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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4024 NUMERICAL SOLUTION OF PARTIAL DIFEREN.EQUATIONS ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR MELTEM ADIYAMAN

Offered to

Mathematics (Evening) Mathematics (English)

Course Objective

This course aims to introduce students to basic numerical methods and theory underlying numerical methods for approximation of partial differential equations.

Learning Outcomes of the Course Unit

1   will be able to apply numerical methods to partial differential equations. 2   will be able to write an appropriate program to find numerical solution of a partial differential equation. 3   will be able to investigate errors of the method used to find approximate solution of a partial differential equation. 4   will be able to investigate the stability of the methods interms of eigenvalues. 5   will be able to interpret obtained data and graphics.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Finite difference approximation to derivatives, notations for functions of several variables 2 An explicit finite difference approximation to parabolic equations 3 Local truncation error and consistency, stability of the method, convergence 4 Crank-Nicolson implicit method and its error analysis 5 Stability analysis by the matrix method, the eigenvalues of a common tridiagonal matrix 6 Von Neumann method 7 Physical examples and their numerical solutions 8 Examples for midterm, Mid-term exam 9 Solutions of mid-term examination 10 Finite difference approximation to elliptic equations 11 Error analysis of finite difference approximation to elliptic equations 12 Lax s equivalence theorem and examples 13 Finite difference approximation to hyperbolic equations 14 Presentations of homeworks

Recomended or Required Reading

Textbook(s): Solution of Partial Differential Equations, G. D. Smith, Claredon Press, Oxford. Supplementary Book(s): Numerical Analysis, D. Kincaid, W Cheney 2nd ed. ISBN 0534338925References: Materials: Presentations

Planned Learning Activities and Teaching Methods

Lecture Notes Presentations Solving problem

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + ASG * 0.25 + FIN * 0.50 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + ASG * 0.25 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

Midterm, Final

Language of Instruction

English

Course Policies and Rules

1. Attending at least 70 percent of lectures is mandatory. 2. Plagiarism of any type will result in disciplinary action

Contact Details for the Lecturer(s)

e-mail: meltem.evrenosoglu@deu.edu.tr tel: (232) 3018575

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparations before/after weekly lectures 14 2 28 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 1 27 27 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 165

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 5 5 3 5 2 4 2 LO.2 3 5 3 5 4 3 LO.3 5 3 5 5 5 2 4 LO.4 5 5 5 5 3 2 2 LO.5 5 5 3 3 3 3 2 5