# COURSE UNIT TITLE

: MODERN ENGINEERING MATHEMATICS

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
EED 4007 MODERN ENGINEERING MATHEMATICS ELECTIVE 4 0 0 6

#### Offered By

Electrical and Electronics Engineering

#### Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

#### Course Coordinator

PROFESSOR VALERIY YAKHNO

#### Offered to

Electrical and Electronics Engineering

#### Course Objective

To teach the fundamentals and main methods of mathematical modeling real phenomena and processes.

#### Learning Outcomes of the Course Unit

 1 To be able to use and express the fundamental concepts ofmathematical modeling. 2 To be able to analyze and use mathematical models for acoustic, electromagnetic, elastic waves in different media and materials. 3 To be able to state initial value and initial boundary value problems for the wave, acoustic, and Maxwell s equations. 4 To be able to apply different methods for solving initial value and initial boundary value problems for the partial differential equations and Maxwell s system. 5 To be able to simulate acoustic, elastic and electromagnetic waves in different materials.

Face -to- Face

None

None

#### Course Contents

 Week Subject Description 1 Mathematical models of acoustic, elastic, electromagnetic wave phenomenon in materials and media: Electromagnetic waves in anisotropic crystals and dielectrics, geological media, biological tissues. 2 Maxwell's equations in magnetoelectric bi-anisotropic, magnetoelectroelastic and piezoelectric materials. Maxwell's equation in composite anisotropic materials, boundary conditions, matching conditions. 3 Statements of problems: Initial value and initial boundary value problems for wave and Maxwell's equations 4 The method of characteristics for the initial value problem of the Maxwell's equations. 5 Midterm 1 6 The reduction of the initial value problem of the Maxwell's equations to several initial value problems for the scalar partial differential equations; solving initial value problem for Maxwell's equations. 7 The Fourier transform and the Fourier series methods for solving the initial value and initial boundary value problems of wave equation. 8 The Fourier series methods for solving the initial boundary value problems for Maxwell's equations with perfect conductor conditions. Fourier transform method for solving the initial value problem of Maxwell's equations . 9 The Green's functions method for the ordinary differential equations 10 The Green's functions for wave equations.The solution of the initial value problem by the Green's function method. 11 Midterm 2 12 The Green's functions for the Maxwell's equations. 13 The finite element and finite difference methods for partial differential equations. 14 The boundary element method for the partial differential equation problems.

Erwin Kreyszig, Advanced Engineering Mathematics, 8th Ed., John Wiley & Sons Inc., 2001

Eom H.J., Electromagnetic Wave Theory for Boundary-Value Problems, Springer, Berlin, 2004

Yee K.S., Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Transactions on Antennas and Propagation, AP-14, vol.3, 302-307, 1966.

Yakhno V.G., Deriving the Time-Dependent Dyadic Green s Functions in Conductive Anisotropic Media, International Journal of Engineering Science, vol. 48, 332-342, 2010.

Referanslar:
lecture notes of Prof. Dr. Valery Yakhno

Lectures
Homeworks
Examinations

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE 1 MIDTERM EXAM 1 2 MTE 2 MIDTERM EXAM 2 3 PRJ PROJECT 4 FIN FINAL EXAM 5 FCG FINAL COURSE GRADE MTE 1 * 0.125 + MTE 2 * 0.125 + PRJ * 0.25 + FIN * 0.50

*** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

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Projects
Examinations

English

To be announced.

#### Contact Details for the Lecturer(s)

valery.yakhno@deu.edu.tr

#### Office Hours

Will be determined in the beginning of the term

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