Not Solving Differential Equations

AbstractOne can learn a lot about a differential equation without solving it. Using the relationship between the sign of the derivative of a function and its behavior, given by the Mean Value Theorem, makes many important properties of solutions clear, and allows one to consider variations that are difficult or ugly to solve exactly. Additional informationNotes on contributorsJames S. WolperJames Wolper (wolpjame@isu.edu) received his Ph.D. in Mathematics from Brown University. He is an Emeritus Professor at Idaho State University. Most of his research has been in Algebraic Geometry, most recently into the statistical properties of periods of Riemann Surfaces.