General course:To equip participants with tools, including infinite series, for differential equations. Emphasis is also placed on the students acquire mathematical understanding at a deep enough level to be able to familiarize themselves with advanced topics in mathematical analysis and its applications.Learning objectives:A student who has met the objectives of the course will be able to:Determine the solutions to the nth order homogeneous differential equationsDetermine the solutions of linear homogeneous differential equationsMaster the transfer function and apply it to the solution of inhomogeneous differential equationsDetermine whether a given model is linear or nonlinear, and make simple inquiries regarding nonlinear systems behaviorEvaluate and justify the stability of linear differential equationsMaster key convergence conceptsAssess how many links to include in an infinite series to achieve a desired approximationFind the Fourier series of periodic functions, clarify convergence and approximation-theoreticUsing Maple for calculations and control of resultsApply Fourier series and other series for differential equationsMaster key evidence in the theory of infinite series and differential equationsDraw up evidence of simple claims within the theory of infinite series and differential equationsContent:Solving homogeneous and inhomogeneous differential equations and systems of differential equations. Transfer function. Infinite series, power series, Fourier series. Use of the infinite series of differential equations, including Fourierrkkemetoden and power series method. Stability. Introduction to nonlinear differential equations. Use of Maple on the above topics. Key definitions, concepts, and evidence in the above topics.