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| ESM2018 | Engineering Mathematics | 3+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of ENERGY SYSTEMS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Doç. Dr. Esma ULUTAŞ | | Co-Lecturer | | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | To equip the students with the knowledge of applied mathematics to the such extent that they can understand the mathematical expressions taking place in their curriculum and that they can model, analyze, and interpret any engineering problem that they may face during their professional life.
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| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | model an engineering problem mathematically. | 1,5,11 | 1 | | LO - 2 : | recognize Fourier series, integrals, and transforms and know how to use them in the solution of engineering problems. | 1,5,11 | 1 | | LO - 3 : | recognize and define partial differential equatins and accompanying boundary and/or initial conditions. | 1,5,11 | 1 | | LO - 4 : | solve various forms of the heat equation and the wave equation through the use of the separation of variables technique. | 1,5,11 | 1 | | LO - 5 : | understand the theory of complex analytic functions. | 1,5,11 | 1 | | LO - 6 : | use the methods for analytic functions in solving more complicated heat conduction and fluid flow problems as well as simpler problems of mechanical vibrating systems. | 1,5,11 | 1 | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Mathematical modeling. Fourier analysis: Fourier series, integrals, and transforms. Partial differential equations: The method of separation of variables, solution of the heat conductin equation and the wave equation by separating variables. Complex analysis: complex numbers and functions, complex integration, Taylor series, Laurent series, residue integration and its use in the calculation of real integrals, geometrical interpretation of analytical functions, complex analysis and potential theory, sample applications to heat transfer and fluid mechanics problems. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Elements of mathematical modeling: Modeling, analysis, and interpretation. The interrelation of the physical laws including the conservation of mass, the conservation of energy, the conservation of linear momentum and the modeling. | | | Week 2 | Some modeling examples from various physical problems and engineering applications. | | | Week 3 | Fourier analysis: Fourier series, Fourier sine and cosine series. | | | Week 4 | Fourier itegral, Fourier sine and cosine transforms. | | | Week 5 | Partial differential equations: Basic concepts, the wave equation and its solution by separating variables, the use of Fourier series in the solution process. | | | Week 6 | Solution of heat equation by Fourier series. | | | Week 7 | Solution of heat equation by Fourier integrals and transforms. | | | Week 8 | Complex analysis: Complex numbers and functions, limit, continuity, and derivatives of a complex function. | | | Week 9 | Midterm exam | | | Week 10 | Complex integration: Line integral in the complex plane, Cauchy's integral theorem. | | | Week 11 | Taylor series: Power series, functions given by power series, power series as Taylor series. | | | Week 12 | Laurent series and residue integration method, residue integration of real integrals. | | | Week 13 | Geometrical interpretation of analytical functions. | | | Week 14 | Complex analysis and potential theory, application to heat transfer problems. | | | Week 15 | Complex analysis and potential theory, application to fluid mechanics problems. | | | Week 16 | End of the term exam | | | |
| 1 | Kreyszig, E. 2006; Advanced Engineering Mathematics, John Wiley, Singapore. | | | |
| 1 | O'Neil, P. V. 2003; Advanced Engineering Mathematics, Thomson, New York. | | | 2 | Greenberg, E. 1998; Advanced Engineering Mathematics, Prentice Hall, New Jersey. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 50 | | End-of-term exam | 16 | | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 3 | 13 | 39 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Arasınav için hazırlık | 15 | 1 | 15 | | Arasınav | 3 | 1 | 3 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 125 |
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