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Resources
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1. Nagle, Saff and Snider, Fundamentals of Differantial Equations and Boundary Value Problems (6. Edition), Pearson, Addison Wesley. 2. Çengel, Y. A. ve Palm, W. J. (Türkçesi: Tahsin Engin), Mühendisler ve Fen Bilimciler İçin Diferansiyel Denklemler, 2012, Güven Kitabevi, İzmir. 3. Richard Bronson, Differential Equations, Second ed. , McGraw Hill.
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Content
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Classification of differential equations: Open solution, closed solution, initial value problems, existence and uniqueness of solution, First order ordinary differential equations: Separable differential equations, exact differential equations, Integral factor and reducible equations, first order linear differential equations, Bernoulli differential equations, First order homogeneous equations, special transformations. Riccati equation, applications of first order differential equations, Theory of higher order homogeneous linear differential equations, linear dependence and independence, nonhomogeneous linear differential equations, Reduction of order. Homogeneous linear equations with constant coefficients, Solution of non-homogeneous differential equations: Indefinite coefficients method, method of changing parameters, Cauchy Euler differential equations, Laplace transforms: Definition and properties of Laplace transform, Inverse Laplace transforms. Solution of initial value problems by Laplace transform method, Series solutions of differential equations: Power series solutions: Solution around ordinary point, Systems of linear differential equations: Differential operators, operator method and Laplace transform method, Fourier series for periodic functions, Fourier cosine and sine series
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