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Vector Calculusby Peter Baxandall
Synopses & Reviews
Traditionally, linear algebra, vector analysis, and the calculus of functions of several variables are taught as separate subjects. This text explores their close relationship and establishes the underlying links. A rigorous and comprehensive introductory treatment, it features clear, readable proofs that illustrate the classical theorems of vector calculus, including the inverse and implicit function theorems. Prerequisites include a knowledge of elementary linear algebra and one-variable calculus.
Starting with basic linear algebra and concluding with the integration theorems of Green, Stokes, and Gauss, the text pays particular attention to the relationships between different parametrizations of curves and surfaces, and it surveys their application in line and surface integrals. Concepts are amply illustrated with figures, worked examples, and physical applications. Numerous exercises, with hints and answers, range from routine calculations to theoretical problems.
This introductory text offers a rigorous, comprehensive treatment. Classical theorems of vector calculus are amply illustrated with figures, worked examples, physical applications, and exercises with hints and answers. 1986 edition.
This introduction to the differential and integral calculus of functions of several variables offers a rigorous and comprehensive treatment. The classical theorems of vector calculus are amply illustrated with figures, worked examples, and physical applications. Numerous exercises, with hints and answers, range from routine calculations to theoretical problems.1986 edition.
Table of Contents
1. Basic linear algebra and analysis
2. Vector-valued functions of R
3. Real-valued functions of R(superscript m)
4. Vector-valued functions of R(superscript m)
5. Path integrals in R(superscript n)
6. Line integrals in R(superscript n)
7. Double integrals in R(superscript 2)
8. Surfaces in R(superscript 3)
9. Integration over surfaces
10. Triple integrals in R(superscript 3)
11. Differential forms
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