The URL of this page is http://www.physics.smu.edu/scalise/P4321sp22/
Physics 4321 / 7305 - Methods of Theoretical Physics
Course Information - Spring 2022
"The physicist in preparing for his work needs three things: mathematics,
mathematics and mathematics." -- Wilhelm Roentgen, The Mathematical Gazette,
Volume 22, Number 252, December 1938, 1225
- Coronavirus Impact: Masks are required in this course. This masking policy is subject to change
during the semester, and any changes will be posted clearly here and in Canvas announcements.
You should also be prepared to go fully online if the need should arise.
- Lecturer:
Professor Randall J. Scalise
- Meeting time and place: T,Th 11:00AM-12:20PM Anette Caldwell Simmons Hall 213
- Office hours: after lecture and by appointment.
- Contact:
- Prerequisites:
- 4321: Prerequisites or corequisites: MATH 3302 (formerly MATH 2339 prior to Fall 2017), MATH 3313 (formerly MATH 2343 prior to Fall 2017).
- 7305: Working knowledge of complex variables, Fourier transforms, and partial differential equations.
- Exam Dates: Open book, open notes, open Mathematica, closed internet.
- Midterm - Thursday 3 March 2022 in class online
- Final - Saturday 7 May 2022 11:30 AM - 2:30 PM online
- Old midterm exams 4321,7305.
- Practice final exam
- Syllabus
- Mathematica tutorial PostScript 4 pages,
537511 bytes; PDF 4 pages, 32563 bytes
- Grading:
- Homework - 60% (drop lowest)
- Midterm Examination - 20%
- Final Examination - 20%
A student who is absent from class without valid reason for two
consecutive weeks will be referred to the
CCC
Program and, if unresponsive, may be administratively dropped from the class by the instructor.
PHYS 4321 and PHYS 7305 share the same lectures, but the 7305 homework assignments and examinations
are more advanced than the 4321 assessments.
- Course Objectives: By the end of the course, undergraduate students (PHYS 4321) should be able to:
- Describe, explain, and compare sine, cosine, and exponential Fourier series and transforms
- Describe and explain generalized functions (distributions) and Green functions
- Apply techniques to solve linear homogenous and nonhomogeneous differential equations and interpret the solutions,
particularly the damped, driven harmonic oscillator and Laplace's equation
- Use complex variables, complex functions, and Cauchy's theorem; matrices, determinants, and linear algebra
- Practice the calculus of variations and construct the Euler-Lagrange equations
- Describe and explain first and second order differential operators in Cartesian, Cylindrical, and Spherical coordinate systems
- solve problems in all the areas above
- Course Objectives: By the end of the course, graduate students (PHYS7305) should be able to:
- Create and analyze sine, cosine, and exponential Fourier series and transforms
- Formulate generalized functions (distributions) and Green functions for a specific problem
- Construct solutions to linear differential equations, homogeneous and nonhomogeneous, particularly
the damped, driven harmonic oscillator and Laplace's equation using separation of variables
- Analyze complex variables, complex functions, and Cauchy's theorem; matrices, determinants, and linear algebra
- Formulate the calculus of variations and the Euler-Lagrange equations
- Construct and interpret first and second order differential operators in Cartesian,
Cylindrical, and Spherical coordinate systems
- solve problems in all the areas above
- Course Format: Class time will be used for lecturing, not for problem solving.
- Expectations: Students are expected to attend all lectures
and to be able to answer questions posed by the lecturer in class.
Students should not use lecture time to do anything other than
listen attentively and take notes. Homework assignments should be
started well in advance of the due date.
- Texts:
There is no course textbook, but any of the following may be useful.
They are in the library and you can find them used (any edition) at
abebooks.com
- Lecture slides
- Fourier Series, Fourier Transform: 01, 02, 03,
Peter Olver's notes. See also
- Generalized functions,Distributions: 04, 05
- Differential equations: 06, 07
- Numerical Approximations to Solutions of Differential Equations
- Green functions (PDF format), Green functions (1/2), Green functions (2/2),
Green function for heat equation, Green function example problem
- Nonlinear Simple Pendulum
- Curvilinear Coordinates: 08 [video audio only],
09 [video audio only].
See also Curvilinear coordinates,
Orthogonal coordinates,
Scale factors (h's).
- First-order Differential Operators:
Gradient:10, [video audio only];
Divergence, Curl:11, [video audio only];
- Second-order Differential Operators:
Laplacian, etc.: 12, [video audio only].
- Lecture notes
- 26Jan16. Mathematica notebook, PDF file.
- 28Jan16. See also
Aleph number,
Georg Cantor's diagonalization.
- 04Feb16. See also
Gaussian integrals.
- 09Feb16.
- 18Feb16. See also Green function example
Mathematica notebook, PDF.
