In this introductory course on ordinary differential equations we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations we handle first order differential equations and then second order linear differential equations we also discuss some related concrete mathematical modeling problems which can be handled by the methods introduced in this course. Introduction to ordinary differential equations todd kapitula department of mathematics and statistics university of new mexico september 28 2006. Lies group theory of differential equations has been certified namely 1 that it unifies the many ad hoc methods known for solving differential equations and 2 that it provides powerful new ways to find solutions the theory has applications to both ordinary and partial differential equations. These lecture notes provide an introduction to the theory and application of symmetry methods for ordinary differential equations building on minimal prerequisites their primary purpose is to
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