Course Information

Course Name	Turkish	Kısmi Diferansiyel Denklemler I
	English	Partial Differantial Equat. I
Course Code	MAT 512E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	3	-	-
Course Language		English
Course Coordinator		Semra Ahmetolan
Course Objectives		To introduce the concept of characteristics and the method of characteristics to solve Cauchy problem for the first order quasi-linear and nonlinear equations. To define first the classical and weak solutions of first order quasi-linear equations and then the linear equations of higher order equations. Also to define the distributional solutions of linear equations To investigate certain classical and weak solutions of the Wave, the Laplace and the Heat equations.
Course Description		First order equations; the Cauchy problem, the method of characteristics, general solutions, weak solutions. Higher order equations; the Cauchy problem, the Cauchy-Kovalewski theorem. Second order equations in two variables. First order systems. Linear equations and generalized solutions. The one dimensional wave equation. The wave equation in higher dimensions; spherical means, Kirchhoff`s formula and Huygens`principle. The Laplace equation; Dirichlet and Neumann problems, the maximum principle, Green`s functions. The heat equation in a bounded domain, the initial value problem and the fundamental solution, regularity.
Course Outcomes		Find classical and weak (discontinuous) solutions of first order quasilinear equations. Solve the Cauchy problem for the first order quasilinear and nonlinear equations by the method of characteristics . Define and investigate the Cauchy problem and characteristics for a higher order equations Classify second order equations , calculate canonical forms and find general solutions of some of them. Classify first order system and find the solutions of hyperbolic systems. Define weak and Generalised (distribution ) solutions of linear equations. Find the classical and weak solutions of the one dimensional wave eqution. Apply the method of spherical means to the Cauchy problem for the wave equations in higher dimensions Construct the solutions of the Dirichlet and Neumann problems for the Laplace equation in special domains and define Green`s functions for these problem in a general domain. Construct the solutions of the Heat equation in a bounded domain and for the initial value problems
Pre-requisite(s)
Required Facilities
Other
Textbook		• McOwen, R.,(1996), Partial Differential Equations, Prentice Hall, New Jersey.
Other References		• John, F.(,1982), Partial Differential Equations, Springer, New York • Evans, L. C.,(1998), Partial Differential Equations, AMS, Prvidence, Rhode Island. • Garabedian, P. R., (1964), Partial Differential Equations , John Wiley, New York • Williams, W. E.. (1980), Partial Differential Equations,Clarendon Press, Oxford.

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