Lectures on Selected Topics in Mathematical Physics: Introduction to Lie Theory with Applications

This book provides an introduction to Lie theory for first-year graduate students and professional physicists who may not have come across the theory in their studies. In particular, it is a summary overview of the theory of finite groups, a brief description of a manifold, and then an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, but systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus, but it does not assume additional mathematical training. Interested readers should have a fair chance of finding symmetries of a second-order differential equation and should be able to use it to reduce the order of the differential equation.