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.

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

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.

Set 4

2015/11/4

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, further methods, separation of variables, Fourier transform methods

Set 6

2015/11/23

8

Chapter 12: Series Solutions of Differential Equations, Legendre polynomials, Legendre series, generating function, Rodrigues formula, recurrence relations, orthogonality conditions, spherical harmonics. Chapter 13: Partial Differential Equations: Laplace and Poisson equation in spherical polar coordinates, Legendre's equations (Legendre polynomals and Associated Legendre polynomials).

Exam this week

2015/11/18

9

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, hydrogen atom and the Schrodinger equation, associated Laguerre polynomials, Laguerre polynomials.

Set 7

2015/12/2

10

Chapter 12: Series Solutions of Partial Differential Equations, Bessel's equation, Bessel functions Jp, J-p, Np, Ip, H-p, spherical Bessel functions, recurrence relations, orthogonality conditions and weight functions, asymptotic forms of Bessel functions. Chapter 13: Partial Differential equations: Laplace equation in cylindrical coordinates, Bessel functions, solution by series method, wave equation, mixed boundary value problems.

none

...