1	Course Title:	GEOMETRIC ALGEBRA AND APPLIED ANALYSIS II
2	Course Code:	MAT4114
3	Type of Course:	Optional
4	Level of Course:	First Cycle
5	Year of Study:	4
6	Semester:	8
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:	English
14	Mode of Delivery:	Face to face
15	Course Coordinator:	Prof. Dr. Kadri Arslan
16	Course Lecturers:
17	Contactinformation of the Course Coordinator:	arslan@uludag.edu.tr
18	Website:
19	Objective of the Course:	To introduce Fourier analysis, complex analysis and partial differential equation techniques and principles, teach their use and application through various problems in engineering.
20	Contribution of the Course to Professional Development	Contribution to academic development

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Learning Outcomes:

1 Students gain essential knowledge and skills for further study in partial differential equations, Fourier analysis, complex analysis, conformal mapping and related fields.; 2 Students learn the basic knowledge about the solution of partial differential equations, Fourier analysis and complex analysis with Laurence series.; 3 Students practice on engineering problems related to given course content.;

22	Course Content:

Week	Theoretical	Practical
1	Fourier series, forced oscillations, orthogonal functions.
2	Orthogonal series, Fourier integral, Fourier cosine and sine transforms.
3	Partial differential equations, basic concepts of PDEs.
4	Solution by separating variables, use of Fourier series,
5	Heat equation, solution by Fourier series, steady two-dimensional heat problems.
6	Laplacian in polar coordinates, Laplace’s equation in cylindrical and spherical coordinates, solution of PDEs by Laplace transforms.
7	Complex numbers and their geometric representation, polar form of complex numbers, powers and roots.
8	Cauchy–Riemann equations, Laplace's equation, exponential function, trigonometric, hyperbolic functions.
9	Complex integration, Line integral in the complex plane, Cauchy’s integral formula.
10	Power series, functions given by power series, Taylor and Maclaurin series.
11	Laurent Series, singularities and zeros, residue integration method.
12	Geometry of analytic functions, conformal mapping.
13	Complex analysis and potential theory, electrostatic fields, use of conformal mapping.
14	Heat Problems, Fluid Flow.

23	Textbooks, References and/or Other Materials:	Duffy, D. G., "Advanced Engineering Mathematics with Matlab”, CRC Press. (2022). James, G., David Burley, D., Clements D., Dyke P., and Searl J., "Advanced Modern Engineering Mathematics, Prentice Hall. (2011).
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 is carried out according to the priciples of Bursa uludag University Associate and Undergraduate Education Regulation.
Information

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ECTS / WORK LOAD TABLE

Activites	NUMBER	TIME [Hour]	Total WorkLoad [Hour]
Theoretical	14	3	42
Practicals/Labs	0	0	0
Self Study and Preparation	14	9	126
Homeworks, Performances	0	0	0
Projects	0	0	0
Field Studies	0	0	0
Midtermexams	1	6	6
Others	0	0	0
Final Exams	1	6	6
Total WorkLoad			180
Total workload/ 30 hr			6
ECTS Credit of the Course			6

26	CONTRIBUTION OF LEARNING OUTCOMES TO PROGRAMME QUALIFICATIONS
PQ1 PQ2 PQ3 PQ4 PQ5 PQ6 PQ7 PQ8 PQ9 PQ10 LO1 1 1 2 0 2 2 2 3 3 3 LO2 1 2 3 0 2 3 3 4 3 4 LO3 2 2 2 0 3 3 3 3 4 3

LO: Learning Objectives

PQ: Program Qualifications

Contribution Level:

1 Very Low

2 Low

3 Medium

4 High

5 Very High