TY  - BOOK
AU  - Loomis,Lynn Harold
AU  - Sternberg,Shlomo
TI  - Advanced calculus
SN  - 9789814583930 
U1  - 515 23
PY  - 2016///
CY  - Singapore : 
PB  - World Scientific, 
KW  - Calculus
N1  - Includes bibliographical references and index; 0. Introduction --
1. Vector spaces -- 
2. Finite-dimensional vector spaces -- 
3. The differential calculus -- 
4. Compactness and completeness -- 
5. Scalar product spaces -- 
6. Differential equations -- 
7. Multilinear functionals -- 
8. Integration -- 
9. Differentiable manifolds -- 
10. The integral calculus on manifolds -- 
11. Exterior calculus -- 
12. Potential theory in E[superscript]n -- 
13. Classical mechanics
N2  - This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. 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.
ER  -