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
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.
(26416 views)
Multivariable Calculusby Wong Yan Loi - National University of Singapore
Contents: Vector Functions; Functions of several variables; Limits and Continuity; Partial Derivatives; Maximum and Minimum Values; Lagrange Multipliers; Multiple Integrals; Surface Area; Triple Integrals; Vector Fields; Line Integrals; etc.
(12588 views)
The Calculus of Functions of Several Variablesby 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.
(21830 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.
(11991 views)