Dr Ian M Littlewood
MWF 11 to 11:50
In this class we will try to cover those mathematical techniques which are required to make the transition from the introductory physics classes to the upper division ones. The exact topics to be discussed will depend on the results of a diagnostic exam to be held during the first class period. However, it is expected that we shall touch on a least some topics from each of the following: vector calculus, multiple integrals, complex numbers, matrices, determinants, and Fourier series.
For the first time this course will also have the objective of introducing you to one of the sophisticated mathematical packages which are used by professional physicists in the course of their work. From the choices available, we have selected Maple as the standard package for use in this department, as have the Mathematics Department on campus. You will find it to be of great help to you in the subsequent courses as you work towards you physics degree, and into the future as you pursue a career in physics. (It's also fun!)
The advantages of a mathematical tool such as Maple are numerous. In this class we shall focus on the following:Please note, although we shall be using Maple extensively, it is a tool to be used once you have understood the basic principles. As with all tools it is not a substitute for learning.
The ability to evaluate complex expressions, many of which cannot be solved analytically, at east not at the level appropriate for an undergraduate student. The ability to plot complicated expressions, and understand their implications. The ability to save considerable time by evaluating expressions which although not at an advanced level are nevertheless cumbersome enough to require extensive calculation.
I shall be directly integrating the mathematical techniques from this class with the use of Maple for evaluating and understanding the more complex mathematical expressions. I will try to link the mathematics to specific physics examples wherever possible.
Copies of Maple are available for your use within the department, and in the university library. However, it is strongly recommended that you get your own student copy of Maple for home use. Not only will it help you in this class, but in the subsequent classes which rely heavily on mathematics, such as Electricity and Magnetism, and Quantum Mechanics, and indeed during your career after you graduate. Instructions for obtaining a copy will be given on the first day of class.
The following example sheets might be useful to you
The following is a tentative order for topics this semester. It is subject to change, depending in the rate at which we cover material, and on the choice of topics to be covered, particularly late in the semester.
Introduction to Maple basic commands symbolic notation plotting and animation integration Complex numbers polar notation Oscillators and waves Differential Equations Separable equations Second order with constant coefficients Wave equation Heat diffusion equation Multiple Integrals Cartesian, cylindrical, and spherical coordinates systems coordinate transformations volume and area elements Vector calculus Divergence, gradient, curl Divergence Theorem Stokes' Theorem Fourier series Matrices and determinants matrix algebra simultaneous equations diagonalization of matrices eigenvalues and eigenfunctions
This is meant to be a practical class, and grading will reflect this. The largest portion of the grade will come from in-class and homework assignments. Some of these will be turned in on paper, others will be Maple assignments. Maple assignments can be emailed to me. There will be a take-home final, but no mid term exam.