# Physics 116C (Fall 2017): Mathematical Methods in Physics III

## Course information

Instructor: Stefano Profumo
Office: ISB, Room 325
Phone Number: 831-459-3039
Office Hours: Mondays, 1PM or by appointment
E-mail: profumo AT ucsc.edu

Teaching Assistant: Logan Morrison
Office: ISB, Room 314
Phone Number: 831-459-4138
Office Hours: Wednesdays 1PM or by appointment
E-mail: loanmorr AT ucsc.edu

## Class Hours

Lectures: MWF, 10:40AM - 11:45AM, N. Sci Annex 101

Discussion Sections: Tuesday 12-1PM, Thimann 391, and Thursday 4-5PM, ISB 235

## Course description

• Fourier series and transforms
• Dirac-delta function
• Green's functions
• Series solutions of ordinary differential equations
• Legendre polynomials and functions
• Bessel functions
• Sets of orthogonal functions
• Partial differential equations

## Prerequisites

• Physics: 116A , 116B
• Mathematics: 23A, 23B

## Required Textbook

• Mathematical Methods in the Physical Sciences by Mary L. Boas

## Other Textbooks

• Mathematical Methods for Scientists and Engineers by Donald A. McQuarrie
• Essential Mathematical Methods for Physicists by George B. Arfken and Hans J. Weber

## Course Outline

Fourier series and transforms Boas, Chapter 7 1-6
Dirac-delta function Boas, Chapter 8.11 7-8
Green's functions Boas, Chapter 8.12 9-11
Series solutions of ordinary differential equations Boas, Chapter 12 12-14
Legendre polynomials and functions Boas, Chapter 12 15-17
Bessel functions Boas, Chapter 12 18-20
Sets of orthogonal functions Boas, Chapter 12 20-22
Partial differential equations Boas, Chapter 13 23-27
Review 28-29

Grades will be based on performance in the following three tasks: weekly homework, midterm, and final exam. The tasks and their relative weights in determining the students' overall course grades are given below:

 35% Weekly Homework (9 problem sets) 25% Midterm Exam (Friday November 3, lecture time) 40% Final Exam (Tuesday, December 12 8:00–11:00 AM)
In addition, up to 10% bonus will be given based upon participating in the "bonus problem" at the beginning of the weekly discussion sections.

### Weekly Homework

Weekly homework assignments will be posted on Canvas each Wednesday and are due at the beginning of class on the Wednesday of the following week, when solutions will also be posted. The homework problem sets are (effectively) not optional, and will consist of a few (typically 10) problems from Boas' textbook. 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. Late homeworks can be submitted to the grader, but will not contribute any points to the final grade. You have one ``late-homework pass''. The Grader will grade each homework, and is responsible for the given grade. Grades for each homework set will consist of 2 points (mostly correct), 1 point (less than 50% correct) or 0 points (no homework returned in time). Homework solutions will be typically made available on the course website the day after the homework due date.

### Midterm and Final

The midterm exam and the final exam will be held in the same classroom as the lectures. The midterm will be a 1 hour written exam in class (regular lecture time) on Friday November 3, on the material covered up to Friday October 27, while the final (Tuesday, December 12 8:00–11:00 AM) will be three hours long and cover the complete course material. Both the midterm and the final will be open-book (you can bring with you any book or notes). Laptop computers and cellular phones of any kind will not be allowed. One or more practice midterm and final will be handed out a week before the exams. You must take the final exam to pass the course.

 The minimal score not to fail the class is 60%. The final grade will follow the percent guideline below: 60% to 70%: C range 70% to 85%: B range 85% to 100%: A range

## Homework exercises

Homework Set number (PDF) Due Date Solutions
HW Set #1 phys116c_HW01.pdf Solutions to HW #1

## 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.