2017-Domokos , Andras - Differential Equations - Theory and Applications – Notes
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Domokos , Andras. 2017. Differential Equations - Theory and Applications – Notes. 126 pp. California State University, Sacramento.
See http://www.csus.edu/indiv/d/domokos/diffeq.pdf . Accessed 6 September 2017.
The author says in the Introduction,
“Differential Equations is a very important mathematical subject from both theoretical and practical perspectives. The theoretical importance is given by the fact that most pure mathematics theories have applications in Differential Equations. For students, all the prerequisite knowledge is tested in this class. The practical importance is given by the fact that the most important time dependent scientific, social and economical problems are described by differential, partial differential and stochastic differential equations. The bridge between Nature or Universe and us is provided by mathematical modeling, which is the process of finding the correct mathematical equations describing a certain problem. This process might start with experimental measurements and analysis, which lead to certain equations, in our case differential equations. Then, these differential equations are solved and their solutions tested for agreement to experimental results. In this process we generate some solutions, which have the role to predict the future behavior of the analyzed problem
“Differential Equations is probably one of the best classes which can make us understand that Nature does not provide us with a complete solution manual. We usually have to find some approximate answers and we are also left with the task of predicting how accurate these answers are, without knowing the correct answer.”
This set of notes concerns itself primarily with solution techniques and has lots of Mathematica code for these strategies. There are no in-depth examples and illustrations for application are in Wolfram Demonstration web pages.
Keywords: technique, differential equation, solving, theory, Laplace Transform, systems, first order, second order, solution technique
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