A good example of a variational principle is Fermat's principle of least time: light will travel from point A in the air to point B in the water by 'choosing' the path that requires the least amount of time. The law of refraction is easily deduced from this principle. In mechanics, Maupertuis's principle of least action plays a similar role in determining the path followed by a particle or a planet in a force field. In this course, students learn about many of the historically important variational principles of physics -- including the principles of Fermat, Maupertuis and Hamilton. Students apply these to fields as diverse as optics, mechanics, quantum mechanics, and general relativity. This is a course in mathematical physics, so most of the work involves actually learning how to solve physics problems associated with variational principles. But readings, lectures and discussion are also devoted to the rich history and philosophical issues surrounding variational principles.
Prerequisites: PHYS 305 and 351 or permission of the instructor.