1	Course Title:	APPLIED MATHEMATICS
2	Course Code:	TEK5001
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. OSMAN KOPMAZ
16	Course Lecturers:	Prof. Dr. OSMAN KOPMAZ
17	Contactinformation of the Course Coordinator:	okopmaz@uludag.edu.tr +90 224 294 19 62 Uludağ Üniversitesi, Mühendislik Mimarlık Fakültesi, Makine Mühendisliği Bölümü, Görükle, 16059 Bursa
18	Website:	http://www20.uludag.edu.tr/~mtd/
19	Objective of the Course:	Teach advanced mathematical methods which are used in solving engineering problems.
20	Contribution of the Course to Professional Development

21

Learning Outcomes:

1 Students who attend this course learn advanced topics and methods of mathematics.; 2 They can model engineering problems, and solve them using mathematical methods.;

22	Course Content:

Week	Theoretical	Practical
1	Review of ordinary differential equations. Series solutions of differential equations. Frobenius method.
2	Special differential equations. Bessel and modified Bessel differential equations. Classical and modified Bessel functions of first and second kind. 1st take-home.
3	Legendre differential equation and Legendre polynomials. General expansion theorem. Orthogonality and completeness. Orthogonal functions.
4	Fourier series. Fourier integrals and transform. Laplace transforms. 2nd take-home.
5	Partial differential equations. Deriving equations in engineering problems. One dimensional wave equation. D’Alembert solution.
6	Method of separation of variables. Initial and boundary value problems. Eigenvalue problems. Eigenvalues and eigenfunctions. Examples from vibrations theory and heat transfer. 3rd take-home.
7	Series solutions. Classification of second order partial differential equations. Elliptic, hyperbolic and parabolic equations. Characteristic curves.
8	Series solutions. Classification of second order partial differential equations. Elliptic, hyperbolic and parabolic equations. Characteristic curves.
9	Calculus of variations. Variations. Variation problems in integral form. Euler-Lagrange equations.
10	Application examples. Constrained variation problems.
11	Variational principles of mechanics. Lagrange equations of motion. Hamilton principle. 4th take-home.
12	Functions of one complex variable. Limit, continuity and derivatives of a complex function. Analyticity. Cauchy-Riemann conditions. Cauchy and Cauchy-Morera theorems.
13	Series expansions of complex functions. Taylor, Maclaurin and Laurent series. Theorem of residues. 5th take-home.
14	Applications of residue theorem. Calculation of improper integrals. Obtaining inverse Laplace transforms.

23	Textbooks, References and/or Other Materials:	C.R. Wylie - L. C. Barrett, Advanced Engineering Mathematics, McGraw Hill Publ. Comp. E. Kreyszig, Advanced Engineering Mathematics, J. Wiley Publ. Comp. B. Karaoğlu, Fizik ve Mühendislikte Matematik Yöntemler, Seçkin Yayıncılık.
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	25
Quiz	0	0
Homeworks, Performances	5	25
Final Exam	1	50
Total	7	100
Contribution of Term (Year) Learning Activities to Success Grade		50
Contribution of Final Exam to Success Grade		50
Total		100
Measurement and Evaluation Techniques Used in the Course
Information

25

ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	13	6	78
Homeworks, Performances	5	20	100
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	2,5	2,5
Others	0	0	0
Final Exams	1	2,5	2,5
Total WorkLoad			225
Total workload/ 30 hr			7,5
ECTS Credit of the Course			7,5

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 LO1 4 4 4 0 0 0 4 0 LO2 4 4 4 0 0 0 4 0

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High