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This book, in its seventh edition, has always enjoyed a reputation
for expository excellence. The text is both a learning manual
as well as a reference manual. It is based on a dual geometric-analytic
approach to each topic of discussion. The concepts and theorems
are first visualized and understood heuristically, and then
are reduced to an algebra-calculus framework for computation
or mathematical scrutiny. The text is unique in its presentation
of the laplacian and the vector potential and can be used at
several levels. The first four chapters constitute a compact
one-semester introduction to the subject. Chapter five and the
appendices address deeper topics in differential geometry, potential
theory, physics, and engineering. |
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Chapter
1: |
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| Vector Algebra |
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| Vector Functions of a Single
Variable |
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| Scalar and Vector Fields |
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| Line, Surface and Volume Integrals |
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Advanced Topics
- The Divergence Theorem
- Greens Formulas: Laplace's and Poisson's Equations
- The Fundamental Theorem of Vector Analysis
- Green's Theorem
- Stokes' Theorem
- The Transport Theorems
- Matrix Techniques in Vector Analysis
- Linear Orthogonal Transformations
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| Historical Notes |
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| Two Theorems of Advanced Calculus |
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| The Vector Equations of Classical
Mechanics |
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| The Vector Equations of Electromagnetism |
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| Constrained Optimization |
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