COURSE TIME:
Tuesdays and Thursdays 1:40  3:00 pm
COURSE LOCATION: Roessler 55
INSTRUCTOR:
Richard Scalettar
TEACHING ASSISTANT:
Alexis Giguere
TEACHING ASSISTANT:
ChihFan Chen
GRADING:


TEXT:
None required. See below.
Homework assignments (due weekly on Fridays) will also contain some numerical work. If the coding looks like it will be too heavy, I will make those problems optional, for extra credit. I plan to delay getting too deep into numerical work for a few weeks, so that I can take advantage of material you will learn in Physics 102.
I have not selected a specific textbook. Most standard books on mathematical physics will have discussions of the material I present. I personally like "Mathematical Methods in the Physical Sciences", by Mary Boas, quite a bit. You will probably find a lot of useful initial material for topics we will cover in your second year calculus books, although we will likely go a good deal further, and of course emphasize the physics applications.
Course Outline (Tentative)
1. Complex Numbers
Lecture Notes
1P. Functions of a Complex variable
Lecture Notes, Pt 1
Lecture Notes, Pt 2
Lecture Notes, Pt 3
Lecture Notes, Pt 4
* Nobel Prize 2016 for Topological Materials!
Macroscopic quantization of conductance
2. Power Series; Taylor Expansion
Lecture Notes
3. Linear algebra (with applications to normal modes and quantum
mechanics)
Lecture Notes, Pt 1 (basic matrix
operations, special matrix types)
Lecture Notes, Pt 2 (more on special
matrix types, matrices in classical mechanics
Lecture Notes, Pt 3 (more on matrices in
classical mechanics normal modes)
Lecture Notes, Pt 4 (more on matrices in
classical mechanics normal modes)
Lecture Notes, Pt 5 (more on matrices in
classical mechanics normal modes; projection matrices)
Lecture Notes, Pt 6 (triatomic molecule)
Lecture Notes, Pt 7 (vectors vs
components; operators vs matrices)
Lecture Notes, Pt 8 (energy bands in
solids)
Lecture Notes, Pt 9 (eigenvector
review)
Lecture Notes, Pt 10 (matrices in quantum
mechanics)
4. Vector spaces
Lecture Notes, Pt 1 (intro)
Lecture Notes, Pt 2 (example: the space
of differentiable functions; more theory)
Lecture Notes, Pt 3 (quantum mechanical
time evolution)
5. Fourier Series and Fourier Integrals
Lecture Notes, Pt 1 (general
theory)
Lecture Notes, Pt 2 (three applications:
qm of particle in box, wave equation, LRC circuit)
Lecture Notes, Pt 3 (application 4:
Laplace's Eqn; comments on numerics)
Life of Fourier (Lagrange and Laplace
unsatisfied...)
Lecture Notes, Pt 4 (Fourier
integrals; wave functions in position and momentum space; diffusion
equation)
X. Vector Calculus
Lecture Notes
6. Legendre Series
7. Partial Differential Equations: Integrated into previous lecture
materials
Problem Sets
Assignment 1
Solutions
Assignment 2
Solutions
Assignment 3
Solutions
Assignment 4
Solutions
Assignment 5
Solutions
Midterm Exam and Solutions
Assignment 6
Solutions
Assignment 7A
Assignment 7B
Assignment 7C
Solutions
Sample Exams
Fall 2015 Midterm Exam
Solutions
Fall 2015 Final Exam
Solutions
Grab Your Popcorn!
My movie of Gaussian wave packett hitting a barrier
Anatoliy's movie of wavepacket spreading in a box