208 Deady,
TR, 16:00-17:50
Instructor: James Imamura
Office: 444 Willamette Hall (or 441 Willamette Hall)
E-mail: imamura@uoregon.edu
Phone: 541-346-5212
Office Hours: MWF 10-noon, 444 (or 441) Willamette Hall
or by appointment
Course: Physics 421: Mathematical Methods for Physicists
Course CRN: 15056
Text: Mathematical Methods in the Physical Science, 3rd Ed., Mary L. Boas
Class: 16:00-17:50, TR,
208 Deady
Material:
Grading:
Total: 220 pts
Tests:
Week |
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Chapters 3.4,3.5,6.1-6.3: vector analysis and vector operations, addition, subtraction, multiplication (scalar, dot product, cross product), multiplication involving 3 or more vectors (Triple Scalar Product, Triple Vector Product, Laplace's Identity, and applications); vector functions. rotations (Chapter 3.7) [in particular, pages 127-130] and vectors (Chapter 10.2). Chapters 6.4 differentiation of vectors of single variable. |
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Chapter 10.8-10.10: curvilinear coordinate systems, polar coordinates, cylindrical coordinates, spherical polar coordinates, length element, scale factors, metric. Chapter 4.1-4.5,4.11: Partial Differentiation and applications. Chapters 6.5-6.7: differential vector operators of multiple variables, gradient in Cartesian and curvilinear coordinates, physical meaning of gradient. |
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Chapters 6.5-6.7: differential vector operators of multiple variables, divergence, curl, Laplacian; vector identities, Chapter 6.8-6.12: line integrals, surface integrals, volume integrals; conservative versus nonconservative fields. Divergence Theorem, Dirac delta-function |
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Chapters 6.8,6.10-12: Green's Theorem, Green's Identities, Uniqueness of solutions to Laplace and Poisson's equations, Boundary conditions (Dirichlet, Neumann, and Cauchy), linear differential equations, Stokes's Theorem, Helmholtz Theorem, solenoidal and irrotational vector fields. Chapter 7, Fourier Series and Transforms, Schrodinger equation, particle in a box |
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Chapter 7: Fourier series and periodic functions (sine-cosine series and exponential form), particle in a box continued, Dirchlet's conditions, Sturm-Liouville equation, self-adjoint, second-order, linear differential equations, eigenvalues and eigenfunctions, orthogonality conditions. |
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Chapter 7: Fourier Series, Euler's formulas,
odd and even functions, Parseval's theorem and
aplications (definite integrals, series summation),
Bessel's inequality.
Fourier integrals and
Fourier transforms and nonperiodic functions (sine-cosine
transforms), Dirichlet's Theorem, Parseval's theorem, solutions of
integrals, solutions of partial differential equations using Fourier
transforms (13.9). |
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Chapter 13: Partial Differential Equations: d'Alembert's solution to wave equation (4.11,13.1.2) and extension to general second order linear partial differential equations, classification of partial differential equations, hyperbolic, parabolic, and elliptic equations, characteristics, Riemann invariants, further methods, separation of variables, Fourier transform methods (13.9) |
HW 6 and solutions |
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Chapter 13: Partial Differential Equations: Separation of Variables, Heat Diffusion equation, Schrodinger's equation, Laplace and Poisson equation in Cartesian and spherical polar coordinates, Legendre's equations (Legendre polynomals and Associated Legendre polynomials). Chapter 12: Series Solutions of Differential Equations, Legendre polynomials, associated Legendre polynomials, Legendre series, generating function, Rodrigues formula, recurrence relations, orthogonality conditions, spherical harmonics, spherical harmonic addition theorem |
HW 7 and solutions |
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Exam and Thanksgiving |
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Chapter 12: Series Solutions of Differential Equations, Legendre polynomials, associated Legendre polynomials, Legendre series, generating function, Rodrigues formula, recurrence relations, orthogonality conditions, spherical harmonics, spherical harmonic addition theorem, Laguerre polynomials |
HW 8 and solutions |
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