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| FBE5007 | Advanced Engineering Mathematics | 3+0+0 | ECTS:7.5 | | Year / Semester | Spring Semester | | Level of Course | Second Cycle | | Status | Elective | | Department | | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 3 hours of lectures per week | | Lecturer | Prof. Dr. Talat Şükrü ÖZŞAHİN | | Co-Lecturer | Prof. Dr. Ahmet Birinci | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The main objective of this course is to acquaint the graduate students with advanced level engineering mathematics so that they can formulate, apply, and solve the physical problems of interest by use of both advanced level analytical and numerical methods of engineering (or applied) mathematics. |
| Programme Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | PO - 1 : | gain the ability to solve problems encountered in engineering applications using mathematical principles, | | 1, | | PO - 2 : | apply differential equations to engineering problems, | | 1, | | PO - 3 : | defines mathematical concepts used in his/her field of science, | | 1, | | PO - 4 : | interprets the relationships between the mathematical concepts learned, | | 1, | | PO - 5 : | applies the mathematical relationships she has established to solve problems she may encounter | | 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), PO : Learning Outcome | | |
| Mathematical preliminaries (ordinary and partial differential equations); ordinary differantial equations; Cauchy-Euler differantial equation; Solution of differential equations with series (Taylor and Frobenius series); special functions; (gamma, faktorial, orthogonal, Bessel, dirac delta, heaviside unit step functions); Legendre, Laguerre, Hermit differential equations and polynomials; boundary value problems; Laplace transforms; Solution of constant coefficient differential equations using Laplace transform; convolution; Fourier series; fourier integrals; Fourier transforms; partial differential equations and engineering applications.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Mathematical preliminaries | | | Week 2 | Ordinary differantial equations | | | Week 3 | Ordinary differantial equations | | | Week 4 | Cauchy-Euler differantial equation | | | Week 5 | Solution of differential equations with series | | | Week 6 | Special functions | | | Week 7 | Legendre, Laguerre, Hermit differential equations and polynomials | | | Week 8 | Boundary value problems | | | Week 9 | Mid-term exam | | | Week 10 | Laplace transforms, convolution | | | Week 11 | Fourier series | | | Week 12 | Quiz | | | Week 13 | Fourier integrals, fourier transforms | | | Week 14 | Partial differential equations and engineering applications | | | Week 15 | Partial differential equations and engineering applications | | | Week 16 | Final exam | | | |
| 1 | Kreyszig, E. (2011). Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York (10th Edition). | | | |
| 1 | Stroud, K. A., and Booth,D. J. (2011) .Advanced Engineering Mathematics, Bloomsbury Academic (5th edition) | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 2 | 30 | | Quiz | 12 | | 2 | 20 | | 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 | 14 | 3 | 42 | | Sınıf dışı çalışma | 12 | 5 | 60 | | Arasınav için hazırlık | 10 | 2 | 20 | | Arasınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 12 | 2 | 24 | | Dönem sonu sınavı | 1 | 1 | 1 | | Total work load | | | 148 |
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