PH420 Mathematical Methods of Physics I (Fall, 2020)

Lecture Format: Asynchronous online video

All lectures are prerecorded video streamed from the course web site
Students are required to watch all video lectures by the specified dates.

Discussions and Q&A session: Tue. & Thu. 11:00am -- 12:15 am

Students are required to attend online discussion and question sessions held during the regular class hours. Topics of the discussion are listed in the course schedule. The discussion will be recorded and the videos are available if you should miss the sessions. However, excessive absence in the discussion hour may result in a low course grade.

Course Description:

Through this course students will learn mathematical methods necessary in physics core courses such as classical mechanics, electromagnetism, and quantum mechanics. The mathematical methods covered in this course include complex analysis, linear algebra, vector calculus, series expansions, ordinary differential equations including special functions, and partial differential equations. Students successfully completing this course will develop sufficient mathematical skills necessary to complete the physics core courses.  In addition to basic mathematical skills,  various mathematical tools such as Mathematica are intensively used in this course.

Suggested Textbook

Mathematical Methods in Physical Sciences, 3rd Ed.
by Mary L. Boas.
Wiley, 2006
ISBN: 978-0-471-19826-0


Course Schedule and Lecture Notes
Score Card

Past Exams

2014, 2015, 2016
2017, 2018, 2019
Learning Objectives:

Biophysical processes involved in the following biological processes

  • Differential and integral calculus
  • Series expansions including Taylor, Fourier, and Laurent expansions.
  • Complex variables, functions of complex variables, residue theorem and contour integrals
  • Matrices, linear algebra, and eigenvalue problems
  • Vector calculus
  • Ordinary differential equations, special functions
  • Partial differential equations
  • Calculus of Variation


The use of Mathetmatica is required in this course. Mathematica 10 is installed on all computers in the classroom. However, it is highly desirable for you to have your own Mathematica on your personal computer. It is free for UAB students. The following web page will explain how to get your own copy of Mathematica: Free online tutorials are also available. See


At the end of each lecture note, homework problems are assigned. Homework must be turned in electronically by email.  Allowed formats are PDF (.pdf) and Mathematica notebook (.nb). Hand written pages should be scanned in PDF. Do not send picture taken by a cellphone camera app. Use scanner app instead. Microsoft Office Lens (a free app for Android and iPhone) is recommended.


Three midterm exams and a final comprehensive exam will be given. Students must take all four exams. Make-up exam is allowed only when reasonable excuse is presented.


Exams and assignments carry the following maximum possible points. Midterm exams (15 pts. each), Final exam (30 pts.), Homework and other assignments (25 pts.). The total maximum possible points is 100. Letter grades are determined by the rule given in the table.

Grade Total Score
A 85 or above
B 75 or above
C 60 or above
D 50 or above
F Otherwise

About Instructor

Dr. Ryoichi Kawai

Office Hour: by appointment
Tel: (205) 934-3931
Fax: (205) 934-8042
(My PGP public key)


Campbell Hall 309
Department of Physics
University of Alabama at Birmingham
1300 University Blvd.
Birmingham, AL 35294

© Dr. Ryoichi Kawai, 2020 All Rights Reserved. No part of this website or any of its contents may be reproduced, copied, modified or adapted, without the prior written consent of the author, unless otherwise indicated for stand-alone materials.