COURSE SYLLABUS

ADVANCED ENGINEERING MATHEMATICS

1	Course Title:	ADVANCED ENGINEERING MATHEMATICS
2	Course Code:	MAK5001
3	Type of Course:	Compulsory
4	Level of Course:	Second Cycle
5	Year of Study:	1
6	Semester:	1
7	ECTS Credits Allocated:	6
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	None
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. MURAT REİS
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	reis@uludag.edu.tr
18	Website:	https://www.youtube.com/watch?v=xzwvv8HxFrY&list=PLsxmiXTQvQn_RwSszpm2nARgRDVs01sqU
19	Objective of the Course:	To learn advanced mathematical methods used in solving engineering problems.
20	Contribution of the Course to Professional Development	This course contributes to the student's ability to analyze and solve engineering problems.

Learning Outcomes:

1	Students taking this course learn advanced math topics and methods.;
2	They can model engineering problems and solve them using mathematical methods.;

22	Course Content:

Week	Theoretical	Practical
1	Review of ordinary differential equations.
2	Ordinary differential equations engineering applications
3	Series solutions of differential equations. Frobenius method.
4	Special differential equations. Bessel and modified Bessel differential equations and series solutions. First and second order classical and modified Bessel functions.
5	Legendre differential equation and Legendre polynomials.
6	General expansion theorem. Orthogonality and completeness. Orthogonal functions.
7	Fourier series. Fourier integrals and Fourier transform.
8	Laplace transform
9	Partial differential equations. Equation extraction in engineering problems. One dimensional wave equation. D'Alembert solution.
10	Method of Separation of variables. Initial and boundary value problems. Eigenvalue problems. Eigenvalues and eigenfunctions. Theory of vibration and examples of heat transfer
11	Serial solutions. Classification of second order partial differential equations. Elliptic, hyperbolic and parabolic equations. Characteristic curves.
12	Calculus of variations. Variations. Variation problems in integral form. Euler-Lagrange equation.
13	Variational principles of mechanics. Lagrange equations of motion. Hamilton principle.
14	Functions of a single complex variable. Limit, continuity and derivative in complex functions. Analytics. Cauchy-Riemann conditions. Cauchy and Cauchy-Morera theorems.

23	Textbooks, References and/or Other Materials:	Differential Equations for Engineers and Scientists, Yunus Cengel
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	0	0
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	100
Total	1	100
Contribution of Term (Year) Learning Activities to Success Grade		0
Contribution of Final Exam to Success Grade		100
Total		100
Measurement and Evaluation Techniques Used in the Course	Absolute evaluation is used.
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

	PQ1	PQ2	PQ3	PQ4	PQ5	PQ6	PQ7	PQ8	PQ9	PQ10
LO1	4	4	4	4	0	0	0	0	0	0
LO2	4	4	4	4	0	0	0	0	0	0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High