- Guest lecture: Tuesday 26 March 2020, Professor Stephen Sekula on Monte Carlo methods
- 25Feb16. Second root to dD/dw=0; Green function homework solution.
- 01Mar16. Practice midterm solutions.
- 22Mar16. See also Visualizing Divergence and Curl.
- 24Mar16. See also
Mixed partial derivatives.
- 29Mar16. See also
Separation of variables
[video audio only].
- 31Mar16. See also
Particle in a two-dimensional box.
- 05Apr16. See also Separation of variables 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8.
- 07Apr16.
See also Variational Calculus, 1/2, 2/2
- Evolutionary computation (Genetic Algorithms)
- 12Apr16. Complex functions of a complex variable
1/2. See also
- The Octonions by John C. Baez
- 14Apr16. Complex functions of a complex variable 2/2. See also
Cauchy's integral theorem.
- 19Apr16. See also
Residue.
- Linear Algebra, Matrix Operations:
1/3, 2/3, 3/3. See also
LU Decomposition.
- Group Theory:
1/2,2/2
See also
- Dirac Belt Trick
- Knot Theory Rope Trick
- Paperclip trick
- Pages 1 - 10 (PDF format)
- Pages 11 - 20 (PDF format)
- Pages 21 - 29 (PDF format)
- Green functions (PDF format), Green functions (1/2), Green functions (2/2)
- Nonlinear Simple Pendulum
- Pages 30 - 40 (PDF format)
- Pages 41 - 50 (PDF format)
- Pages 51 - 55 (PDF format)
- Pages 56 - 66 (PDF format)
Separation of variables 1/6, 2/6, 3/6, 4/6, 5/6, 6/6.
- Vibrating Rectangular Membrane - solutions to the wave equation in 2 dimensions
- 2D Vibrations of a Membrane
- Pages 67 - 77 (PDF format)
- Pages 78 - 88 (PDF format)
- Variational Calculus, 1/2, 2/2,
Feynman Lectures: Principle of Least Action
- Complex Numbers;
Complex Variables and Functions;
Conformal Mapping;
Contour Integration and Residues; Laurent Expansion; Laurent Series Examples; Residue Examples;
Lecture slides: 1/2, 2/2
- Group Theory:
1/2,2/2
- 26Apr16. See also
- Introduction to the general theory of relativity,
- General relativity,
- Is Middle Earth flat?,
- Curved Space - Feynman lecture II-42
audio,
- Relativistic rocket I,
- Relativistic rocket II,
- Tests of general relativity,
- What Do You Mean, The Universe Is Flat? (Part I),
- What Do You Mean, the Universe Is Flat? Part II: In Which We Actually Answer the Question,
- metric tensor and Christoffel symbols for a sphere,
- Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe,
- The Universe Never Expands Faster Than the Speed of Light by Sean Carroll,
- Covariance and contravariance of vectors.
- Breit-Wigner links
- Homework Due dates are strictly enforced. 50% if late; 0%
once the solutions are posted. You may work together, but the work
that you turn in should be unique. Identical work will receive a grade
that is divided among all parties. It is possible to find answers to
some homework problems on the internet; do not do this. The point,
after all, is not to fool me into thinking that you have learned
physics, but rather actually to learn some physics.
- homework #1 (PDF format) - due Friday 28 January 2022 at 11:59:59pm
- homework #2 (PDF format) - due Friday 4 February 2022 at 11:59:59pm
(Mathematica example notebook PDF format, Fourier.nb)
- homework #3 (PDF format) - due Friday 11 February 2022 at 11:59:59pm
- homework #4 (PDF format) - due Friday 18 February 2022 at 11:59:59pm
- homework #5 (PDF format) - due Friday 25 February 2022 at 11:59:59pm
- No homework due Friday 4 March 2022 because of the midterm exam on 3 March
- homework #6 (PDF format) - due Friday 11 March 2022 at 11:59:59pm
- No homework due Friday 18 March 2022 because of Spring Break
- homework #7 (PDF format) - due Friday 25 March 2022 at 11:59:59pm
- homework #8 (PDF format) - due Friday 1 April 2022 at 11:59:59pm
- homework #9 (PDF format) - due Friday 8 April 2022 at 11:59:59pm
pseudocode for Monte Carlo assignment #11
- No homework due Friday 15 April 2022 because of the holiday
- homework #10 (PDF format) - due Friday 22 April 2022 at 11:59:59pm
- homework #11 (PDF format) - due Friday 29 April 2022 at 11:59:59pm (counts as two homeworks)
You may find the discussion of Olbers' Paradox
in chapter 2 of Barbara Ryden's Introduction to Cosmology useful.
Be careful to use "flat" variables.
- Homework Solutions
- Disability Accommodations, Religious and Excused Absences
- Official University Calendar
- Links:
- SMU Required Syllabus Statements
Back to Professor Scalise's Home Page
