COURSE UNIT TITLE

: PARTIAL DIFERENTIAL EQUATIONS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3056 PARTIAL DIFERENTIAL EQUATIONS COMPULSORY 4 0 0 6

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR MELTEM ALTUNKAYNAK

Offered to

Mathematics

Course Objective

Aim of this course is to develop a basic understanding of the partial differential equations and related problems such as, initial value, boundary value and initial-boundary value problems in real world.

Learning Outcomes of the Course Unit

1   will be able to classify and define the methods to solve partial differential equations
2   will be able to define the canonical forms of partial differential equations
3   will be able to solve one dimensional homogeneous and inhomogeneous wave equations under initial conditions using method of characteristics
4   will be able to define domain of dependence for Cauchy problem of one dimensional wave equation using D'Alembert's solution
5   will be able to classify the initial value, boundary value and initial-boundary value problems for linear second order partial differential equations
6   will be able to solve initial-boundary value linear second order problems using Fourier series expansion

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 General definitions. Surfaces and curves in 3-D. One parameter and two parameter systems of surfaces.
2 Integral curves and first integrals of vector fields
3 Construction of an integral surface of a vector field containing given curve
4 First order equations in two independent variables. The Cauchy problem for quasilinear equations. Existence and Uniqueness of the solution
5 The Cauchy Kovalevsky theorem. Series solutions
6 Linear partial differential operators and their characteristic curves and surfaces
7 Classification of lineer second order equations and their reduction to a canonical form. Midterm
8 Linear second order equations in two independent variables, the Cauchy problem
9 The one dimensional wave equations; initial value problem, d'Alambert's solution
10 The domain of dependence inequality. The energy method. Uniqueness in the initial value problem. Domain of dependence and range of influence
11 Sturm Liouville problems and generalized Fourier series
12 The inhomogeneous one dimensional wave equation. The initial boundary value problems and their solutions by separation of variables
13 The inhomogeneous one dimensional heat equation. The initial boundary value problems and their solutions by separation of variables
14 One dimensional Laplace equation. The boundary value problems and their solutions by separation of variables

Recomended or Required Reading

Textbook(s): Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou , Dale W. Thoe , Dover Publications Inc.

Supplementary Book(s):
1.Linear partial differential equations for scientists and engineers by Tyn Myint-U, and Lokenath Debnath, Birkhauser Boston Inc.
2.Introduction to partial differential equations, Peter J. Olver, 2014, Springer.
Materials: Lecture notes, problem solving
3.Partial Differential Equations: An Introduction , Walter A. Strauss

Planned Learning Activities and Teaching Methods

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FIN FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50
4 RST RESIT
5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50


*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

E-mail: meltem.topcuoglu@deu.edu.tr
Office:

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparation for midterm exam 1 30 30
Preparations before/after weekly lectures 13 3 39
Preparation for final exam 1 30 30
Midterm 1 2 2
Final 1 2 2
TOTAL WORKLOAD (hours) 155

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.155344
LO.25534
LO.3555344
LO.455534
LO.5553455
LO.645553455

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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