COURSE SYLLABUS

SPECIAL FUNCTIONS ON MATHEMATICS

1	Course Title:	SPECIAL FUNCTIONS ON MATHEMATICS
2	Course Code:	MAT3043
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	3
6	Semester:	5
7	ECTS Credits Allocated:	5
8	Theoretical (hour/week):	3
9	Practice (hour/week) :	0
10	Laboratory (hour/week) :	0
11	Prerequisites:	Have taken the courses of Differential Equations I, II, Partial Differential Equations and Analysis III, IV and get passed grade
12	Recommended optional programme components:	None
13	Language:	Turkish
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. EMRULLAH YAŞAR
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	Prof.Dr. Emrullah Yaşar e-mail:eyasar@uludag.edu.tr;emrullah.yasar@gmail.com
18	Website:
19	Objective of the Course:	To construct the necessary background for students of the mathematics department to examine and analyze mathematical models emerging in other disciplines.
20	Contribution of the Course to Professional Development	Gains the background to follow the new developments in the field of mathematics.

Learning Outcomes:

1	Learns the necessary methods to examine the mathematical models encountered in applied science.;
2	Using this knowledge, it provides a mathematical approach to interdisciplinary issues.;
3	Can interprate the application of derivative and integration;
4	Can interprate the application of area and volume ;
5	Apply the Taylor and Fourier series to other areas.;
6	understand the Gamma and beta ve error functions;
7	Makes calculations on line integrals, Stokes theorem and tensor calculus.;
8	Knows some basic notations on complex calculus.;
9	can solve the partial differential equations.;
10	Can describe population dynamics, chaos and bifurcation.;

22	Course Content:

Week	Theoretical	Practical
1	Vectors, Linear Independence, Scalar and Vector Product, Triple Scalar Product, Triple Vector Product, Levi-Civita Tensor, Scalar and Vector Fields, Gradient, Divergence, Rotational, Laplacian
2	Derivative and its applications, integral and applications Length, area and volume elements in derivative, chain, cartesian, spherical and cylindrical coordinate systems,
3	Area and volume applications, Dirac delta function.
4	İnfinite sequences Taylor and Fourier sequences
5	Gamma, beta and error functions
6	Vector analysis,
7	Laplacian, line integral, Stokes theory, tensor analysis, metric tensor, numerical tensor.
8	Complex function theory: Complex arithmetic, imaginary numbers, complex functions, finding residues, conformal mapping.
9	Partial differential equations Laplace equation and its applications in cartesian, spherical and cylindrical systems
10	Heat conduction equation, quantum harmonic oscillator, vibrating membrane.
11	Integral transformations Fourier transformation, Laplace transformation, Melin transformation
12	Nonlinear dynamics and chaos Stable and unstable fixed points, logistic graphics,
13	Population dynamics, chaos and bifurcation.
14	Probability theory Mean and standard deviation, Some well known District and Continous probablity Distributions: Binomial, Gaussian and Poisson distribution

23	Textbooks, References and/or Other Materials:	MATHEMATICAL METHODS FOR STUDENTS OF PHYSICS AND RELATED FIELDS, S Hassanı, 2 nd edition Mathematical Methods in the Physical Sciences, M.L. Boas, John Wiley&Sons
24	Assesment

TERM LEARNING ACTIVITIES	NUMBER	PERCENT
Midterm Exam	1	40
Quiz	0	0
Homeworks, Performances	0	0
Final Exam	1	60
Total	2	100
Contribution of Term (Year) Learning Activities to Success Grade		40
Contribution of Final Exam to Success Grade		60
Total		100
Measurement and Evaluation Techniques Used in the Course	Measurement and evaluation are performed according to the Rules & Regulations of Bursa Uludağ University on Undergraduate Education.
Information

ECTS / WORK LOAD TABLE

CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High