# 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.

#### Recomended or Required Reading

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.

None

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

None

#### Workload Calculation

 Activities Number Time (hours) Total Work Load (hours) Lectures 14 4 56 Preparation for midterm exam 2 2 4 Preparation for final exam 1 2 2 Preparing assignments 4 4 16 Design Project 4 3 12 Preparations before/after weekly lectures 14 4 56 Midterm 2 2 4 Projects 4 1 4 Final 1 2 2 TOTAL WORKLOAD (hours) 156

#### Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13
LO.15534
LO.25534
LO.35534
LO.45534
LO.55534