## Math 556: Methods of Mathematical Physics, I

**Instructor: **Richard Laugesen
**e-mail: **laugesen@illinois.edu
**Homepage: **
`www.math.uiuc.edu/~laugesen`

**Office:** 376 Altgeld Hall
**Phone:** 333-1329
**Class meets:** MWF 2pm, in 241 Altgeld Hall
**Office Hours:** Tuesday 5-6pm in office,
Wednesday 4:30-5:30pm in 243 Altgeld Hall,
Friday 11:30am-12:30pm in office,
or by appointment at other times

### Text

*Principles of Applied Mathematics: Transformation and Approximation*
Revised Updated edition (2000), by J. P. Keener.
We cover Chapters 1-5, and 7.

The course aims to show what advanced
mathematics can tell us about fundamental problems in physics and engineering
### Course outline

Review of finite dimensional linear algebra, including minimax principle for
eigenvalues

Metric spaces and orthogonal polynomial bases

Integral equations/compact operators, and their spectral theory

Differential/unbounded operators, and Green functions and eigenfunctions

Calculus of variations

Transform and spectral theory, including Fourier, Laplace and Z transforms
### Prerequisites

Advanced calculus and ordinary differential equations (undergraduate).
**Homework: **
7 or 8 overall. Extensions are given by prior arrangement only.
Your lowest homework score will be dropped.

I encourage students to work together on the homework.
But you must write up your own solutions in your own words, so that you
really learn the material before the tests. Please write on the first
page of your homework the names of all people with whom you discussed it
(this is an ethical matter: "give credit where credit is due").

**In-class Test:** Wednesday 5 October.

**Take-home Test:** Thursday 17 November - Friday 18 November.

**Final exam:** 1:30-4:30pm, Friday 16 December

You may not use books, notes, calculators or computers during the in-class
test or the final exam.

**Grading policy:**
There will be no
makeup tests except for medical reasons or family emergencies. Vacation
or leisure plans are never a valid excuse for missing a test or exam.

Your letter grade for the course will be based on your total
score out of 500 points:

Final exam: | 200 pts (40% of grade) |

Test 1: | 100 pts (20% of grade) |

Test 2: | 100 pts (20% of grade) |

Homework: | 100 pts (20% of grade) |

**How to Succeed:**
Always re-work your lecture notes before the next class, checking every
step, filling in missing details and keeping a running list of definitions.
Read the textbook as you re-work your notes. We cover only the most essential
points in class, and the text has helpful additional comments; reading them
will help you get the big picture. Before each class, ask me about the
points you didn't follow in the last class.

Go over your HW solutions the day you get them back.

If you have any inquiries or concerns,
please contact me by e-mail at
laugesen@illinois.edu.

- Richard Laugesen