Course Information

Course Name	Turkish	Kısmi Diferansiyel Denklemler
	English	Partial Differential Equations
Course Code	MAT 234E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	3	-	-
Course Language		English
Course Coordinator		Cihangir Özemir
Course Objectives		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. To develop a basic understanding of the theory and methods of solutions for these problems.
Course Description		Partial Differential Equations-Introductory Concepts, First-Order Linear Equations, Ideas On Derivations of The Fundamental PDE’s, Types of PDE Problems, Classification of Second-Order Linear Equations. Initial Value Problem for The Wave and The Heat/Diffusion Equations on The Whole Line, Energy Methods and Maximum Principle for Uniqueness. The Homogeneous Heat/Diffusion Equation on The Half-Line, The Homogeneous Wave Equation On The Half-Line and On A Finite Interval By The Method of Reflections. The Inhomogeneous Wave and Heat/Diffusion Equations On The Whole Line. The Wave and Heat/Diffusion Equations Under Initial and Boundary Conditions by The Method Of Separation of Variables. Harmonic Functions, Laplace's Equation, Maximum Principle, Uniqueness, Invariance, Poisson's Formula. Green's Identities and Green's Functions.
Course Outcomes		Students completing this course will be able to: Solve the basic first-order homogeneous variable coefficient linear PDEs, have an idea on how the basic PDEs of applied mathematics are derived, have the knowledge on types of PDE problems and classify second order linear PDEs, Solve one dimensional homogeneous wave and heat/diffusion equations (in two independent variables) under initial conditions, and employ energy methods or maximum principle to prove the uniqueness of the initial-boundary value problem, Solve the homogeneous heat/diffusion equation on the half-line, the homogeneous wave equation on the half-line and on a finite interval, the inhomogeneous wave and heat/diffusion equations on the whole line, Solve one dimensional wave and heat/diffusion equations under initial and boundary conditions by employing the method of separation of variables, Define boundary value problems for the Laplace and Poisson equations, integral representations of their solutions and Green`s functions, and also to solve these problems in rectangular and circular regions by the method of separation of variables and to have an idea about the uniqueness of the solutions of boundary value problems.
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