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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 3052 PARTIAL DIFERENTIAL EQUATIONS COMPULSORY 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

INSTRUCTOR MELTEM ALTUNKAYNAK

Offered to

Mathematics (Evening) 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'Alambert'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. Linear partial differential operators and their characteristic curves and surfaces. 6 Classification of lineer second order equations and their reduction to a canonical form. 7 Linear second order equations in two independent variables, the Cauchy problem. 8 Midterm 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): Linear partial differential equations for scientists and engineers by Tyn Myint-U, and Lokenath Debnath, Birkhauser Boston Inc. Materials: Presentations of lectures

Planned Learning Activities and Teaching Methods

Lecture notes, Presentation, Solving problems

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 QUZ QUIZ 3 ASG ASSIGNMENT 4 FIN FINAL EXAM 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + FIN * 0.50 6 RST RESIT 7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + QUZ * 0.10 + ASG * 0.10 + RST * 0.50

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: (232) 3018586 E-mail: ali.sevimlican@deu.edu.tr Office: (232) 3018584

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 4 52 Preparations before/after weekly lectures 12 3 36 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparation for quiz etc. 2 3 6 Preparing assignments 2 10 20 Final 1 2 2 Midterm 1 2 2 Quiz etc. 1 1 1 TOTAL WORKLOAD (hours) 169

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 LO.1 5 3 4 4 LO.2 5 3 4 LO.3 5 5 3 4 4 LO.4 5 5 3 4 LO.5 5 3 4 5 5 LO.6 4 5 5 3 4 5 5