Physics 401/501 Mathematical and Computational Physics

Welcome to the Mathematical and Computational Physics course web page. This course is offered Fall Semester 2002. Here we will provide information about the course as well as materials. Both lecture materials and other background materials will be provided as the course developes.

Instructor: Professor Comer Duncan

Contact Information: Office in Overman Hall Room 173, office phone 419 372 8108, office hours by appointment; email: gcd@chandra.bgsu.edu

Course Information

Course materials:

Mathematical Methods for the Physicist by George Arfken and Hans Webber, Fifth Edition, Harcourt/Academic Press.
Hand-outs on various computational physics methods occasionally will be provided.
When possible, links in this web page to the lectures and selected hand-outs will be made as the term proceeds.
A bibliography of some key references will be provided.
Matlab will be a partial tool, with several Matlab examples provided as the term proceeds.
Fortran 90 will be a partial tool and elements of f90 will be covered as needed; no prior experience with f90 programming is required. However, experience with a high level language [such as C, C++] and computer literacy is a plus.

Course Objectives:

This course is an introduction to the methods of analytical and computational physics for upper division undergraduate science majors. The emphasis will be on the development of tools useful in formulating and solving problems in the physical sciences. Among the topics to be covered are:

Unix
Matlab
fortran 90 language elements
Vector Analysis
Linear algebra and matrix methods applied to physical science
Ordinary differential equations--both analytical and numerical methods
Fortran programming as used in computational physics-- some examples

If time permits, we shall also cover introductory aspects of

An introduction to chaos

There may be other topics that can be covered. We shall tailor the topics somewhat to the interests of the students and instructor.

Exams and grading:

The course is a lecture based course which meets two days per week from 2:30 to 4:10 p.m. There will be problem sets assigned almost every week, and the solutions are always due one week after being assigned. There will be nominally three in class hour exams given after the conclusion of the major sections of the course material. In lieu of an in class final exam, there will be a term project involving computational applications of the concepts discussed in the course to some problem area in physics. We will discuss the details of the term project in November. The term project will be due on the day that the in class final exam would normally be given.

The conventional A: > 89%, B: > 79%, C: > 69 %, D: > 59% will be followed. Each exam counts 20%, the problem sets count 15%, and the term projects count 25%.

Tentative Course Outline

Chapters and Sections	Topic	Approx. time
Chap. 1, sections 1.1 - 1.5	Vector Basics	1 week	vectors_1 , vectors_2 , vectors_3, vectors_4 , vectors_5
Chap. 1, sections 1.6-1.9	Grad, Div, Curl	1 week
Chap. 1, sections 1.10 - 1.13	Gauss thm., Stokes thm., Potentials	1 week
Chap. 1, sections 1.14 - 1.16	Gauss' law, Dirac Delta Function, Helmholtz's thm.	1 week
Numerical Approx. in Vector Analysis	Basic vector operations, gradient, divergence and curl --done in fortran90	2 weeks
EXAM I in class	Covering the material from Chap. 1 and selected numerical algorithms	just after Chap. 1 material completed
Chap. 3, sections 3.1 - 3.3	Determinants, Matrix algebra, special matrices in physics	1 week
Chap. 3, sections 3.4 - 3.5	Eigenvalue Problem and matrix diagonalization	1 week
Numerical Linear Algebra introduction	efficient implementations of numerical linear algebra , intro to some packages	2 weeks
EXAM II in class	Covering the material from Chap. 3 and selected numerical algorithms	just after Chap. 3 material completed
Chap. 8, section 8.2 and 8.4	First order differential equations and examples; singular points	1 week
Chap. 8, section 8.5-8.6	Series solutions, Frobenius method	1 week
Chap. 8, section 8.8	Numerical methods for ordinary diff. eqns plus my notes and codes in f90.	2 weeks
EXAM III in class	Covering the material from Chap. 8 and selected numerical algorithms	just after Chap. 8 material completed
Term Projects	Assigned by instructor to meet interests of individual students. To be discussed later in the term.	Due on day that final exam would be given for this course