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:

Course Information

Course materials:

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: 

If time permits, we shall also cover introductory aspects of 

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
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