CourseSummary - MATHEMATICAL METHODS IN PHYSICS ASTRONOMY...

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MATHEMATICAL METHODS IN PHYSICS & ASTRONOMY 2003–2004 Colin Wilkin ([email protected]) The first year 1B21 course and the second year 2B21 course should together provide all the necessary mathematical techniques for the understanding of the com- pulsory (core) courses in the whole Physics and Astronomy and related degree pro- grammes. The two second year courses which rely heavily on the mathematical formalism developed in 2B21 are Quantum Mechanics and Electromagnetic theory. Since Electromagnetism is in the second semester, the course will start with the things needed for Quantum Mechanics, viz matrices and eigenvalues, partial di ff er- ential equations, and the solutions of the Legendre di ff erential equation. By imposing boundary conditions on this, we will derive quantisation of angular momentum about the same time as you will see it in the Quantum Physics course. The properties of the Legendre polynomials and spherical harmonics derived here should help you un- derstand some of the Quantum phenomena. Though you will have met the gradient di ff erential operator in the 1B21 course, Electromagnetism requires that you be able to apply also the divergence and curl operators, as well as use the divergence and Stokes’ theorem which are introduced at the end of the course. The Fourier analysis is also of use in second year Electromagnetism, but it will required in many other courses such as modern optics or signal processing. Even if it is not true, the assumption has to be made that you have understood and can reproduce most of the first year 1B21 material, including the Notes on Integration. You will have to remember the contents of the Formulae Sheet because it will not be issued in second year examinations. It can therefore do no harm at all if you spent some time going through last year’s notes on the subject. There are about 34 lectures in total in the 2B21 course. The methodology is rather similar to 1B21 but, because there are no associated problem solving classes, there are about 9 discussion classes where I will go over examples. Following sug- gestions from students in past years, most of these examples will be chosen by me so that they fit well with the course and the problem sheets. That seemed to work quite well in the past, but it is not intended to stop students raising their own questions. The discussion classes will normally be in the second slot on Thursday afternoons, except for the first week when I shall lecture for two hours instead — it is hard to discuss problems before getting well into the course.
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