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Course Information

Course Information

Course Title	Code	Semester	L+U Hour	Credits	ECTS
APPLIED PARTIAL DIFFERENTIAL EQUATIONS	MAT4432		0 + 0	3.0	6.0

Prerequisites

None

Language of Instruction	English
Course Level	Graduate Degree
Course Type	Compulsory
Mode of delivery
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Goals	The theory of partial differential equations has many applications in applied mathematics, physical sciences and engineering. This lecture deals with the solutions of first-order linear, semi linear, nonlinear partial differential equations and second order partial differential equations with constant variables. Also, higher order linear partial differential equations are presented.
Course Content	Higher order linear partial differential equations with constant coefficients, irreducible homogeneous equations, exponential type solutions, polynomial solutions, Nonhomogeneous partial differential equations, Linear partial differential equations with constant coefficients, Euler-Poisson-Darboux equation, Euler type of partial differential equations, Canonical form, canonical forms of hyperbolic, parabolic and elliptic type equations, Wave equation, heat equation, the method of seperation of variables , Laplace equation
Learning Outcomes	1) Solves linear partial derivative equations with high coefficient constant coefficients, finds the exponential type and polynomial solutions of irreducible partial differential equations. 2) Defines linear Partial Derivative Equations with variable coefficients. 3) Solves Euler-Poisson-Darboux and Euler type Partial Derivative Equations. 4) Classifies Partial Derivative Equations from the second step. 5) Obtain canonical forms of Partial Derivative Equations of Hyperbolic, Parabolic and Elliptic Type. 6) Introduces the Wave Equation and finds the D'Alembert solution of this equation. 7) Introduce Heat and Laplace Equations and get their solutions.