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

• 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/

Here are solutions to Exam One.

Course Description:

Mathematica

Expected Learning Outcomes:

• 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:

• Tutorial One

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

• 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:

Disabilities:

Some Examples