Version: October 19, 2015

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Material:

Test 1: Wednesday, 2015 October 21

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Chapters 6.4-6.12; differentiation of vectors of single and multiple variables; Chapter 3.7 [in paritcular, pages 127-130], Chapter 10.2: coordinate rotations, notation, and vectors (alternate formultion for vectors in terms of their behavior under rotation, reflection, and invariant lengths--show how scalars, vectors, tensors are defined); Chapters 5.3-5.5, 10.8-10.11: curvilinear coordinate systems, polar coordinates, cylindrical coordinates, spherical polar coordinates, length element, scale factors, physical scale factorss, metric, vector operators in general curvilinear coordinates.

Chapters 6.5-12: differential vector operators of multiple variables, gradient, divergence, curl, Laplacian; vector identities, E & M wave equation; line integrals, surface integrals, volume integrals; conservative and nonconservative fields; Divergence theorem (Gauss's law, delta-functions), Green's Theorem and Identities, Stokes's theorem (Ampere's law), Helmholtz theorem and uniqueness (of solutions to the Laplace and Poisson equations), and the Helmholtz decomposition (irrotational and solenoidal vectors)

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