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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4014 APPLIED MATHEMATICS II ELECTIVE 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

In this course, theory and applications of integral operators and introduction to calculus of variations will be considered.

Learning Outcomes of the Course Unit

1   will be able to solve Volterra integral equations 2   will be able to solve Fredholm integral equations 3   will be able to reduce differential equations to integral equations 4   will be able to find maximum or minimum of a functional using calculus of variations technique 5   will be able to obtain Euler's equation for a functional depends on several functions

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Introduction to integral equations 2 Volterra integral equations 3 Iterated kernels and resolvent for Volterra integral equations 4 Method of successive approximations 5 Fredholm integral equations 6 Iterated kernels and resolvent for Fredholm integral equations 7 Integral equations with degenerate kernels 8 Midterm 9 Fredholm's Theorems 10 Eigenvalue and eigenfunction problems for integral equations 11 The calculus of variations. Examples of some fundamental problems of the calculus of variations 12 Fundamental lemma of the calculus of variations 13 Constructing Euler's equation in elementary case 14 Euler's equation for a functional depends on several functions and higher order derivatives

Recomended or Required Reading

Textbook(s): V.S. Vladimirov, Equations of Mathematical Physics Supplementary Book(s): F.B. Hildebrand Methods of Applied Mathematics

Planned Learning Activities and Teaching Methods

Lecture notes

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

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: ali.sevimlican@deu.edu.tr, tel: (232) 301 85 84 e-mail: meltem.topcuoglu@deu.edu.tr, tel: (232) 301 85 86

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 4 48 Preparation for midterm exam 1 30 30 Preparation for final exam 1 30 30 Final 1 2,5 3 Midterm 1 2,5 3 TOTAL WORKLOAD (hours) 166

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