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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 3026 SPECIAL FUNCTIONS AND DIFERENTIAL EQNS. ELECTIVE 4 0 0 7

Offered By

Mathematics (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR MELTEM ALTUNKAYNAK

Offered to

Mathematics (Evening) Mathematics (English)

Course Objective

This course brings an overview of some special functions which are arise in solving some ordinary differential equations.

Learning Outcomes of the Course Unit

1   will be able to solve Bessel s differential equations 2   will be able to solve Legendre s differential equations 3   will be able to solve eigenvalue and eigenfunction problems for Bessel s and Legendre s operators 4   will be able to use properties of Gamma, Bessel s and Legendre s functions. 5   will be able to solve partial differential equations using spherical functions.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Gamma function and its properties 2 Bessel's differential equation 3 Bessel and Nuemann functions 4 Properties of Bessel and Nuemann functions 5 Sturm-Liouville problem for Bessel's differential operator 6 Properties of eigenvalues and eigenfunctions for Bessel's differential operator 7 Legendre polynomials and their properties. Rodrigue's formula 8 Sturm-Liouville problems for Legendre's differential operator 9 Properties of eigenvalues and eigenfunctions for Legendre's differential operator 10 Associated Legendre polynomials and their properties 11 Associated Legendre differential equation 12 Sturm-Liouville problems for associated Legendre differential operator 13 Spherical functions and their properties. Beltrami's operator 14 Applications of special functions for solving initial boundary value problems for partial differential equations

Recomended or Required Reading

Textbook(s): Theory and problems of Fourier analysis with applications to boundary value problems, M. R. Spiegel Supplementary Book(s): Advanced engineering mathematics, P. V. O Neil References: Special functions and their applications, N. N. Lebedev, R. Silverman

Planned Learning Activities and Teaching Methods

Lecture notes

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 VZ Vize 2 FN Final 3 BNS BNS VZ * 0.40 + FN * 0.60 4 BUT Bütünleme Notu 5 BBN Bütünleme Sonu Başarı Notu VZ * 0.40 + BUT * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Evaluation of exams.

Language of Instruction

English

Course Policies and Rules

Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the undergraduate policy at https://fen.deu.edu.tr/en/

Contact Details for the Lecturer(s)

e-mail: meltem.topcuoglu@deu.edu.tr Office: (232) 3018607

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 4 56 Preparation for midterm exam 1 25 25 Preparation for final exam 1 25 25 Final 1 2,5 3 Midterm 1 2,5 3 TOTAL WORKLOAD (hours) 168

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