Physics 704 is to cover the material in the first 8 chapters of Jackson's book; 705 covers the rest! This is a tall order, for you and for me. The objective in studying this material is not just to learn the physics of electromagnetic phenomena, but also to learn a set of mathematical techniques which are useful in many other branches of physics. In order to present the material in a way which emphasizes how a given technique can be applied in differing physical situations, and thus to avoid a good deal of duplication of material, I have attempted to construct a class schedule which does not follow the order of Jackson exactly. It is given below. We may not adhere to this schedule exactly, but it should be a guide for your reading and we can discuss how to proceed as things deviate from the plan.

Please try to read the appropriate section of the text before class. The material will undoubtedly be mysterious the first time you see it, and you will get more from each class if you have looked at the material in advance.

Assigned problems are listed on the schedule. Doing problems is the essence of a class based on Jackson. I shall collect and grade these every week. Do not get behind! The farther behind you get, the harder it is to catch up. Your grade for the class will be heavily based on these problem grades, although a good deal of credit will be given for a good attempt. There will be a take-home midterm, and a take-home final. Problems and the midterm are due at the beginning of the class period on the day indicated. Assignments turned in late will be accepted only under exceptional circumstances.

Grades will be assigned on the following basis:

Homework problems: 30% Midterm: 35% Final: 35%

Please feel free to discuss all aspects of the class with me at any time. Discuss the homework problems among yourselves as well as with me (exams should not be discussed, however). Try to attend published office hours, but also feel free to knock on my door whenever I am there (I'll tell you if I am busy!) My official office hours are (tentatively) M 2-3pm, W 3-4pm, F 11-12am. It's usually a good idea to make an appointment.

As graduate students, more is expected of you. You may find it helpful, indeed necessary, to use reference materials other than Jackson. You should have access to a mathematical reference work listing integrals as well as properties of mathematical functions such as Legendre polynomials and Bessel functions. The book store has a few copies of Gradshteyn and Ryzhik if you want your own: otherwise using the library should suffice. Other books dealing with the material include: Landau and Lifshitz, Classical Theory of Fields; Morse and Feshbach, Methods of Theoretical Physics; Jeffreys and Jeffreys, Mathematical Physics, especially Chapters 6,18,21,22 and 24.

This class will be a challenge for all of us, and I hope that we can meet it together.

Physics 704 Course Ouline (Tentative). Spring 1997 Date Jackson Topic Problems. Reference W Jan 29 I, esp.I.1,I.2 Overview: fields and particles Appendix. Maxwell's equations. Units. F Jan 31 I.3-6 Nature of the mathematical problem. 1.1,1.2, Linearity. Sources and boundary conditions. Fields in media: D and H. Due Feb 5 M Feb 3 6.1,1.1-4,5.3,6.3 Derivation of Maxwell's equations from experimental results. Boundary conditions. W Feb 5 6.4,6.5 Potentials: è, A, èm 1.3,1.5 Gauge conditions. Due Feb 12 F Feb 7 7.1 Kinds of solutions: static and dynamic. Plane waves. 1.5 è for point charge and dipole. M Feb 10 5.4-5,5.9,1.6 Vector and scalar magnetic 5.1, potentials. Surface charge/current. 6.12 Discontinuities Due Feb 19 W Feb 12 1.11,6.2,6.8 Energy in the EM field. Capacitance. F Feb 14¿ 1.8-10 Effect of boundary conditions. W 19Ù Green's Theorem; uniqueness. Formal theorems (M Feb 17 President's Day holiday.) F Feb 21 2.1-7 Derivation of potential: method of images. Use of images to construct Green function for sphere. 1.7 M Feb 24 2.8 Orthogonal functions: 1.10 Sturm-Liouville problem. Due Feb 26 W Feb 26 2.9,2.10 Fourier integral. Separation of variables. Rectangular 2-D potential problems. F Feb 28 2.11 Use of conformal transformations 2.1 in 2-D problems. 2.7 Due Mar 5 M Mar 3 3-D problems: potential in a cube W Mar 5 8.2,8.3 Boundary conditions on wave solutions: wave guides. Date Jackson Topic Problems. Reference F Mar 7 8.4 Rectangular wave guide. 2.14, 8.4(a) Due Mar 12 M Mar 10 3.1-2 Separation of variables in spherical coordinates. W Mar 12 3.3-4, 5.12 Examples. 3.7, 5.7 Due Mar 19 F Mar 14 3.7 Cylindrical symmetry: Bessel functions. 3.11, 3.14c Due Apr 2 M Mar 17¿ 3.8,8.7 Examples W 19Ù F Mar 21 3.13,5.13 Mixed boundary conditions. M Mar 24 - F Mar 28 SPRING BREAK M Mar 31 -- Other problems reducible to Midterm Laplace's equation. Due Apr 9 W Apr 2 3.9 Green's functions in terms of F Apr 4 orthogonal functions. I. Spherical. M Apr 7 3.10 Examples. 3.13 Due Apr 16 W Apr 9 3.11 II Cylindrical F Apr 11 Prob 3.15 Examples. M Apr 14 3.12 General method using 3.16 eigenfunctions. Due Apr 23 (Do not use the results of 3.15) Class project Due May 19 3.21,3.22** W Apr 16 Examples. F Apr 18 6.6 Green's function for wave 3.20 Due Apr 30 equation: causality. M Apr 21¿ 4.1 Multipole expansions. 6.19 W 23Ù 4.2 Due May 7 F Apr 25 Examples. 4.1 b,c,d M Apr 28 4.2-4.7 Quick survey of dielectrics. 4.7, 4.10 Due May 14 W Apr 30 5.6 Magnetic moment F May 2 5.7 Force and torque. M May 5 7.1,7.2 Properties of waves: Polarization Date Jackson Topic Problems. Reference W May 7 ¿ 7.3,7.4 Fresnel formulae F May 9 Ù M May 12 7.5 - 9 Dispersive media; group velocity. W May 14 5.6 F May 16 7.11 Pulses. 7.10 Due May 21 M May 19 Examples W May 21 Student reports. May Final Examination. (Official date) May Take-home final examination due