COURSE TIME:
Tuesdays and Thursdays 1:40 - 3:00 pm
COURSE LOCATION: Roessler 55
INSTRUCTOR:
Richard Scalettar
TEACHING ASSISTANT:
Anatoliy Dovbnya
TEACHING ASSISTANT:
Valentina Prilepina
GRADING:
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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)
Problem Sets
Exams
Grab Your Popcorn!
Course Objective:
The goal of this course is to familiarize you with the basic tools
of mathematical physics. I will mix traditional
exposition of textbook material with modern applications.
These will mostly be drawn from condensed matter physics, since
I am most familiar with the mathematical physics
which is useful for current research in that field.
As an example, when we discuss matrix diagonalization and eigenvalues,
we will see how this can be used to compute energy bands in solids,
and unusual features like flat bands, disorder localized modes,
the 'Dirac' spectrum of graphene, etc
of interest in current research.
1. Complex Numbers
Lecture Notes
2. Power Series; Taylor Expansion
Lecture Notes
3. Linear algebra (with applications to normal modes and quantum
mechanics)
Lecture Notes, Pt 1
Lecture Notes, Pt 2
Lecture Notes, Pt 3
Lecture Notes, Pt 4
Lecture Notes, Pt 5
Lecture Notes, Pt 6
Lecture Notes, Pt 7
Lecture Notes, Pt 8
4. Vector spaces
Lecture Notes, Pt 1
Lecture Notes, Pt 2
Lecture Notes, Pt 3
5. Fourier Series and Fourier Integrals
Lecture Notes, Pt 1
Lecture Notes, Pt 2
Lecture Notes, Pt 3
Life of Fourier (Lagrange and Laplace
unsatisfied...)
Lecture Notes, Pt 4
X. Vector Calculus
Lecture Notes
6. Legendre Series
7. Partial Differential Equations: Integrated into previous lecture
materials
Assignment 1
Solutions
Assignment 2
Solutions
Assignment 3
Solutions
Assignment 4
Solutions
Assignment 5
Solutions
Assignment 6
Solutions
Assignment 7
Solutions
Assignment 8
Solutions
Midterm Exam
Solutions
My movie of Gaussian wave packett hitting a barrier
Anatoliy's movie of wavepacket spreading in a box