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This text explores their close relationship and establishes the underlying links. A rigorous and comprehensive introductory treatment, it features clear, readable proofs that illustrate the classical theorems of vector calculus, including the inverse and implicit function theorems. Prerequisites include a knowledge of elementary linear algebra and one-variable calculus. Starting with basic linear algebra and concluding with the integration theorems of Green, Stokes, and Gauss, the text pays particular attention to the relationships between different parametrizations of curves and surfaces, and it surveys their application in line and surface integrals.
Concepts are amply illustrated with figures, worked examples, and physical applications. Numerous exercises, with hints and answers, range from routine calculations to theoretical problems.
Reprint of the Oxford University Press, New York, 1986 edition. Note: these are all the books on Goodreads for this author. To add more, click here. If not, help out and invite Peter to Goodreads.
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Vector Calculus by Peter Baxandall. Thanks for telling us about the problem. Not the book you’re looking for? This introduction to the differential and integral calculus of functions of several variables offers a rigorous and comprehensive treatment.