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| MAT1008 | Mathematics - II | 4+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of METALLURGICAL and MATERIALS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Doç. Dr. Ümit ERTUĞRUL | | Co-Lecturer | Other instructors assigned for the course | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide basic mathematical tools for engineering students. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | Analyse problems requiring vector and matrix algebra, including eigenvalue and eigenvector problems | 1,2 | | | LO - 2 : | Solve linear system of qquations | 1,2 | | | LO - 3 : | Analize convergence of sequences and series. | 1,2 | | | LO - 4 : | understand functions of two and three variables and their properties | 1,2 | | | LO - 5 : | know the concepts of limit and continuity of functions of two and three variables | 1,2 | | | LO - 6 : | know the concepts of derivative and apply it to engineering problems | 1,2 | | | LO - 7 : | know the concepts of integration and apply it to engineering problems | 1,2 | | | 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 | | |
| Vektors, vektor algebra, lines and planes in space, matrices, system of linear equations, matrix algebra, Gauss elimination, eigenvalues and eigenvectors. Sequences, convergence of squences, series, convergence tests(integral ,comparision, ratio, and root tests). Power series and their convergence, Taylor series. Polar coordinates. Vector valued functions, curvature and acceleration. Multi-valued functions, limit, continuity, partial derivatives, chain rule, directional derivative, extreme values for functions of two variables, Lagrange multipliers. Double integrals, transformation of domains in double integrals, integration in polar coorrdinates, appli,cation of double integrals(mass, moment). Line integrals. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Vectors in the plane, vectors in three-dimensional space, algebraic operations on vectors, cross product and scalar triple product of vectors. | | | Week 2 | Lines and planes in space, cylinders and second-degree surfaces. | | | Week 3 | Systems of linear equations and matrices, matrix operations and determinant. | | | Week 4 | Solution by Gaussian elimination, eigenvalues and eigenvectors. | | | Week 5 | Sequences and convergence, infinite series, geometric series, telescoping series, harmonic series. | | | Week 6 | Convergence tests for series, comparison test - limit comparison, ratio test and root test, alternating series test, power series, Taylor and Maclaurin series.
| | | Week 7 | Multivariable functions, level curves, limits and continuity in multivariable functions, partial derivatives, higher-order partial derivatives.
| | | Week 8 | Chain rule, implicit functions, gradients, and directional derivative.
| | | Week 9 | Mid-term exam | | | Week 10 | Applications of partial derivatives: classification of critical points, partial derivatives with constrained variables. | | | Week 11 | Double integrals (rectangular), double integrals (in general regions), area calculation with double integrals
| | | Week 12 | Polar coordinates, region transformation in polar coordinates, double integrals in polar coordinates. | | | Week 13 | Region transformation, change of variables in double integrals. | | | Week 14 | Applications of double integrals: mass moment calculation, applications of double integrals: mass moment calculation, parameterization of curves in the plane. | | | Week 15 | Calculations with parametric curves. | | | Week 16 | Final exam | | | |
| 1 | Dennis G. Zill, Warren S. Wright, Matematik Cilt I-II(Calculus Early Transcendentals, 4. basımdan çeviri) Çeviri Editörü: Prof. Dr. İsmail Naci Cangül, Nobel Yayınevi, 2011. | | | 2 | C. Henry Edwards, David E. Penney: Calculus, Matrix Version (6th Edition), Prentice Hall, 2003. | | | |
| 1 | Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001. Calculus ve Analitik Geometri, Cilt I-II, Beta Yayınları, İstanbul. | | | 2 | Robert A. Adams, Christopher Essex: Kalkülüs Eksiksiz Bir Ders Cilt I- II (Calculus a Complete Course 7. Baskıdan çeviri), Palme Yayıncılık, Ankara, 2012 (Çevirenler: Prof. Dr. Mehmet Terziler, Yrd. Doç. Dr. Tahsin Öner) | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | | 50 | | End-of-term exam | 16 | | | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 150 |
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