PHYSICS 201: MATHEMATICAL METHODS FOR SCIENTISTS, SPRING 2006

Tim Gfroerer, Davidson College

 

Email: tigfroerer@davidson.edu

Class Discussion: MWF 11:30am – 12:20pm, Dana 153

Office: Dana 155, Lab: Dana 049

Text: Mathematical Methods in the Physical Sciences,

Phone: x2319

         2nd edition, Mary L. Boas

Office Hours:  Monday through Thursday, 2:00 – 4:00 pm (and more generally, most other normal working hours when I'm not preparing for or teaching a class).  Questions naturally arise in the process of learning and doing physics. In fact, the really good questions are what keep physicists going. I expect you to have lots of questions and I hope that you will come by my office talk to me about them.

 

Course webpage:  http://webphysics.davidson.edu/faculty/thg/201-2006.htm

I will post announcements, class demonstrations, assignments, and solutions here.

 

Objectives:  This course is designed to introduce a broad range of mathematical techniques that are used to solve scientific problems.  Clearly, the course cannot achieve the depth of individual math courses on each subject and we will not be as detailed in our proofs.  Our purpose is to give you some experience with a variety of important mathematical techniques so that you will be familiar with them when you see them again.  We will emphasize how the techniques can be used to solve various problems in the sciences. I will assume that you have had two semesters of calculus, but I will survey the mathematical and scientific background of the class to set an appropriate level and pace for the course.  We will focus on the following topics:

 

Power series Chapter 1
Complex analysis Chapter 2
Linear algebra Chapters 3 and 10
Vector calculus Chapter 6
Fourier analysis Chapters 7 and 15
Differential equations Chapter 8

 

Class Discussion:  Attendance at and participation in class discussions are critical for learning new math.  Reading the relevant sections before class will definitely facilitate this part of the learning process.  Please ask questions!  The college’s 25% rule on attendance will be in effect.

 

Homework:  A course like this has one vital purpose: enabling you to solve new kinds of problems.  Building problem solving skills take  lots of practice.   To this end, I will assign a substantial amount of homework.  I encourage you to work together on the homework sets, but you must participate in the process of obtaining the solution to each problem.  When working with a partner, keep in mind that reviews and the final will test your individual problem-solving ability.  Do not consult solution sets or another student’s work from any previous class.  Always show your arguments, realizing that clarity and neatness count.  Homework will be collected for grading at the beginning of class on the dates designated and late homework will not be accepted.

 

Seminar Attendance: Seminars broaden your scientific perspective and show you how physics is being used in the world beyond Davidson. Attendance at all physics seminars is strongly encouraged – extra credit will be given.

 

Computers: As you know, programs like Mathematica can simplify traditional mathematical operations like series expansion, integration, and matrix analysis.  Indeed, these applications can use numerical methods to solve problems that do not have an analytical solution. The programs (and spreadsheet applications like Excel) include graphical tools that can be used to calculate and plot functions of interest so that we can visualize the behavior of our solutions.  We will demonstrate and use some of these features in this course and you may use these programs to solve or check homework problems whenever you think they might help.  Be sure to clearly document your usage of these programs.  Please be aware that you cannot use these programs on reviews.

 

Reviews and Final Exam: We will have 3 closed-book take-home reviews on the following weeks: 2/13, 3/27, and 4/24.  The comprehensive final exam will be take-home and open-book, to be completed during the self-scheduled exam period.

 

Grading:

 

 Homework 30%
 3 Reviews 45%
 Final Exam 25%