokes Theorem. Each section of each chapter after the first has a set of problems. Solutions to all problems are given at the back of the book.