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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

Offered to

Mechanical Engineering Mechanical Engineering (Evening) Computer Engineering Metallurgical and Materials Engineering Electrical and Electronics 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.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

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.

Recomended or Required Reading

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

Planned Learning Activities and Teaching Methods

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 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.25 + ASG * 0.25 + RST * 0.50 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

Examinations

Language of Instruction

English

Course Policies and Rules

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

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 2 28 Preparation for midterm exam 2 2 4 Preparation for final exam 1 4 4 Design Project 3 2 6 Preparations before/after weekly lectures 14 2 28 Midterm 2 2 4 Projects 3 2 6 Final 1 2 2 TOTAL WORKLOAD (hours) 82

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