Advanced Calculus by Lynn H. Loomis, Shlomo Sternberg

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.