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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 6044 NUMERICAL METHODS FOR TWO-POINT BOUNDARY VALUE PROBLEMS ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR MELTEM ADIYAMAN

Offered to

Mathematics (English) Mathematics (English)

Course Objective

This course aims to give the numerical methods for two-point Boundary value Problems together with the error analysis.

Learning Outcomes of the Course Unit

1   will be able to know the existence theorems for initial value and two point boundary value problems. 2   will be able to know numerical methods for initial value problems and iterative methods for solving nonlinear problems 3   will be able know and analyze the finite difference methods for two-point Boundary Value Problems 4   will be able to know integral equation methods for Boundary Value Problems 5   will be able to understand solution methods of eigenvalue problems

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Existence and uniqueness Theory of Initial value Problems 2 Existence and uniqueness theory of two-point boundary value problems 3 Numerical methods for initial value problems 4 Iterative solution of nonlinear systems, Contracting maps 5 Shooting methods for linear second order boundary value problems and systems 6 Shooting methods for non-linear second order boundary value problems 7 Finite Difference Methods to linear second order boundary value problems 8 Midterm 9 Difference Corrections and Extrapolation methods 10 Green's Functions, Equivalent Integral equations 11 Numerical Solution of integral equations 12 Introduction to Sturm-Liouville Eigenvalue Problems 13 Initial value methods for eigenvalue methods 14 Finite difference methods for eigenvalue problems

Recomended or Required Reading

Numerical Methods for two-point Boundary Value Problems, Herbert B. Keller

Planned Learning Activities and Teaching Methods

Lecture notes Presentation Homeworks

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.20 + ASG * 0.40 + FIN * 0.40 5 RST RESIT 6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.20 + ASG * 0.40 + RST * 0.40

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

sennur.somali@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 3 39 Preparations before/after weekly lectures 13 3 39 Preparation for midterm exam 1 20 20 Preparation for final exam 1 30 30 Preparing assignments 10 6 60 Midterm 1 3 3 Final 1 3 3 TOTAL WORKLOAD (hours) 194

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 LO.1 5 5 5 4 3 2 3 4 LO.2 5 5 5 5 5 4 5 5 3 4 4 LO.3 5 5 5 5 5 4 5 5 3 4 4 LO.4 5 5 5 5 5 4 5 5 3 4 4 LO.5 5 5 5 5 5 4 5 5 3 4 4