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
Multivariable Calculusby Jerry Shurman - Reed College
A text for a two-semester multivariable calculus course. The setting is n-dimensional Euclidean space, with the material on differentiation culminating in the Inverse Function Theorem, and the material on integration culminating in Stokes's Theorem.
(15980 views)
Calculus Volume 3- 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.
(11808 views)
Multivariable and Vector Analysisby 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.
(19176 views)
Calculus IIIby 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.
(26291 views)