Course Information

Course Name	Turkish	Kısmi Diferansiyel Denklemler
	English	Partial Differential Equations
Course Code	MAT 234	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	4	3	3	-	-
Course Language		Turkish
Course Coordinator		İrma Hacınlıyan İrma Hacınlıyan
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		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: I. 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, II. 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, III. 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, IV. Solve one dimensional wave and heat/diffusion equations under initial and boundary conditions by employing the method of separation of variables, V. 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.
Pre-requisite(s)		MAT201-E / MAT210-E / MAT232-E min DD
Required Facilities
Other
Textbook		W.A. Strauss, Partial Differential Equations, An Introduction, 2nd Ed., Wiley, 2008.
Other References		Y. Pinchover & J. Rubinstein, An Introduction to Partial Differential Equations, Cambridge University Press, 2005. T. Myint-U & L. Debnath, Linear Partial Differential Equations for Scientists and Engineers, 4th Ed., Birkhauser, 2007. R. Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 5th Edition, Pearson, USA. W.E. Williams, Partial Differential Equations, Oxford University Press, 1980. P. O’Neil, Beginning Partial Differential Equations, 3rd Ed., Wiley, 2014.

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