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 won’t do “proofs.”  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:

Lecturenotes

           Homework: Homework is assigned each week and is due the following week.  Mathematically can, unfortunately, not be learned through “osmosis;” 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.

Hw 1 (due 9/7)

Hw2 (due 9/14)

Hw3 (due 9/21)

Hw4 (due 9/28)

Hw5 (due 10/5)

Hw6 (due 10/12)

Hw7 (due 10/19)

Hw8 (due 10/26)

Hw9 (due 11/2)

Hw10 (due 11/9)

Hw11 (due 11/16)

Hw12 (due 11/23)

Hw13 (due 11/30)

Hw14 (due 12/7)

 

                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, “old material”]

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 “extra credit” 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 3rd ed. (Wiley, New York, 2006)

(3)   G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists 5th 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 2nd 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 2nd 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 3rd Ed. (Wiley, New York, 1998).

(13)R. Abraham and J. E. Marsden, Foundations of Mechanics (Benjamin/Cummins, Reading, MA, 1978).