Physics 518
Mathematical Physics II

Winter 2007
MWF 3:00 - 3:50
C254 ESC

Instructor:   David Neilsen
david.neilsen@byu.edu

CONTACT INFORMATION
Office: N147 ESC
Office Hours: MWF 1:00--2:00 PM
Telephone: 422-6078
Email: david.neilsen@byu.edu
Grader:Bailey Hsu

INTRODUCTION
The Physics 517-518 series in mathematical physics gives an introduction to the mathematics required in the graduate core curriculum, as well as the mathematics you will use in your research. We will cover many topics familiar from your undergraduate education, but (hopefully!) with greater sophistication. This semester we will cover many topics of interest in solving differential equations:
  • Fourier Series;
  • Infinite-dimensional vector spaces;
  • Classical polynomials;
  • Ordinary differential equations;
  • Partial differential equations
  • Transform methods for differential equations;
  • Green functions; and
  • Perturbation theory
We will discuss the mathematical principles for each topic in class, but we will not be especially rigorous. Students are expected to develop practical problem solving skills in addition to an understanding of the underlying theory. Course homework assignments and exams will focus on the practical application of theory to solving problems. A student's mastery of these skills will be determined by performance on all course assignments and exams.

REQUIRED TEXTS
  • Mathematics for Physicists, by Dennery and Krzywicki
  • Mathematical Methods for Physicists by Arfken and Weber
We will use both Arfken and Weber and Dennery and Krzywicki in this class. Dennery and Krzywicki is written from a mathematical point of view, although the book's topics and style were chosen for physicists. Arfken and Weber is a classic text that is comprehensive in scope, and has many worked examples and homework problems.

SUPPLEMENTARY TEXTS
These books are not required for this class, but they are classics in the discipline. You can profitably consult these books to supplement the material the course material. Copies are available in the HBLL.
  • Mathematical Methods of Physics, by Matthews and Walker
  • Methods of Theoretical Physics, by Morse and Feshbach
  • Advanced Mathematical Methods for Scientists and Engineers, by Bender and Orszag
  • Geometrical methods of mathematical physics, by Bernard Schutz

SCHEDULE
A tentative course schedule lists reading assignments, lecture topics, homework due dates, and exam dates. The schedule is available on the course web page.

EVALUATION
Grades will be calculated based on class participation (including reading quiz scores), homework, a mid-term exam and a final exam. The relative weights for each category are:

Class Participation 10%
Homework 30%
Midterm 30%
Final Exam 30%

READING
Mathematical physics can be a challenging course. Please come to class having read the sections of the text scheduled for discussion, and be prepared with your questions. This will allow for the most effective use of lecture time.

To encourage reading before class, I will sometimes give short quizzes at the beginning of the class. Quizzes will cover material from the reading assignment and/or the previous lecture. Quiz scores will be included in the "Class participation" portion of your grade. The four lowest quiz scores will be dropped, and no make-up quizzes will be given.

HOMEWORK
Working problems is essential for understanding mathematical physics. Homework will usually be assigned every week, and will be collected at the beginning of class on the due date. Late homework will be accepted for reduced credit for up to one week after the original deadline. Homework received by the next class period after the original deadline will be penalized 20%, and homework received during the remaining week will be penalized 50%.

It is your responsibility to ensure that your homework is legible, logically organized, and can be understood by a reasonable person. Therefore, you are required to explain the logic of your homework solutions in complete English sentences. This is not an onerous task. I am not looking for paragraphs that repeat information from the text. ("Both potential and kinetic energy can be defined. Energy is conserved. Energy makes me happy.") Rather, I am looking for evidence that you understand the concepts relevant for the problem and have a logical plan to find the solution. English sentences should be the signposts that guide the reader through the solution.

COLLABORATION
I strongly encourage you to work together on homework assignments. In talking through problems, you will find that will understand them much more thoroughly. This process should be beneficial for everyone involved. However, the written solutions that you turn in must represent your own work.

EXAMS
There will be both a mid-term and a final exam for this course. There will be no make-up exams.

GRADE APPEALS
Errors are occasionally made in grading homework and exams. Appeals for grade changes should be submitted to me in writing. Appeals should be submitted in a timely manner, usually within two weeks after the assignment has been returned. After the last day of class I will only consider appeals relating to the final exam.
HELP
Feel free to visit with me during my office hours (MWF 1:00--2:00 PM) or at other times by arrangement. I will try to accommodate student questions any time I am in my office. I strongly encourage you to work together and collaborate on the assignments. However, the work that you turn in must be your own.

HARASSMENT
Harassment of any kind is inappropriate at BYU. Specifically, BYU's policy against sexual harassment extends not only to employees of the university but to students as well. If you encounter sexual harassment, gender-based discrimination, or other inappropriate behavior, please talk to your professor, contact the Equal Employment Office at 422-5895 or 367-5689, or contact the Honor Code Office at 422-2847.

STUDENTS WITH DISABILITIES
BYU is committed to providing reasonable accommodation to qualified persons with disabilities. If you have any disability that may adversely affect your success in this course, please contact the University Accessibility Center at 422-2767. Services deemed appropriate will be coordinated with the student and instructor by that office.

CHILDREN IN THE CLASSROOM
The serious study of the physical and mathematical sciences requires uninterrupted concentration and focus in the classroom. Having small children in class is often a distraction that degrades the educational experience for the entire class. Please make other arrangements for child care rather than bringing children to class with you. If there are extenuating circumstances, please talk with your instructor in advance.