Physics 401/501

Mathematical and Computational Physics


Welcome to the Mathematical and Computational Physics course web page. This course is offered Fall Semester 1999. 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.


Note that we intend to make extensive use of this web page. Please refer to it on a regular basis for occasional extra materials, lecture notes, and hand-outs. The url for this web page is: 
http://chandra.bgsu.edu/~gcd/p401.html  ... Bookmark this page.
 

Course Instructor:

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.
 

Course Meeting Time and Places:
 



 

Tentative Course Syllabus

Meeting Date Lecture Topic Supporting Materials
Aug. 25 Introduction & Unix I UNIXhelp for Users Tutorial Material
Aug.  30 Unix II  UNIXhelp for Users Tutorial Material
Sept.  1 Taylor expansion of a function; Introduction to Mathematica Taylor Expansion Notes :Boas, Chap. 1
Sept.  6 Labor Day-- No Class Work through Unix help web pages
Sept.  8 Numerical Differentiation Numerical Differentiation Notes 
Sept.  13 Numerical Integration I  Numerical Integration Notes
Sept. 15  Matrix Algebra I Boas Chap 4 
Sept.  20 Matrix Algebra II Boas Chap 4 
Sept.  22 Eigenvalue Problem Notes on Eigenvalue Problem;   Mathematica  Notebook
Sept.  27 Linear Equation Solvers I Boas Chap 4 and Mathematica Notebook
Sept.  29 Linear Equation Solvers II  Boas Chap 4 and Mathematica Notebook
Oct.  4

Exam I

Covers all material from beginning through Linear Eqn.
Oct.  6 Complex numbers and functions Boas Chap 2 
Oct.  11 Finding Roots Notes on Newton's Method; Mathematica Notebook
Oct.  13 Introduction to Chaos Logistic Map Notes 
Oct.  18 Differential Equations I Boas Chap  8 
Oct.  20 Differential Equations II Boas Chap  12 
Oct.  25 Differential Equations III Boas Chap   12
Oct.  27 Numerical Methods for Diff. Eqns. I Numerical Methods for Differential Equations Notes 
Nov.  1 Numerical Methods for Diff. Eqns. II Numerical Methods for Differential Equations Notes 
Nov.  3 Numerical Methods for Diff. Eqns. III Numerical Methods for Differential Equations Notes 
Nov.  8 Chaotic Dynamics Using Differential Equation Solvers: Examples Lorentz system and others as examples
Nov.  10 Exam II Covers all material since the first exam
Nov.  15 Vector Analysis I: scalar & vector product Notes on Vector Analysis ; Boas Chap 6
Nov.  17 Vector Analysis II: velocity & acceleration in noninertial frames Notes on Vector Analysis ; Boas Chap 6
Nov.  22 Vector Analysis III: gradient and directional derivative Notes on Vector Analysis ; Boas Chap 6
Nov.  29 Vector Analysis IV: divergence and Gauss' law Notes on Vector Analysis ; Boas Chap 6
Dec.  1 Vector Analysis V: line integrals and conservative vector fields Notes on Vector Analysis ; Boas Chap 6 
Dec.  6  Vector Analysis VI: curl and Stokes' theorem Notes on Vector Analysis ; Boas Chap 6
Dec.  8 Special Topic TBA 
Dec. 13-17 Exam Week TBA 

Requirements for the course:

A knowledge of calculus at the level of Mathematics 232 is assumed. Any further study in mathematics would be helpful, but not necessarily a requirement. Being computer literate is a real plus. If you already know a high level language [such as C, C++, fortran, or even basic] that will help but is not a prerequisite.Elements of fortran90 and Mathematica will be a main components of the course delivery.

Examinations:

There will be two examinations in class. The first will be approximately half way through the semester and the second will be during the final exam week. There will be problem sets given approximately every two weeks, but probably not more than seven sets. It is also possible that I will assign two projects during the term. These will be more in depth studies of some topic from the physical sciences which can be meaningfully understood using the tools covered in this course.