Advanced Calculus
by Lynn H. Loomis, Shlomo Sternberg
Publisher: Jones and Bartlett Publishers 1989
ISBN/ASIN: 0867201223
ISBN-13: 9780867201222
Number of pages: 592
Description:
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.
Download or read it online for free here:
Download link
(58MB, PDF)
Similar books
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.
(20793 views)
- OpenStax
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.
(7129 views)
by George Cain, James Herod
The text covers Euclidean three space, vectors, vector functions, derivatives, more dimensions, linear functions and matrices, continuity, the Taylor polynomial, sequences and series, Taylor series, integration, Gauss and Green, Stokes.
(15900 views)
by Kenneth Kuttler - Brigham Young University
This book presents the necessary linear algebra and then uses it as a framework upon which to build multivariable calculus. This is the correct approach, leaving open the possibility that at least some students will understand the topics presented.
(8028 views)