Physics 325: Introduction to Mathematical Physics

Department of Physics and Astronomy

Sonoma State University

Fall 2018

Class: Tu Th 9:20-10:35 am, Darwin 31

Instructor: Dr. Hongtao Shi

Phone: 664-2013


Office: Darwin 300J

Office Hours: M 9:45-11:00 am, Th 3:45-5:00 pm, and by appointment

Course Description: This course is designed for you to become more adept at applying mathematical tools to physics problems and get prepared for other upper division courses. You are solely responsible for learning and applying mathematical symbolic processing software, such as Mathematica, Mathcad, to the homework problems. Both are available in many on-campus computer labs, or you can purchase them online.

Course Objectives: You are required to demonstrate (a) knowledge, understanding and use of the principles of physics, (b) ability to use reasoning and logic to define a problem in terms of physics principles, and (c) ability to use mathematics and computer applications to solve physics problems. By the end of this course it is to be expected that the students will have acquired a concrete understanding of the following topics: Coordinate Systems, Vector Algebra and Calculus, Reciprocal Vectors, Complex Numbers, Partial Differentiation, Differential Equations, Stationary Values under Constraints, Matrices, Eigenvalues and Eigenfunctions, Orthonormal Functions, Fourier Series and Integrals, and Fourier Transformation.

Prerequisites: Physics 214: Introduction to Physics II and Mathematics 261 Calculus IV

Required Textbook: Mathematical Methods for Physics and Engineering, 3rd ed., by K.F. Riley, M.P. Hobson, & S.J. Bence, Published by Cambridge, ISBN: 0-521-67971-0.

Recommended Reference Book: B. Torrence and E. Torrence, The Student's Introduction to MATHEMATICA, 2nd Edition, Cambridge, 2009, ISBN 978-0-521-71789-2.

Course Schedule

Hands-on Start to Mathematica

A Student's First Course in Mathematica

Beginner's Guide to Mathematica (Michigan State University)

Mathematica Tutorials: Part I, Part II (Brown University)

Multivariable Calculus

Course Outline:


Sections to be covered

1. Preliminary Algebra
2. Preliminary Calculus
2.1, 2.2
3. Complex Numbers
5. Partial Differentiation
5.1-5.5, 5.9
14. Differential Equations I
14.1, 14.2
7. Vector Algebra
10. Vector Calculus
10.1-10.3, 10.6, 10.7, 10.9
11. Line, Surface, and Volume Integrals
11.1, 11.3-11.5
12. Fourier Series
8. Matrices and Vector Spaces
8.1-8.6, 8.8-8.11, 8.13

Grading Policy:

Homework, Quizzes and Exams 30% Final Exam, Thursday, 12/13, 8:00-9:50 am
  20% Test 1
  20% Test 2
  30% Homework Assignments
Course Grade Percent Course Grade Percent Course Grade Percent























Below 60



Other Reference Books and Tools:

  1. Mathematical Methods for Physicists by George B. Arfken, Hans J. Weber & Frank Harris (Academic Press, 2005)
  2. A Physicist's Guide to Mathematica by Patrick Tam (Academic Press, 2009)
  3. Mastering Mathematica: Programming Methods and Applications by John W. Gray (Academic Press, 1998)

Attendance is not mandatory (see policy). You will suffer if you often miss the classes.

2. Reading and homework will be assigned every week from the book, due the following week.

3. There is no tolerance for late homework submission without a legitimate reason, as solutions will usually be posted the day after due date.

4. The lowest homework grade will be dropped when I compute your term grade.

5. You are encouraged to work in a study group in doing the homework, discussing the problems, but I expect you to write up your own solutions handed in for grading.

6. All exams are closed book/notes and must be taken at the assigned time. You can bring one (1) index card to the class with equations and formulas. No makeup will be given without a legitimate reason such as medical emergency. So arrange accordingly. Be aware that the makeup exam/quiz may be entirely different from the original one.

7. I reserve the right to raise your grade if exceptional effort and class participation are observed through the semester.

Disability: If you have a disability and need special consideration, please contact the Office of Disabled Student Services ( DSS ), located in Salazar Hall, Room 1049, Phone 664-2677.

Important University policies, such as add/drop classes, cheating and plagiarism, grade appeal procedures, can be found at

Email me if you have questions or comments.

Last updated August 16, 2018