Monographs and textbooks in pure and applied mathematics ;
Volume Designation
189
GENERAL NOTES
Text of Note
Includes index.
CONTENTS NOTE
Text of Note
Ch. 1. Some Preliminaries -- Ch. 2. Vector Spaces -- Ch. 3. The Derivative -- Ch. 4. The Structure of Vector Spaces -- Ch. 5. Compact and Connected Sets -- Ch. 6. The Chain Rule, Higher Derivatives, and Taylor's Theorem -- Ch. 7. Linear Transformations and Matrices -- Ch. 8. Maxima and Minima -- Ch. 9. The Inverse and Implicit Function Theorems -- Ch. 10. The Spectral Theorem -- Ch. 11. Integration -- Ch. 12. Iterated Integrals and the Fubini Theorem -- Ch. 13. Line Integrals -- Ch. 14. Surface Integrals -- Ch. 15. Differential Forms -- Ch. 16. Integration of Differential Forms -- Appendix 1. The Existence of Determinants -- Appendix 2. Jordan Canonical Form.
0
SUMMARY OR ABSTRACT
Text of Note
Addressing linear algebra from the basics to the spectral theorem and examining a host of topics in multivariable calculus, including differentiation, integration, maxima and minima, the inverse and implicit function theorems, and differential forms, this thoroughly revised Second Edition of an invaluable reference/text - widely successful through five printings - continues to provide unified, integrated coverage of the two fields.
Text of Note
Demonstrating that mathematics is a noncompartmentalized discipline of interrelated subjects, Calculus in Vector Spaces, Second Edition introduces the derivative as a linear transformation ... presents linear algebra in a concrete context based on complementary ideas in calculus ... explains differential forms on Euclidean space permitting Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting ... gives a new clarification of compactness as defined in terms of coverings and in terms of sequences ... supplies a novel treatment of eigenvalues and eigenvectors ... and more.