MATH 301, 601 Mathematical Methods for the Physical Sciences
PHYSICS 301 Theoretical Physics, PHYSICS 605 Mathematical Physics
Rob Thompson Hunter College Fall 2023
Monday/Wednesday 4:00-5:15 Room: HW 406
e-mail:
robert.thompson@hunter.cuny.edu
Office: HE 902 Hours: M 2:30-4:00pm, W 1:30-3:30, and by appointment.
The final Exam is on Wednesday December 20, 3:00-5:00pm.
The exam is comprehensive, meaning it will cover the following sections.
Note that there is not enough time (two hours) to include problems from every one of these topics on the exam. Nevertheless, you
should review them all.
The exam will be closed book, but you can (and should prepare) a sheet with formulas. You can use two (2) sides of an 8.5x11 paper.
- 2.1 Periodic Functions
- 2.2-2.3 Fourier Series
- 2.4 Half range expansions
- 2.5 Mean Square approximation and Parseval's Identity
- 2.9 Uniform Convergence and Fourier Series
- 3.3 One dimensional Wave equation
- 3.5 One dimensional Heat Equation
- 3.7 Two dimensional Heat and Wave equations
- 3.8 Laplace's equation on rectangular coordinates
- 4.1,4.2,4.3 Wave equation in polar coordinates on a disk
- 4.4 Laplace's equation in polar coordinates on a disk
- 4.7, 4.8 Bessel functions
The second exam will be Wednesay, December 6..
Here are the Solutions to Exam Two.
Exam covered the following sections:
- 3.7 Two dimensional Heat and Wave equations
- 3.8 Laplace's equation on rectangular coordinates
- 4.1,4.2,4.3 Wave equation in polar coordinates on a disk
- 4.4 Laplace's equation in polar coordinates on a disk
- 4.7, 4.8 Bessel functions
Formula Sheet
The exam will be in class, 1hour,15min. It will be closed book,however you are allowed to use a formula sheet.
The formula sheet can be one side of an 8.5x11 inch paper, prepared by you ahead of time.
Here are a few additionl problems to work on to prepare for the exam.
- 3.7/4,5,13
- 3.8/6
- 4.3/2
- 4.4/10
- 4.8/4,6,9,13,17
The first exam was on Monday, October 16. The exam covered the following sections:
- 2.1 Periodic Functions
- 2.2-2.3 Fourier Series
- 2.4 Half range expansions
- 2.5 Mean Square approximation and Parseval's Identity
- 2.9 Uniform Convergence and Fourier Series
- 3.3 One dimensional Wave equation
- 3.5 One dimensional Heat Equation
Here are some additional problems you can do for practice:
- 2.9/9,10,14,18,29
- 3.3/4,7,14
- 3.5/
Course Description:
This course is an introduction to some topics in Mathematical Physics,
specifically Fourier Series and Partial Differential Equations. PDEs
have applications in numerous areas of science and engineering,
including Physics, Chemistry, Biology, Economics, Mathematical
Finance, and many others, as well as being of intrinsic mathematical
interest. This course will provide the students with the techniques necessary to set up and solve problems
in PDEs, with an emphasis on the heat equation, the wave equation, Laplace's equation, Poisson's equation, and Schrodinger's equation.
Mathematica
We will be using Mathematica in this course, mostly to help with visualization.
The College has a site license, you can obtian the software from ICIT. For math majors, the course satisfies the symbolic compution proficiency
requirement.
Expected Learning Outcomes:
Students will be able to:
- Model certain basic physical
situations such as the diffusion of heat in a material, the vibration
of a string, or a potential field, by a means of a PDE together with
initial-boundary value conditions.
- Compute Fourier series and evaluate their convergence properties.
- Solve initial-boundary value problems using various techniques.
Basic Information About the Course:
- Prerequisites: MATH 254 or any equivalent undergraduate course in ordinary differential equations.
