Physics 410: Mathematical Methods for Physicists

318 Willamette Hall, MW, 14:00-15:50


Instructor: Jimmy Imamura
Office: 444 Willamette Hall (or 441 Willamette Hall)
E-mail: imamura@uoregon.edu
Phone: 541-346-5212
Office Hours: Tu/Th, 444 (or 441) Willamette Hall or by appointment


Course: Physics 410: Mathematical Methods for Physicists
Course CRN:
Text: Mathematical Methods in the Physical Science, 3rd Ed., Mary L. Boas
Class: 14:00-15:50, MW
Room: 318 Willamette Hall


Material:


Grading:


Tests:


Week

Material

Homework

Due

1

Chapters 6.4, differentiation of vectors of single and multiple variables, Chapter 3.7 [in paritcular, pages 127-130], Chapter 10.2: coordinate rotations, notation, and vectors; Chapters 5.3-5.5, 10.8-10.11: curvilinear coordinate systems, polar coordinates, cylindrical coordinates, spherical polar coordinates, length element, scale factors, metric

Set 1

2015/10/7

2

Chapter 10.2: coordinate rotations, notation, and vectors; Chapters 5.3-5.5, 10.8-10.11: curvilinear coordinate systems, polar coordinates, cylindrical coordinates, spherical polar coordinates, length element, scale factors, metric 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 versus nonconservative fields

Set 2

2015/10/14

3

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 versus nonconservative fields. Divergence Theorem, Green's Theorem, Green's Identity, Stokes's Theorem.

Set 3

2015/10/21

4

Chapters 6.8,6.10-11: Stokes's Theorem, Helmholtz Theorem.

Chapter 7, Fourier Series and Transforms

No homework this week. Test Wednesday of this week.

...

5

Chapter 7: Fourier series and periodic functions (sine-cosine series and exponential form), Dirchlet's conditions, orthogonality conditions, Euler's formulas, odd and even functions, Parseval's theorem, Fourier integrals and transforms and non-periodic functions.

2015/11/4

Set 4

6

Chapter 7: Fourier transforms and nonperiodic functions (sine-cosine transforms), Dirichlet's Theorem, Parseval's theorem, solutions of integrals, solutions of partial differential equations.
Chapter 13: Partial Differential Equations, d'Alembert's solution of wave equation.

Set 5

2015/11/11

7

Chapter 13: Partial Differential Equations: d'Alembert's solution to wave equation and extension to general second order linear partial differential equations, classification of partial differential equations, hyperbolic, parabolic, and elliptic equations, characteristics, Riemann invariants, Maxwell's equations and electric scalar potential, Laplace equation in Cartesian coordinates, Poisson equation, Helmholtz equation, Diffusion equation (e.g., Schrodinger equation), classical wave equation, telegrapher's equation.

Set 6

2015/11/18

8

Chapter 12: Series Solutions of Partial Differential Equations, Legendre polynomials, Legendre series, generating function, Rodrigues formula, recurrence relations, orthogonality conditions, spherical harmonics. Chapter 13: Partial Differential Equations: d'Alembert's solution to wave equation, Maxwell's equations and electric scalar potential, Laplace equation in Cartesian coordinates (solution using Fourier series), Diffusion equation (Schrodinger equation), classical wave equation.

Set 7

2014/11/26

9

Chapter 12: Series Solutions of Partial Differential Equations, Legendre polynomials, Legendre series, generating function, Rodrigues formula, recurrence relations, orthogonality conditions, spherical harmonics. Chapter 13: Partial Differential Equations: d'Alembert's solution to wave equation, hyperbolic, parabolic, and elliptic equations, characteristics, Riemann invariants, Maxwell's equations and electric scalar potential, Laplace equation in Cartesian coordinates (solution using Fourier series), Diffusion equation (Schrodinger equation), classical wave equation.

Set 8

2014/12/5