MATHEMATICAL METHODS FOR ENGINEERS

Course Description

Aim of this course is to provide students with a strong foundation in complex analysis and numerical methods, essential tools in mathematics, computer science, physical sciences, and engineering. Topics begin with complex numbers, their algebra, and polar representation, followed by complex functions, limits, continuity, analyticity, and the Cauchy-Riemann equations. Students will study line integrals, the Cauchy integral formula, isolated singularities, and the residue theorem. The numerical methods section covers numerical error, solutions of nonlinear equations, convergence analysis, and direct and iterative methods for solving systems of linear equations. Additional topics include interpolation, curve fitting, and numerical differentiation and integration. Applications involve examples with both real and complex variables to equip students with practical problem-solving skills.

MATHEMATICAL METHODS FOR ENGINEERS

Evaluation Tools (Active Term)

Course outcomes

1. 01 Able to identify complex numbers and functions
2. 02 Able to solve complex derivation
3. 03 Able to solve complex integration
4. 04 Able to use complex calculus to solve engineering problems

Course Syllabus

Reference Books & Course Materials

1. 01 Ruel v. Churchill, Complex variables and Applications, 7th edition. McgrawHill, 2004. ISBN 978–0–07–305194–9—ISBN 0–07–305194–2
2. 02 Numerical Analysis, Richard L. Burden, J. Dougles Faires, 9th Edition. ISBN-13: 978-0-538-73351-9
3. 03 Mühendisler İçin Sayısal Çözümleme Yrd. Doç. Dr. Vedat Tavas, Prof. Dr. Osman Yazıcıoğlu, Prof. Dr. Oğuz Borat,
4. 04 Komplex fonksiyonlar teoresi, Turgut Başkan, Nobel Yayınevi, 1998.

Learning Outcomes

1. L01 Able to identify complex numbers and functions
2. L02 Able to solve complex derivation
3. L03 Able to solve complex integration
4. L04 Able to use complex calculus to solve engineering problems

Program Outcomes

1. P01 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems.
2. P02 Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3. P03 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4. P04 Ability to devise, select, and use modern techniques and tools needed for analysing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively
5. P05 Ability to design and conduct experiments, gather data, analyse and interpret results for investigating complex engineering problems or discipline specific research questions
6. P06 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7. P07 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8. P08 Recognition of the need for lifelong learning ; ability to access information, to follow developments in science and technology, and to continue to educate him/herself
9. P09 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10. P10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11. P11 Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.

Po-Lo Matrix