Methods of Mathematical Physics
Last Updated: 11/17/2008
Fall and Winter quarters
Faculty: David McAvity mathematics, physics
Faculty Signature Required: Winter quarter
Major areas of study include upper division mathematics and physics.
Class Standing: Sophomores or above; transfer students welcome.
Accepts Winter Enrollment: This program will accept new students who have appropriate background. Contact faculty at Academic Fair or by email. New students should expect to complete some catch-up work during the December break.
Prerequisites: A full year of college level calculus and calculus-based physics. Students interested in advanced mathematics but who do not have the necessary background in physics should contact David McAvity for advice at firstname.lastname@example.org.
A close examination of the complex and varied world around us reveals a high degree of underlying order. Our goal as scientists is to understand and explain this order and we do this most precisely using the language of mathematics. Indeed, the degree to which the universe lends itself to a mathematical description is remarkable. The goal of this advanced program is to introduce the mathematical language we use to describe and create physical models of our world. To that end, we will examine a number of key physical theories and systematically develop the mathematical tools that we need to understand them.
We will begin, in fall quarter, with a detailed study of classical mechanics – the mathematical description of the clockwork universe envisioned by Newton and others who followed him. We will focus initially on linear approximations for which analytical solutions are possible. The mathematical methods we will learn for this purpose include differential equations, vector calculus and linear algebra. In winter quarter we will move beyond linear approximations and study non-linear systems and chaos and the implications of these ideas for the determinism implied by classical mechanics. We will also extend the Newtonian synthesis to the realm of the very fast and very massive by considering Einstein’s theories of special and general relativity. Mathematical topics associated with these ideas include Riemannian geometry, tensor calculus and variational calculus.
The work in this program will consist of lectures, tutorials, group workshops, student presentations, computer labs and seminars on the philosophy and history of mathematics and physics.
Credits: 16 per quarter
Special Expenses: $125 for a graphing calculator.
Program is preparatory for careers and future studies in physics, mathematics, chemistry, engineering and education.
Planning Units: Scientific Inquiry
|November 17th, 2008||Winter quarter enrollment details added.|