PHY 325: Introduction
to Theoretical Physics
Text: K. F. Riley and M. P. Hobson, Essential Mathematical Methods
for the Physical Sciences (Cambridge University Press, New York, 2011). We follow the text closely. Students
are expected to read the text on their own.
Web page: Introduction
to Theoretical Physics Fall 2011
All homework and lecture notes will be posted on this site!
Instructor: Ulrich Zurcher, u.zurcher@csuohio.edu
Science Building, Room 114, Phone: 687-2429
Lecture: SI-147, MWF 2:45-3:50
Office hours: TBA, and any time you find the
instructor in the Science Buildingl!
Course Material: The course is an introduction to
mathematical methods in physics. It is not a math course in the
sense that we wonÕt do Òproofs.Ó
Rather, we focus how (higher) math is used in Analytical Mechanics
[i.e., Langrangian and Hamiltonian mechanics], Electricity and Magnetism, and
Quantum Physics. We only cover
analytical methods in the course; some numerical methods are covered in
homework assignments.
Tentative Outline:
Week |
Topic [Section in Riley & Hobson] |
1/2 |
Matrices & Vectors [1.1-20] |
2/3 |
Vector Calculus [1.1-9] |
4 |
Line, surface and volume integrals [3.1-9] |
5 |
Fourier Series [4.1-8] |
6 |
Fourier and Laplace transform [5.1-5] |
7 |
Higher order ODE [6.1-6] |
8 |
Series solutions of ODE [7.1-6] |
9 |
Eigenfunctions for DE [8.1-5] |
10 |
Special functions [9.1-3,5] |
11 |
Partial Diff Eq. [10.1-6] |
12 |
Solutions for PDE [11.1-5] |
13 |
Calculus of Variations [12.1-4] |
14 |
Complex Variables [14.1-12] |
14 |
Applications of Complex Variables |
Lecture Notes:
Homework:
Homework
is assigned each week and is due the following week. Mathematically can, unfortunately, not be learned through
Òosmosis;Ó and only by actually doing it. Students are encouraged to work in
groups; however every student submits his/her own solution. Homework solutions are presented in
class by students who will be selected by the instructor. Submitting a solution
implies that the student can talk cogently about a problem. Failure to do so,
will automatically result in a score of 0 [zero] for that set.
Exams:
Four
midterm exams and one (comprehensive) final exam. No make-up exam will be offered
for any exam. Exams
are open book [Riley & Hobson] and open notes! However, no laptops,
graphing calculators are allowed; only scientific calculators such as TI-30 are
allowed.
Exam 1: 8/31 [yes, on the second day of class, Òold materialÓ]
Exam 2: 9/21
Exam 3: 10/19
Exam 4: 11/16
Grades: The grade for PHY325 will be based on a
maximum according to the following scheme:
Midterm Exams |
400 [100 each] |
Homework |
300 |
Final Exam |
300 |
Total |
1000 |
Letter grades then follow:
A:
90-100, A-: 85-90, B+: 80-85, B:75-80, B-: 70-75, C+: 65-70, C: 55-65, D:40-55,
F:<40.
No Òextra creditÓ
work will be offered under any circumstance.
Suggested
Reading:
(1)
K. F. Riley and M. P. Hobson, Essential Mathematical Methods (Cambridge
University Press, New York, 2011-
(2)
M. L. Boas, Mathematical Methods in the Physical Sciences 3^{rd} ed.
(Wiley, New York, 2006)
(3)
G. B. Arfken and H. J. Weber, Mathematical Methods for
Physicists 5^{th} ed. (Academic Press, San Diego, 2001).
(4)
P. M. Morse and H. Feshbach, Methods of Theoretical Physics,
Part I and II (McGraw-Hill, New York, 1953)
(5)
F. B. Hildebrand, Advanced Calculus for Applications 2^{nd} Ed.
(Prentice Hall, Englewood, NJ, 1976).
(6)
R. D. Richtmyer, Principles of Advanced Mathematical Physics (Springer-Verlag,
New York, 1978).
(7)
W. Rudin, Real and Complex Analysis 2^{nd} Ed.
(McGraw-Hill, New York, 1974).
(8)
J. L. Synge and A. Schild, Tensor Calculus (Dover, New York,
1978).
(9)
L. M. Falicov, Group Theory and Its Physical Applications (University of
Chicago Press, Chicago, 1966).
(10)D. Zwillinger, Handbook of
Differential Equations (Academic Press, Boston, 1989).
(11)G. Strang, Linear Algebra and Its
Applications 3rd Ed. (Harcourt, San Diego, 1988).
(12)J. D. Jackson, Classical
Electrodynamics 3^{rd} Ed. (Wiley, New York, 1998).
(13)R. Abraham and J. E. Marsden, Foundations
of Mechanics (Benjamin/Cummins, Reading, MA, 1978).