- Required Textbook: Partial Differential Equations with
Fourier Series and Boundary Value Problems, Third Edition, by
Nakhle
Asmar. You can buy it at the campus bookstore
or directly from Dover publications or anywhere else.
- Homework: Regular homework assignments to be handed in.
- Exams: There will be two midterm exams and a comprehensive
final exam. The first exam will be approximately a third of the way
through the course, the second exam will be approximately three
fourths of the way. The final exam will be after the last class
meeting, on the date scheduled by Hunter College for this particular
section.
- Grading: Homework will count for 20% of your course
grade. The midterm exams will be worth 25% each and the final exam
will count for 30% of your course grade.
If you stop attending the course and do not withdraw, you will
receive a grade of WU.
You may elect to take the course on a credit/no credit basis if you
are eligible, but this is subject to the College's rules, which means
you that you will not be eligible for credit/no credit grading unless
you have attended most class periods, taken all the exams, including
the Final Exam, and completed most of the homework.
Here are some Mathematica tutorials:
Homework Assigments
- Assignment One (Due Wednesday 9/6) :
1.1/5,6,8
1.2/3,4,5
3.1/1-6,7cef,9,11
- Assignment Two (Due 9/20):
2.1/7,8
2.2/5ab,7ab,10ab,13ab,18
2.3/3,4*,6*,17*,25,26,27
2.4/3*,6,9*
2.5/1,2*,7,8
- Assignment Three (Due Wednesday October 13):
3.3/2,5,8*,12,13*
3.5/3,5*,6*,9*,12*,13
3.6/5*,15
- Assignment Four (Due Friday October 20):
2.9/9*,10,14*,18*
- Assignment Five (Due Monday November 20):
3.7/2,3,6*,11*,14
3.8/2,4*,5,11*
- Assignment Five B (Due date not set yet):
3.9/1,4*,5*,12,20
- Assignment Six (Due Wednesday November 29):
4.1/1,5
4.4/1,4,11
4.7/5,10,17,31,33,34
- Assignment Seven (Due Monday December 4):
4.2/1,2,5
4.3/1,4,5
4.8/3,7,8,19,36
Mathematica Homework Assigments
- Mathematica Assignemnt One (Due Sunday, October 15):
Instructions: Solve the given boundary value problem
in terms of the coefficients, either by using the known solution from
the text, or as in #15, coming up with the solution using the methods we've
developed. Then compute the coefficients using Mathematica. Then use Mathematica to
plot the solution, following any instructions given in the problem.
2.3/7,9
3.3/9,15
3.5/7
Topics Covered
We will cover pretty much everything in Chapters Two and Three, and selected topics from Chapters Four, Five and Eleven.
- Chapter Two: Fourier Series
- Chapter Three: PDE's in Rectangular Coordinates
- Chapater Four: PDE's in Polar and Cylindrical Coordinates
- Chapter Five: PDEs in Spherical Coordinates
- Chapter Eleven: Schrodinger's equation
Academic Integrity:
Hunter College regards acts of academic dishonesty (e.g.,
plagiarism, cheating on examinations, obtaining unfair advantage,
and falsification of records and official documents) as serious
offenses against the values of intellectual honesty. The college is
committed to enforcing the CUNY Policy on Academic Integrity and will
pursue cases of academic dishonesty according to the Hunter College
Academic Integrity Procedures.
Disabilities:
If you have a disability that
you believe requires special accommodations: In compliance with the
American Disability Act of 1990 (ADA) and with Section 504 of the
Rehabilitation Act of 1973, Hunter College is committed to ensuring
educational parity and accommodations for all students with documented
disabilities and/or medical conditions. It is recommended that all
students with documented disabilities (Emotional, Medical, Physical
and/ or Learning) consult the Office of AccessABILITY located in Room
E1214B to secure necessary academic accommodations. For further
information and assistance please call (212- 772- 4857)/TTY (212- 650-
3230).
Some Examples
Here is a picture of some
fundamental modes of vibration of string.