# COURSE UNIT TITLE

: MODERN ENGINEERING MATHEMATICS

#### Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
ETE 3018 MODERN ENGINEERING MATHEMATICS ELECTIVE 2 0 0 4

#### Offered By

Faculty of Engineering

#### Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

#### Course Coordinator

PROFESSOR VALERIY YAKHNO

#### Offered to

Electrical and Electronics Engineering
Computer Engineering
Mechanical Engineering
Metallurgical and Materials Engineering
Mechanical Engineering

#### Course Objective

To teach the fundamentals and main methods of problems solving for partial differential equations.

#### Learning Outcomes of the Course Unit

 1 Ability to use and express main partial differential equations (wave, heat-diffusion, Laplace, Poisson, Helmholtz). 2 Ability to state correctly the initial value and initial boundary value problems for the wave, heat-diffusion, Laplace, Poisson, Helmholtz equations. 3 Ability to apply main methods for solving the initial value and initial boundary value problems for the partial differential equations. 4 Ability to obtain and use the explicit formulas for the initial value problems for 1D,2D and 3D wave and heat-diffusion equations. 5 Ability to construct and apply the fundamental solutions for main partial differential equations.

Face -to- Face

None

None

#### Course Contents

 Week Subject Description 1 Main partial differential equations of mathematical physics: transport equation, Wave equation, heat-diffusion equation, the Laplace equation and Helholtz equation. 2 Initial value and initial boundary value problems for the wave and heat-diffusion equations. Boundary value problems for the Laplace, Poisson and Helmholtz equations. Correctness of the problem statements. 4 The solution of the initial value problem for 1D,2D and 3D wave equations by d' Alambert, Poisson and Kirchhoff formulas. 5 Eigenvalue and eigenfunction problems for the second order ordinary differential equations. Finding all eigenvalues and corresponding tho them eigenfunctions. Properties of eigenvalues and eigenfunctions. 6 Separation of the variables method for solving the initial boundary value problems for homogeneous wave and heat-diffusion equations. 7 The Fourier series expansion method for the construction of the solutions of the initial boundary value problems for inhomogeneous wave and heat-diffusion equations. 8 Solving boundary value problems for the Laplace equation by the Fourier series expansion method. 9 The Dirac delta function and its properties. The fundamental solution of the initial value problems for the ordinary differential equations. The Fourier transformation and its properties. 11 Conctruction of the fundamental solutions of the initial value problem for 1D, 2D and 3D wave equations. Applications of the fundamental solutions. 12 Conctruction of the fundamental solutions of the initial value problem for 1D, 2D and 3D heat-diffusion equations. Applications of the fundamental solutions. 13 The fundamental solutions for the Laplace and Helmholtz equations. Applications of the fundamental solutions. 14 Modeling and simulation of acoustic, elastic and electromagnetic waves.

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

Yardımcı kaynaklar: Vladimirov V.S. , Equations of Mathematical Physics, Marcel Dekker, Inc., New York, 1971

Lawrence C. Evans, Partial Differential Equations, American Mathematical Society, Providence, Rhode Island, 2000

Referanslar:
Diğer ders materyalleri: lecture notes of Prof. Dr. Valery Yakhno

Lectures
Homeworks
Examinations
Projects

#### Assessment Methods

 SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 ASG ASSIGNMENT 3 FIN FINAL EXAM 4 FCG FINAL COURSE GRADE MTE * 0.25 + ASG * 0.25 + FIN * 0.50 5 RST RESIT 6 FCG FINAL COURSE GRADE MTE * 0.25 + ASG * 0.25 + RST * 0.50

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

None

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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