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| MM2014 | Applied Mathematics | 3+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MECHANICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Zehra ŞAHİN | | Co-Lecturer | PROF. DR. Zehra ŞAHİN, | | 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. | 1,2 | 1 | | LO - 2 : | recognize Fourier series and know how to use them in the solution of engineering problems. | 1,2 | 1 | | LO - 3 : | recognize and define partial differential equatins and accompanying boundary and/or initial conditions. | 1,2 | 1 | | LO - 4 : | solve various forms of the heat equation and the wave equation through the use of the separation of variables technique. | 1,2 | 1 | | LO - 5 : | 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. | 1,2 | 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 | | |
| Matrices and determinants. Linear algebraic equations and their solutions. Mathematical modeling. Fourier analysis: Fourier series. Partial differential equations: The method of separation of variables, solution of the heat conductin equation and the wave equation by separating variables.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Matrices and determinants, numerical examples | | | Week 2 | Linear algebraic equations and their solutions | | | Week 3 | 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 4 | Some modeling examples from various physical problems and engineering applications. | | | Week 5 | Some modeling examples from various physical problems and engineering applications. | | | Week 6 | Fourier analysis: Fourier series. | | | Week 7 | Fourier sine and cosine transforms. | | | Week 8 | Partial differential equations: Basic concepts, the wave equation and its solution by separating variables, the use of Fourier series in the solution process. | | | Week 9 | Midterm exam | | | Week 10 | Solution of wave equation by separating variables. | | | Week 11 | Solution of wave equation by separating variables. | | | Week 12 | Solution of heat equation by Fourier series. | | | Week 13 | Heat equation: One-dimensional transient conduction problems
| | | Week 14 | Heat equation: Two-dimensional steady-state conduction problems.
| | | Week 15 | Heat equation: Two-dimensional steady-state conduction 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 | 9/05/2021 | 1 | 50 | | End-of-term exam | 15 | 04/07/2021 | 1 | 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 | 14 | 42 | | Sınıf dışı çalışma | 4 | 14 | 56 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 4 | 6 | 24 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 4 | 6 | 24 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 150 |
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