Course Information

Course Name	Turkish	Kısmi Türevli Dif Denkl
	English	Partial Differential Equations
Course Code	MAT 331	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	3	4	4	-	-
Course Language		Turkish
Course Coordinator		Nalan Antar
Course Objectives		1. To develop a basic understanding of occurrence of the partial differential equations and related problems; such as, initial value, boundary value and initial-boundary value problems in the real world. 2. To develop a basic understanding of the theory and methods of solutions for these problems.
Course Description		The single first order equations; general solutions of linear and quasi-linear equations and Cauchy problem, nonlinear equations. Second order linear equations in two independent variables; Cauchy problem and classification, canonical forms. One dimensional wave equation; Cauchy problem, D’Alembert’s solution, Inhomogeneous wave equation. Elliptic equations; Laplace equation, max-min principle, boundary value problems and Green’s functions. Parabolic equations; initial and boundary value problems, fundamental solutions and Green's functions. Analytical methods of solution; separation of variables and integral transform techniques.
Course Outcomes		By the end of the course students will be able to ; I. Find the general solutions of the first order linear, quasilinear and nonlinear differential equations in two independent variables. Solve the Cauchy problems for them either by using the method of characteristics or by employing their general solutions. II. Classify single second order linear partial differential equations in two independent variables, calculate the canonical forms of them and using the canonical forms to find general solutions of some of these equations. III. Solve one dimensional homogeneous and inhomogeneous wave equations under initial conditions. IV. Solve one dimensional wave equations under initial and boundary conditions by employing the method of seperation of variables. Also, they will have an idea about the uniqueness of the solutions of these problems. V. Define boundary value problems for the Laplace and Poisson equations, integral representations of their solutions and Green`s functions. Also, they will be able to solve these problems in rectangular and circular regions by the method of seperation of variables and will have an idea about the uniqueness of the solutions of boundary value problems. VI. Solve heat conduction equations under initial conditions. Also, they will be able to solve initial and boundary value problems by the method of seperation of variables and also will have an idea about the uniqueness of the solutions. VII. Solve the Cauchy and Gorsat problems for linear hyperbolic equations in two independent varibles. VIII. Solve linear partial differential equtions under certain initial and bondary conditions by employing the Laplace transformation or the Fourier transformation method.
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