Multivariable and Vector Analysis
by W W L Chen
Publisher: Macquarie University 2008
Number of pages: 203
This set of notes is suitable for an introduction to some of the basic ideas in multivariable and vector analysis: functions of several variables, differentiation, implicit and inverse function theorems, higher order derivatives, double and triple integrals, change of variables, paths, vector fields, integrals over paths, parametrized surfaces, integrals over surfaces, integration theorems.
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The textbook presents introductory concepts of vector and tensor analysis, suitable for a one-semester course. Volume II discusses Euclidean Manifolds followed by the analytical and geometrical aspects of vector and tensor fields.
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A text-book for the use of students of mathematics and physics, taken from the course of lectures on Vector Analysis delivered by J. Willard Gibbs. Numerous illustrative examples have been drawn from geometry, mechanics, and physics.