Author: Gary Miller
Retail Price: $16.95
Release Date: October 10, 2017
Page Count: 174
A Deeper Look at Elementary Differential Equations
A typical first course in differential equations categorizes equations and offers solution routines. There are still more methods demonstrated in chapter one. The origin of these results and a viewpoint which unifies the subject begins in chapter two. The concept of integrating factors is expanded leading to consideration of the Euler operator. The use of straightforward examples from the elementary theory is intended to make the subject accessible, the outlook interesting, and the execution tractable. As it happens, the Euler operator is at the heart of variational principles, the formulation of physical theories which begin with a Lagrangian. This subject will return in a natural way in the last part of chapter three. Where there are integrating factors there are also symmetries. That is, certain clever changes of variables deliver doable equations. Naturally, there is a geometric aspect to the method and where there is geometry there are physical applications. With that we are led to differential equations originating in the Lagrangian formulation, or, equations which can be reformulated as such. Finally, Lagrangian methods lead to conservation laws, first integrals of differential equations. And, interestingly enough, conservation laws for non-conservative systems.
About the Author
Gary Miller holds the M.Sc. (Queen’s) and Ph.D. (University of New Brunswick), in mathematics. He received an NSERC award while in graduate studies from the Canadian government. His teaching experience includes twenty years in the Persian Gulf. Research interests include mathematical physics, multilinear algebra, and of course, symmetry methods.