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" Calculus in vector spaces / "
Lawrence J. Corwin, Robert H. Szczarba.
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BL
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| Record Number
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847473
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| Main Entry
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Corwin, Lawrence J.,1943-
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| Title & Author
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Calculus in vector spaces /\ Lawrence J. Corwin, Robert H. Szczarba.
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| Edition Statement
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2nd ed.
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| Publication Statement
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New York :: M. Dekker,, ©1995.
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| Series Statement
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Monographs and textbooks in pure and applied mathematics ;; 189
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xi, 583 pages :: illustrations ;; 24 cm.
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| ISBN
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0824792793
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: 9780824792794
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| Notes
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Includes index.
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| Contents
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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.
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| Abstract
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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.
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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.
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| Subject
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Calculus.
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Vector spaces.
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Analysis
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Calculus.
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Espaces vectoriels.
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Lineare Algebra
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Vector spaces.
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Vektoranalysis
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| Dewey Classification
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515/.14
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| LC Classification
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QA303.C823 1995
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| NLM classification
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PA 45blsrissc
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SK 220rvk
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| Added Entry
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Szczarba, Robert Henry,1932-
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