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Mathematical Sciences

Martin Jackson, University of Puget Sound

Date: 3:30pm PST March 6, 2012 Location: JRR Howard Hall, Room 114

JRR Howard Hall, Room 114

Title: Using symmetry to solve differential equations

Rotate the plane around a point and look at what happens to geometric objects. For example, a circle centered at the point of rotation will be  mapped to itself for any angle of rotation so we say that the circle has rotational  symmetry. The idea of symmetry can also be applied to differential equations.  Knowing a continuous symmetry of a differential equation can help us find solutions. My goal for this talk is to introduce the basic ideas in using symmetry to solve differential equations. These ideas were first introduced by Sophus Lie in the late 1800’s and are now a very useful tool in analyzing differential equations. I’ll aim to make these ideas accessible to anyone who has taken calculus.