Textbook Title: Advanced Calculus, Revised Edition
This textbook is based on an honors course in Advanced Calculus given at Department of Mathematics, Hardvard University. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. The textbook’s first half develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and the second half which deals with the calculus of differentiable manifolds. There are exercises of many different kinds spread throughout the book.
Author: Lynn H. Loomis and Shlomo Sternberg
Key words: Math, Mathematics, Algebra, Calculus
Download URL: http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf