Information Package / Course Catalogue - Adnan Menderes University

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Advanced Engineering Mathematics II

Course Code	: EEE662
Course Type	: Area Elective
Couse Group	: Third Cycle (Doctorate Degree)
Education Language	: English
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

To help engineering graduate students complete their mathematical background necessary in graduate level researches.

Course Content

Linear algebra and eigenvalue problems, matrix operators, Sturm-Liouville theory, orthogonal functions, power series and Frobenius methods, Legendre polynomials, Associated Legendre polynomials, spherical harmonics, special functions and their orthogonality, Bessel equation, Bessel functions, Laguerre, Hermit, Gegenbauer, Chebyshev, and Gauss equations, theory of complex functions, complex derivative and integral, complex power series, convergence, Cauchy integral and calculation of rezidu, conformal mapping, Schwarts-Kristoffel transformation, Science&engineering applications of the mathematical methods being studied.

Name of Lecturer(s)

Learning Outcomes

1.	To be able to formulize and solve physical problems
2.	To be able to construct mathematical relations and analyze the results
3.	To be able to understand the mathematical methods used in engineering applications.
4.	To be able to discuss the mathematical methods used in engineering applications.
5.	To be able to apply the mathematical methods used in engineering applications.

Recommended or Required Reading

1.	Erwin Kreyszig, Advanced Engineering Mathematics 10th Edition, Wiley (2011)
2.	W.E. Boyce & R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems Eighth Edition (2005).
3.	Lecture notes.

Weekly Detailed Course Contents

Week 1 - Theoretical

Review of ordinary differential equations and differential equation systems

Week 2 - Theoretical

Science & engineering applications of ordinary differential equations (forced oscillatory motion, R-L-C circuits, and circuit systems, etc.)

Week 3 - Theoretical

Systems of differential equations and their solutions

Week 4 - Theoretical

Science & engineering applications systems of differential equation systems (problems in mechanics, rate and speed change problems of physical quantities, DC/AC circuit solutions, etc.)

Week 5 - Theoretical

Fourier series, Fourier expansion, Science and engineering applications

Week 6 - Theoretical

Fourier and Laplace transform

Week 7 - Theoretical

Science and engineering applications of Fourier and Laplace transform

Week 8 - Theoretical

Review-Midterm Exam

Week 9 - Theoretical

Sturm-Liouville theory, Eigenvalue problems and science & engineering applications

Week 10 - Theoretical

Infinite series and convergence tests, Power series, Taylor series and Binomial expansions

Week 11 - Theoretical

Power series solutions of differential equations

Week 12 - Theoretical

Singularity, Method of Frobenius and solutions of special functions (Bessel, Legendre, etc.)

Week 13 - Theoretical

Orthogonal functions; Bessel functions and Legendre polynomials, spherical harmonics, Science and engineering applications

Week 14 - Theoretical

Project presentations

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Assignment	2	%10
Term Assignment	1	%5
Project	1	%70
Midterm Examination	1	%15

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	3	3	84
Assignment	2	5	3	16
Term Project	1	10	2	12
Project	1	56	2	58
Midterm Examination	1	28	2	30
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12
OÇ-1	5	4	5	4	5	4	5	4	5	5	4	4
OÇ-2	4	5	5	4	4	5	5	4	3	5	4	5
OÇ-3	5	4	5	4	4	5	5	4	5	3	5	5
OÇ-4	4	5	5	4	4	5	5	4	4	5	4	5
OÇ-5	5	5	5	4	4	4	5	5	5	4	4	4

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