Ph 461/561   Mathematical Methods

Physics Department, Oregon State University

Fall 2009 term

One-credit graduate Math Methods: Ph 505

Instructor: Oksana Ostroverkhova (Wngr 413)
Lectures: MWF 11am, Weniger 304

DateLectures AssignmentsNotes
09/28 Complex numbers HW 1 for 461 ; HW 1 for 561 WS 1
09/30 Hyperbolic functions.   WS 2
10/02 Series. HW 2 (for both 461 and 561) WS 3
10/05 Convergence of infinite series. HW 3 for 461 ; HW 3 for 561 WS 4
10/07 Power series. Taylor series. HW 4 for 461 ; HW 4 for 561 WS 5
10/09 Fourier series. HW 5 for 461 ; HW 5 for 561 WS 6
10/12 Matrices and vector spaces. Problem #4 of HW#5 is due on Friday WS 7
10/14 Eigenvalues and eigenvectors. Systems of linear equations. HW 6 for 461 ; HW 6 for 561 WS 8
10/16 Vector algebra.   WS 9
10/19 Vector calculus: Cartesian coordinates. HW 7 (for both 461 and 561) WS 10
10/21 Vector calculus: cylindrical and spherical coordinates. Midterm is set for Wednesday, November 4 (11 AM, Weniger 304). Ch.3,4,7,8,10,11,12. Midterm is a closed book one: prepare your own formula sheet.No calculators.
10/23 Vector calculus: generalized curvilinear coordinates. HW 8 (for both 461 and 561) WS 11
10/26 Line integrals.Green's theorem. Conservative fields.   WS 12
10/28 Surface and volume integrals.   WS 13
10/30 First-order ordinary differential equations.   WS 14
11/02 Higher-order ordinary differential equations.   WS 15
11/04 Midterm   (11 am, Weniger 304)    
11/06 Linear ODEs with variable coefficients. HW 9 (for both 461 and 561)  
11/09 Series solutions of ODEs: expansion about an ordinary point.   WS 16
11/11 Series solutions of ODEs: expansion about regular singularity. HW 10 (for both 461 and 561) WS 17
11/13 Wronskian method of obtaining a second solution. Polynomial solutions.    
11/16 Eigenfunction methods for ODEs. HW 11 (for both 461 and 561) WS 18
11/18 Special functions: Legendre functions and polynomials.   Read up on associated Legendre polynomials and spherical harmonics.
11/20 Special functions: Hermite polynomials. Gamma function. HW 12 (for both 461 and 561) Read up on Laguerre and associated Laguerre polynomials.
11/23 Special functions: Bessel and spherical Bessel functions. Beta function. Problem 20.4 of HW#12 is due next Monday. WS 19
11/25 Partial differential equations: first and second order. HW 13 (for both 461 and 561)  
11/30 PDEs: diffusion-type problems and hyperbolic (wave) equations. HW 14 (for both 461 and 561) WS 20
12/02 Inhomogeneous PDEs. Final exam: Thu Dec 10, 9:30 AM, Weniger 304. Prepare your formula sheet. Closed book, no calculators.