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 the syllabus here.

Homework Assignments & Solutions

• Homework #1 | HW #1 Solutions| Due 25 Jan. 2012


• Homework #2 | HW #2 Solutions| Due 6 Feb. 2012


• Homework #3 | HW #3 Solutions| Due 13 Feb. 2012


• Homework #4 | HW #4 Solutions| Due 20 Feb. 2012


• Homework #5 | HW #5 Solutions| Due 2 March 2012


• Homework #6 | HW #6 Solutions| Due 12 March 2012


• Homework #7 | HW #7 Solutions| Due 23 March 2012


• Homework #8 | HW #8 Solutions| Due 30 March 2012


• Homework #9 (Question #5 is worth 20 points) | HW #9 Solutions| Due 4 April 2012


• Homework #10 |I have included a diagram for problem 5. | HW #10 Solutions| Due 16 April 2012


• Homework #11| HW #11 Solutions| Due 27 April 2012 (Optional)

Computer Project

• Computer project | Due 5 pm, 23 April 2012


• I will post a variety of write-ups purusant to the computer project. First, is a description of the physics and general outline of the program I wrote. Next, I post what I think is a very straightforward solution with full commentary. If the embedded commentary is distracting, there is a version with no comments. Finally, we talked in class about how the nature of the solution might change if the initial parameters were changed. I post a version with a smaller radius and greater angular velocity that has three solutions , the first of which is when the person is at approximately 340 degrees.

Class Notes

• Jan 18: Begin your study of Einstein Summation Notation here.


• Jan 18: Read more about summation notation including the epsilon-delta relationship.


• Jan 18: Before the first computer lab sessions next week, please read getting started with Mathematica.


• Jan 24: Going Further with Functions in Mathematica


• Jan 24: Basic Vector Operations in Mathematica


• Jan 24: Learn how to define and use functions in Mathematica.


• Jan 27: Read here for a fuller review of the gradient and also more examples of using Mathematica for vector analysis.


• Jan 31: To get a better sense of the utility of summation notation, review this derivation of BAC-CAB using term-by-term expansion.


• Feb. 9: This write-up will show you how to solve some fairly elaboratevector proofs via summation notation.


• Feb 1: You can read an introduction to the use of Mathematica in vector calculus.


• Feb 1: We begin our introduction to loops and control structures in Mathematica.


• Feb 6: We begin our study of conditional statements in Mathematica with this introduction to If statements in Mathematica.


• Feb 6: Learn how to define and use functions in Mathematica.


• Feb 8: Begin reading about how we treat various vector functions in Learn how to define and use orthogonal curvilinear coordinatesa.


• Feb 13: Review the properties of hyperbolic functions.


• Feb 13: We begin our study of discretization techniques in scientific programming.


• Feb 13: We continue the discussion of discretization techniques in solving equations .


• Feb 21: I have posted notes for the first hour exam.


• Feb 21: You can review last year's first hour exam with solutions.


• Feb 27: I have posted solutions to the first hour exam.


• Feb. 27: As we begin our study of Fourier series, read this review of series expansions.


• March 2:In your study of Fourier series, you will revisit many techniques of integration..


• March 2:Employing symmetry arguments can be a powerful way to evaluate integrals without having to do explicit calculation.


• March 19:Begin your study of Modules in Mathematica by reading this write up as well as the Mathematica Doc Center description.


• March 20:For lab next week read these notes on numerical solutions of differential equations using Euler's method.


• March 26:Read this short post to learn how to define and plotdiscontinuous functions in Mathematica.


• March 26:Please read this write-up as we begin our study of series solutions of differential equations.


• March 27:We will soon begin our study of Legendre polynomials and their use in physics.


• March 27:You can read up on the use of Legendre polynomials in Mathematica.


• March 31:Read an introduction to another method of numerical solutions, the Runge-Kutta technique for solving differential equations.


• March 31:Learn more about loop control structures.


• April 4:I have posted one of the homework solutions submitted for the last question on the last homework (#9). This is an excellent use of Mathematica's logical operators.


• April 13:I have posted notes for the second hour exam to be given on 20 April.


• April 16:The list ofequations and results for the second hour exam is posted.

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• April 16:Solutions to the second hour exam.


• April 23:Our final topic this year will be Laplace's equation in spherical coordinates.


• April 26:Please read notes for the final exam.