Hoş Geldiniz, Misafir . Oturum Aç . English
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Dersin Haftalık Planı

 Hafta Konu 1 1. Introduction: Basic Definitions, Typical Problems 2. First Order Equations in Two Independent Variables: Basic properties of the linear equation, solution of linear equations, Cauchy problem, quasi-linear equations, solution of quasi-linear equations, 3. The general first order nonlinear equation, exact solution, general solution and singular solution. 4. Linear Second Order Equations in Two Independent Variables; Cauchy problem, classification of lineear second order equations and their reduction to a canonical form (hyperbolic equations), 5. Continue the reduction of the equations to canonical forms (elliptic and parabolic equations), 6. Hyperbolic Equations -One Dimensional Wave Equation; D’Alembert’s solution, the mixed initial value –boundary value problem for the one-dimensional equation, Cauchy problem, inhomogeneous wave equation 7. Separation of Variables (one dimensional wave equations) 8. Elliptic equations; Laplace equation, max-min principle, boundary value problems, 9. Integral represantations and Green’s functions, 10. Parabolic equations; Initial and boundary value problems, fundamental solutions and Green's functions 11. Hyperbolic Equations: Cauchy and Goursat problems 12. Analytical methods of solutions; Integral transform techniques. 13. Fourier Transformation 14. Laplace Transformation 2 1. Introduction: Basic Definitions, Typical Problems 2. First Order Equations in Two Independent Variables: Basic properties of the linear equation, solution of linear equations, Cauchy problem, quasi-linear equations, solution of quasi-linear equations, 3. The general first order nonlinear equation, exact solution, general solution and singular solution. 4. Linear Second Order Equations in Two Independent Variables; Cauchy problem, classification of lineear second order equations and their reduction to a canonical form (hyperbolic equations), 5. Continue the reduction of the equations to canonical forms (elliptic and parabolic equations), 6. Hyperbolic Equations -One Dimensional Wave Equation; D’Alembert’s solution, the mixed initial value –boundary value problem for the one-dimensional equation, Cauchy problem, inhomogeneous wave equation 7. Separation of Variables (one dimensional wave equations) 8. Elliptic equations; Laplace equation, max-min principle, boundary value problems, 9. Integral represantations and Green’s functions, 10. Parabolic equations; Initial and boundary value problems, fundamental solutions and Green's functions 11. Hyperbolic Equations: Cauchy and Goursat problems 12. Analytical methods of solutions; Integral transform techniques. 13. Fourier Transformation 14. Laplace Transformation

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