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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 CIVIL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Erhan COŞKUN | | Co-Lecturer | Other instructor assigned for the course | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course is designed to introduce the fundamental mathematical concepts of Calculus that would serve as a foundation for subsequent engineering courses at the indermediate level. |
| 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 | | |
| Vectors, the cross product, lines and planes in space, cylinders, surfaces of the second degree, matrices, linear equation systems, elementary matrix operations, Gauss elimination, eigenvalues and eigenvectors. Sequences and convergence, infinite series, convergence tests for infinite series, alternating series and their convergence, absolute and conditional convergence, power series and its interval of convergence, Taylor Series. Funtions of several variables, limits and continuity, partial derivatives, the chain rule, gradients and directional derivatives, extreme value of functions defined on restricted domains. Double integrals, polar coordinates, change of variables in double integrals and double integrals in polar coordinates, applications of double integrals (moment and centres of mass).
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Vectors and vector algebra, lines ann planes in space. | | | Week 2 | Linear system of equations, matrices and matrix algebra. | | | Week 3 | Gauss elimination method, eigenvalues and eigenfunctions. | | | Week 4 | Squences and their convergence, series and their convergence. | | | Week 5 | Convergence tests for series and power series. | | | Week 6 | Taylor and Maclaurin series | | | Week 7 | Conics, polar coordinate system | | | Week 8 | Calculus of vector-valued functions | | | Week 9 | Mid-term exam | | | Week 10 | Multivariable functions, limit, continuity and partial derivatives. | | | Week 11 | Chain rule, directional derivatives and gradient vectors | | | Week 12 | Extreme values, absolute maxima and minima,Lagrange multipliers (Single constraint case) | | | Week 13 | Double integrals and their applications (Area) | | | Week 14 | Substitutions in Double Integrals, Double integrals in Polar Coordinates and polar curves and their applications (mass and density, center of mass ). | | | Week 15 | General assessment | | | Week 16 | Final exam | | | |
| 1 | Dennis G. Zill, Warren S. Wright, Matematik Cilt 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. | | | |
| 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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