Physics 116A (Winter 2008): Mathematical Methods in Physics I
Course information
Instructor: Stefano Profumo
Office: ISB, Room 325
Phone Number: 831-459-3039
Office Hours: Tuesdays and Thursdays 2:30 - 3:30 PM (or by app.)
E-mail: profumo AT scipp.ucsc.edu
Teaching Assistant: John Kehayias
Office: ISB, Room 262
Phone Number: 831-459-5010
Office Hours: Wednesdays 4:00 - 5:00 PM
E-mail: kehayias AT physics.ucsc.edu
Homework Grader: Ben Nelson
E-mail: benelson AT ucsc.edu
Click here to download the syllabus in PDF format
Class Hours
Lectures: Tuesdays and Thursdays, 12:00 PM - 1:45 PM, Phys. Sc. 114
Discussion Section: Wednesday evening, 5:00 PM - 6:30 PM, ISB 231 
Starting Wednesday January 16 Discussion Section will be in ISB 235
Course description
Infinite series including power series, asymptotic expansions, special functions defined by an integral, complex numbers and some functions of a complex variable, topics in linear algebra including matrices and determinants, solving systems of linear equations, eigenvalue problems and matrix diagonalization, introduction to tensors.
Prerequisites
- Physics: 5A/L, 5B/M, 5C/N
- Mathematics: 23A, 23B
Required Textbook
- Mathematical Methods in the Physical Sciences by Mary L. Boas
Other Introductory Textbooks
- Mathematical Methods for Scientists and Engineers by Donald A. McQuarrie
- A Mathematical Methods for Physicists by George B. Arfken and Hans J. Weber
- Advanced Engineering Mathematics by Erwin Kreyszig
Course Outline
| Topic |
Reading |
Period |
| Infinite Series, Power Series |
Boas, Chapter 1 |
Jan 8 - Jan 15 |
| Complex Numbers |
Boas, Chapter 2 |
Jan 17 - Jan 24 |
| Linear Algebra and Vector Spaces |
Boas, Chapter 3 |
Jan 29 - Feb 26 |
| Tensor Analysis |
Boas, Chapter 10 |
Feb 28 - Mar 4 |
| Special Functions |
Boas, Chapter 11 |
Mar 6 - Mar 11 |
| Review |
|
Mar 13 |
Course Grading and Requirements
Student evaluations will be based on their performance in the following four tasks. The tasks and their relative weights in determining the students' overall course grades are given below:
- 40% Weekly Homework (9 problem sets)
- 15% First Midterm Exam (Tuesday, January 29, 2008, 12:00 PM)
- 15% Second Midterm Exam (Tuesday, February 26, 2008, 12:00 PM)
- 30% Final Exam (Wednesday, March 19, 8:00 - 11:00 AM)
Weekly homework assignments will be handed out each Thursday and are due at
the beginning of class on the Thursday of the following week. The homework problem
sets are not optional. You are encouraged to discuss the class material and homework
problems with your classmates and to work in groups, but all submitted problems
should represent your own work and understanding. In order that homework can be
graded effciently and returned quickly, there will be a 50% penalty for late homework.
This penalty may be waived in special circumstances if you see the instructor before the original
due date. Homework solutions will be made available each Monday (following the
Thursday due date); no late homeworks will be accepted after that.
The two midterm exams and final exams will be held in the same classroom as
the lectures. Each midterm will be a one hour exams, and will be followed by a
shortened lecture of 45 minutes. The final exam will be three hours long and cover
the complete course material. You must take the final exam to pass the course.
Homework exercises
The solutions are password protected, please email the instructor if you don't know the username and password.
FOR THOSE USING THE 2ND EDITION: CLICK HERE TO DOWNLOAD THE CORRELATION LIST OF 2ND AND 3RD EDITION PROBLEM NUMBERS FOR PROBLEMS WHICH APPEAR IN BOTH EDITIONS (PASSWORD PROTECTED)
Galileo's Corner
La filosofia e' scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli occhi (io dico l'universo), ma non si puo' intendere se prima non s'impara a intender la lingua, e conoscer i caratteri, ne' quali e' scritto. Egli e' scritto in lingua matematica, e i caratteri son triangoli, cerchi, ed altre figure geometriche, senza i quali mezzi e' impossibile a intenderne umanamente parola; senza questi e' un aggirarsi vanamente per un oscuro laberinto. (Galileo Galilei, Il Saggiatore, 1623)
Philosophy (Knowledge) is written in that great book which ever lies before our eyes (I call it the Universe), but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word; without knowledge of those, it's a useless wandering in a dark labyrinth.
Feynman's Corner
Physics is like sex: sure, it can give practical results, but that's not why we do it
Last reviewed 03/13/2008 by Stefano Profumo.
