| Dersin Amacı | Matematiksel düşünceyi geliştirmek. Matematik, Fizik ve mühendislikte karşılaşılan problemleri çözebilmek. |
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| Dersin İçeriği | Differential Equations, The Definition and Classification, Order and Degree of Differential Equations, Solutions of Differential Equations: The Integral Curve, İmplicit-Explicit Solution, Particular Solution, The General Solution, Singular Solution, İnitial Value Problem. Derivation of Differential Equations. First Order Differantial equations: Separable Differential Equations, Variables that can be converted Separable Differential Equations Differential Equations, Homogeneous Functions, Homogeneous Differential Equations, Becomes homogeneous differential equations that can be converted. Linear Equations, Method of Integrating Factors, Method of Variation Parameters, Bernoulli Equations, Exact Equations and Integrating Factors , Exact Equtions, The Method of İntegrating Factors Based on a Single Variable, Riccati Equations. First Order Higher Degree Differential Equations: Clairaut and Lagrange's Equations. Second Order Linear Equations: Homogeneous Equations with Constant Coefficients, Characteristic Equation, Fundamental Solutions of Linear Homogeneous Equations, Linear independence and Wronskian Determinant, Complex Roots of The Characteristic Equation, Real Valued Solutions, Repeated Roots, Reduction of Order. Nonhomogeneous Equations Method of Undetermined Coefficients, Method of Variation Parameters. Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients. Characteristic Polynomial ,Characteristic Equation, Real and Unequal Roots, Complex Roots , Repeated Roots, The Method of Undetermined Coefficients, The Method of Variation of Parameters. Some Special Second Order Equations: Equations with the Dependent Variable Missing, Equations with the Independent Variable Missing. Euler Differential Equation with Variable Coefficients. Series Solutions of Second Order Linear Equations: Review of Power Series, Series Solutions Near an Ordinary Point. The Laplace Transform: The Laplace Transform, Definition of Laplace Transform. The Inverse Laplace Transform, Definition of Inverse Laplace Transform. Solution of Initial Value Problems with the help of the Laplace Transformation. Systems of Linear Equation First Order Differential Equation: Elimination and Determinant Method |
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| Ders Kitabı / Malzemesi / Önerilen Kaynaklar | - Elementary Differential Equations and Boundary Value Problems. William E. Boyce and Richard C.DiPrima, Eighth Edition,2005,U.S.A.
- Diferansiyel Denklemler . Prof.Dr. Mustafa Bayram . Yildiz Teknik Üniversitesi Fen Edebiyat Fakültesi, Matematik Bölümü . 2011. İstanbul
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