by Lynn H. Loomis, Shlomo Sternberg
Publisher: Jones and Bartlett Publishers 1989
Number of pages: 592
A great book. Starts with two very good chapters on linear algebra, adapted to the needs of calculus, and then proceeds to introduce you to the contemporary way to do multivariate calculus, including existence theorems connected to completeness. Very thorough treatment of integration, including integration of forms on manifolds, up to the Stokes theorem, built upon a fine chapter on differential manifolds, exterior differential forms, riemannian metrics, etc. Good illustrations and beautiful typesetting add to the joy of reading it. Plenty of exercises and chapters on applications to physics and differential geometry.
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by Dan Sloughter - Furman University
Many functions in the application of mathematics involve many variables simultaneously. This book introducses Rn, angles and the dot product, cross product, lines, planes, hyperplanes, linear and affine functions, operations with matrices, and more.
by W W L Chen - Macquarie University
Introduction to multivariable and vector analysis: functions of several variables, differentiation, implicit and inverse function theorems, higher order derivatives, double and triple integrals, vector fields, integrals over paths, etc.
by Paul Dawkins - Lamar University
These lecture notes should be accessible to anyone wanting to learn Calculus III or needing a refresher in some of the topics from the class. The notes assume a working knowledge of limits, derivatives, integration, parametric equations, vectors.
The textbook guides students through the core concepts of calculus. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.