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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MAT 4013 APPLIED MATHEMATICS I ELECTIVE 4 0 0 7

Offered By

Mathematics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

DOCTOR MELTEM ALTUNKAYNAK

Offered to

Mathematics (Evening) Mathematics

Course Objective

In this course, mathematical modelling of two and three dimensional initial and boundary value problems for heat and wave, and their solutions, will be considered.

Learning Outcomes of the Course Unit

1   Will be able to solve initial and boundary value problem for heat equation 2   Will be able to solve initial and boundary value problem for wave equation 3   Will be able to define Fourier transform and its properties 4   Will be able to use Fourier integral formulas for solving initial and boundary value problems in unbounded domains 5   Will be able to construct Green s function for heat and wave operators

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Some concepts from differential equations 2 Well posed and ill posed problems 3 Fourier 's method 4 Eigenvalue-eigenfunction problem for Laplace operator 5 Initial and boundary value problems for heat equation in 2D and 3D 6 Initial and boundary value problems for wave equation in 2D and 3D. 7 Laplace equation in 2D and 3D. 8 Fourier transforms. Solving intial and boundary value problems using Fourier transforms. 9 Fourier integral formulas 10 Application of Fourier integral formulas to initial and boundary value problems 11 Dirac delta function. Green' s function of initial value problem for ordinary differential equations 12 Fourier transform of dirac delta function and its properties 13 Construction of Green' s function for heat and wave operators 14 Solving initial value problems using Green' s functions

Recomended or Required Reading

Textbook(s): P.V. O' Neil, Advanced Engineering Mathematics Supplementary Book(s): V.S. Vladimirov, Equations of Mathematical Physics

Planned Learning Activities and Teaching Methods

Lectures and problem solving

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, tel: (232) 301 8607

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