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By Norbury, John W., Professor

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Physics Literature

Excerpt
Excerpt: Chapter 1 - Matrices: 1.1 Einstein Summation Convention; Even though we shall not study vectors until chapter 2, we will introduce simple vectors now so that we can more easily understand the Einstein summation convention. We are often used to writing vectors in terms of unit basis vectors as ...

Contents 1 MATRICES 5 1.1 Einstein Summation Convention . . . . . . . . . . . . . . . . 5 1.2 Coupled Equations and Matrices . . . . . . . . . . . . . . . . 6 1.3 Determinants and Inverse . . . . . . . . . . . . . . . . . . . . 8 1.4 Solution of Coupled Equations . . . . . . . . . . . . . . . . . 11 1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.7 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.8 Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 VECTORS 19 2.1 Basis Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Scalar Product . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Vector Product . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.4 Triple and Mixed Products . . . . . . . . . . . . . . . . . . . 25 2.5 Div, Grad and Curl (di?erential calculus for vectors) . . . . . 26 2.6 Integrals of Div, Grad and Curl . . . . . . . . . . . . . . . . . 31 2.6.1 Fundamental Theorem of Gradients . . . . . . . . . . 32 2.6.2 Gauss' theorem (Fundamental theorem of Divergence) 34 2.6.3 Stokes' theorem (Fundamental theorem of curl) . . . . 35 2.7 Potential Theory . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.8 Curvilinear Coordinates . . . . . . . . . . . . . . . . . . . . . 37 2.8.1 Plane Cartesian (Rectangular) Coordinates . . . . . . 37 2.8.2 Three dimensional Cartesian Coordinates . . . . . . . 38 2.8.3 Plane (2-dimensional) Polar Coordinates . . . . . . . 38 2.8.4 Spherical (3-dimensional) Polar Coordinates . . . . . 40 2.8.5 Cylindrical (3-dimensional) Polar Coordinates . . . . 41 2.8.6 Div, Grad and Curl in Curvilinear Coordinates . . . . 43

Book Id: WPLBN0000659715
Format Type: PDF eBook
File Size: 690.61 KB.
Reproduction Date: 2005
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