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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 5077 ASPECTS OF APPLIED MATHEMATICS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSOCIATE PROFESSOR BURCU SILINDIR YANTIR

Offered to

Mathematics Mathematics

Course Objective

The aim of this course is to introduce fundamental concepts of applied mathematics and build relations between other theoretical fields of mathematics.

Learning Outcomes of the Course Unit

1   Will be able to understand the motivation of Dirac delta function and the concepts of generalized functions that originate from physics and real analysis. 2   Will be able to use the properties of generalized functions. 3   Will be able to utilize Gamma, Beta, Bessel's functions and their relations 4   Will be able to analyze adjoint operators and Green's functions. 5   Will be able to utilize the method of Green's functions.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Good and fairly good functions. 2 Generalized functions (Dirac Delta function, Heaviside function). 3 Theory of generalized functions. 4 Fourier transform of generalized functions. 5 Fourier transform of generalized functions. 6 Theory of special functions: Gamma function and its properties. 7 Beta function and its properties. 8 Bessel's equation, Bessel's function. 9 ODE's and PDE's that can be reduced to Bessel's equation 10 Hypergeometric functions and their properties 11 Relations between hypergeometric functions and other special functions 12 Adjoint operators, generalized Green's identity 13 The method of Green's functions. 14 Sturm-Liouville problems, eigenfunction expansions. 15 Applications of Green functions 16 Review of the semester

Recomended or Required Reading

Textbooks: [1] Peter J. Olver, Introduction to partial differential equations, Springer, 2014. [2] Lawrence C. Evans, Partial differential equations, Graduate Studies in Mathematics, Volume 19, AMS, 1997. [3] Francis B. Hildebrand, Methods of Applied Mathematics, Prentice Hall, 1992. [4] J. David Logan, Applied Mathematics, John Wiley Inc. New York, 1997.

Planned Learning Activities and Teaching Methods

Lecture notes, presentations, problem solving.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 ASG ASSIGNMENT 2 PRS PRESENTATION 3 FCG FINAL COURSE GRADE ASG * 0.50 + PRS * 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

At least 70 percent of attendance to lectures is mandatory.

Contact Details for the Lecturer(s)

e-mail: burcu.silindir@deu.edu.tr Office: (232) 301 18590

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 4 52 Preparing assignments 1 35 35 Preparing presentations 1 45 45 Project Final Presentation 1 3 3 Project Assignment 1 3 3 TOTAL WORKLOAD (hours) 177

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