Physics 301/Math 355:
Mathematical Methods of Physics

This is the course website for Physics 301/Math 355: Mathematical Methods of Physics. Please visit this site frequently; all homework assignments will be posted here, as well as detailed solutions to all homeworks. These solutions will be made available for public viewing as soon as homework is collected in at the beginning of class. This site will also post a series of classnotes to elucidate issues raised in class, provide greater detail about certain topics, provide tutoring in the use of Mathematica, and also to show how the material done in class can be extended.

You can always view here.

Homework Assignments & Solutions

• Homework #1 | HW #1 Solutions| Due 21 Jan. 2009
• Homework #2 | HW #2 Solutions| Due 28 Jan. 2009
• Homework #3 | HW #3 Solutions| Due 4 Feb. 2009
• Homework #4 | HW #4 Solutions| Due 11 Feb. 2009
• Homework #5 | HW #5 Solutions| Due 18 Feb. 2009
• Homework #6 | HW #6 Solutions| Due 27 Feb. 2009
• Homework #7 | HW #7 Solutions| Due 11 Mar. 2009
• Homework #8 | HW #8 Solutions| Due 18 Mar. 2009
Homework #9 | HW #9 Solutions| Due 27 Mar. 2009
Do only part a) for Boas questions 11-14 (questions 2-5 on the HW).
• Homework #10 | HW #10 Solutions| Due 3 Apr. 2009
• Homework #11 | HW #11 Solutions| Due 8 Apr. 2009
• Homework #12 | HW #12 Solutions| Due 24 Apr. 2009

Class Notes

• Jan 12: Getting Started With Mathematica


• Jan 12: An Introduction to Einstein Summation Notation


• Jan. 26:Using Vectors in Mathematica


• Jan. 28:The Kronecker Delta and More About Vector Identities


• Jan. 30:Read here for the solutions to today's quiz plus more Mathematica goodies.


• Jan. 30:You can read and study many examples of proving vector identities utilizing Einstein Summation Notation.


• Feb. 5:To see the value of using Einstein summation notation, see what it takes to prove the BAC-CAB Rule using term by term component expansion instead of Einstein Summation Notation.


• Feb. 10 As we begin our study of other orthogonal coordinate systems, you can read how to calculate scale factors and basis vectors in non-Cartesian coordinate systems. Note: I added several sections to this document on Th. Feb. 12, so please make sure you re-read this if you have not seen this most recent update.


• Feb. 13:I have posted solutions to this morning's quiz.


• Feb. 15: Read more details about finding scalar potentials and how to derive the scalar potential that generates a conservative vector field.


• Feb. 17:The first hour exam is Monday. Information regarding the exam is posted.


• Feb. 17:You can review a recent midterm with its solutions here.
  
• Feb. 17:Please review my current draft of the list of useful equations and results for the test Monday. Let me know Friday in class if there should be additional items.


• Feb 19:I have written and am posting a Mathematica code for finding scale factors that yields clear results in an immediately usable form.


• Feb. 23:You can review the first hour exam and its solutions.


• Feb. 27:Please review these notes on series expansions before class a week from Monday. Have a wonderful break. See you in March.


• March 9: If you would like a refresher on various methods of integration, please read this review of integration technique.


• March 16:: In class, several students asked about typing special symbols in Mathematica; this link will give you a quick over of using special symbols and characters in Mathematica.


• March16:: A number of you are starting to do more serious programming in Mathematica. You can see how to define and use functions in Mathematica.


• March 18:: As you have seen, the integrals encountered in Fourier analsysis can often be solved by recalling the properties of odd and even functions.


• March 20:: You can learn more about using Graphics in Mathematica at this link.
  
• March 20:: I have posted solutions to this morning's quiz so you can review how to determine more complicated expressions for the Fourier coefficients.


• March 26:I have posted a file that will help you with some of the details of series solutions to differential equations.


• April 8:Read more about Legendre polynomials, generating functions and multipole expansions by reading this document.


• April 12:The second hour exam will be given this Friday, 17 April. It will cover Fourier Series, series solutions to differential equations, and anything we covered re Legendre Polynomials through class last Wednesday. In particular, you should be able to be able to solve problems that arise from the material in Boas, Ch 7, Secs. 1-9 and Chapter 12, Secs 1 and 2. If I ask you to solve for Fourier coefficients, I will provide you with the values of any indefinite integrals you might need, but you will need to evaluate those integrals at the appropriate limits. Additionally, I will ask Mathematica based questions; these might include asking you to correct errors in Mathematica statements, write Mathematica statements to perform certain calculations, or write short Mathematica programs. I will expect that you know (specifically but not exclusively) how to use the Plot, Manipulate, and Sum functions as the apply to the mathematics we have studied.


• A list of useful equations and identities is now viewable.


• April 18:I have graded the second hour exams; class average was 76.25; 30% of the class earned grades 90% or higher and half the class earned grades 80% or higher. You can review solutions to the exam.


• April 23:This write-up shows how to solve Laplace's equation in spherical coordinates.


• April 24:Read solutions to the final quiz.


• April 27: Please read notes for the final exam including a description of my office hours for the week.


• May 1:A list of formulae for the final exam are posted for review.