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 Should have sufficient knowledge in mathematics, science, and subjects specific to the relevant engineering discipline.
2. P02 Should have the ability to use theoretical and applied knowledge in mathematics, science, and related engineering disciplines in complex engineering problems.
3. P03 Should have the ability to detect, define, formulate, and solve complex engineering problems.
4. P04 Should have the ability to select and apply appropriate analysis and modeling methods to solve complex engineering problems.
5. P05 Should have the ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions.
6. P06 Should have the ability to apply modern design methods.
7. P07 Should have the ability to develop, select, and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications.
8. P08 Should have the ability to use information technologies effectively.
9. P09 Should have the ability to design experiments, for the study of complex problems or discipline-specific research topics.
10. P10 Should have the ability to conduct experiments, collect data, analyze and interpret results for the study of complex problems or discipline-specific research topics.
11. P11 Should have the ability to work in intradisciplinary teams.
12. P12 Should have the ability to work in interdisciplinary teams.
13. P13 Should have the skills to work individually.
14. P14 Should have the ability to communicate effectively verbally and in writing.
15. P15 Should have the knowledge of at least one foreign language.
16. P16 Should be able to write effective reports, understand written reports, and prepare design and production reports.
17. P17 Should have the ability to make effective presentations.
18. P18 Should have the ability to give and have clear and understandable instructions.
19. P19 Should gain consciousness (awareness) about the necessity of lifelong learning.
20. P20 Should have the ability to access information.
21. P21 Should have the ability to follow developments in science and technology and constantly renew himself/herself.
22. P22 Should gain the awareness of professional and ethical responsibility and should act in accordance with ethical principles.
23. P23 Should gain knowledge about the standards used in engineering applications.
24. P24 Should gain knowledge about project management, risk management, and change management practices in business life.
25. P25 Should gain awareness about entrepreneurship, and innovation.
26. P26 Should gain knowledge about development in sustainability.
27. P27 Should gain knowledge about the effects of engineering practices on health, environment, and security at universal and social dimensions and the problems of the age reflected in the field of engineering.
28. P28 Awareness should be gained about the legal consequences of engineering solutions.

Po-Lo Matrix