Loomis Lynn. Advanced Calculus

Jones and Bartlett Publishers, 1990. — 580 p.This is a great book on Calculus. 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.This book is based on an honors Calculus course given in the 1960s. The book contains more material than was normally covered in any one year. It can be used (with omissions) for a year's course in Advanced Calculus, or as a text for a 3-semester introduction to analysis. There are exercises spread throughout the book.