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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 : | understand basic vector and matrix operations
| 1,2,4 | | | LO - 2 : | solve linear system of equations | 1,2,4 | | | LO - 3 : | Analize convergence of sequences and series. | 1,2,4 | | | LO - 4 : | understand functions of two and three variables and their properties | 1,2,4 | | | LO - 5 : | know the concepts of limit and continuity of functions of two variables | 1,2,4 | | | LO - 6 : | know the concepts of derivative of functions of two variables and apply it to engineering problems | 1,2,4 | | | LO - 7 : | know the concepts of integration of functions of two variables and apply it to engineering problems | 1,2,4 | | | 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 | | | Week 2 | Lines and planes in spaces, surfaces of the second degree | | | Week 3 | Linear system of equations, Matrices and determinant
| | | Week 4 | Gauss elimination, eigenvalues and eigenvectors. | | | Week 5 | Diziler, seriler ve yakınsaklıkları | | | Week 6 | Power series, Taylor and Maclaurin series | | | Week 7 | Multivariable functions, limit, continuity and partial derivative. | | | Week 8 | Chain rule, implicit functions, gradient and directional derivative | | | Week 9 | Midterm exam | | | Week 10 | Applications of partial derivative, classification of extremum points. | | | Week 11 | Double integration, areas. | | | Week 12 | Polar coordinates, domain transformation, double integrals in polar coordinates | | | Week 13 | Applications of double integrals | | | Week 14 | Areas of surface and surface integrals. | | | Week 15 | Preview | | | Week 16 | End-of-term exam | | | |
| 1 | George B. Thomas, Maurice D. Weir, Joel R. Hass: Thomas Kalkülüs, Cilt 1-2, Pearson, 2012 (Çeviri Editörü: Mustafa Bayram). | | | |
| 1 | Kolman, B., Hill, D.L. (Çev Edit: Akın, Ö.) 2002. Uygulamalı lineer cebir. Palme Yayıncılık, Ankara. | | | 2 | C. Henry Edwards, David E. Penney: Calculus, Matrix Version (6th Edition), Prentice Hall, 2003. | | | 3 | Dennis G. Zill (Eser Sahibi), Warren S. Wright (Eser Sahibi), İsmail Naci Cangül (Çeviriri editörü) Matematik Cilt 2 CALCULUS: Calculus Early Transcendentals, Nobel Yayınevi, 2024. | | | 4 | Robert A. Adams, Christopher Essex: Kalkülüs Eksiksiz Bir Ders Cilt I (Calculus a Complete Course 7. Baskıdan çeviri), Palme Yayıncılık, Ankara, 2012 (Çevirenler: Prof. Dr. Mehmet Terziler, Yrd. Doç. Dr. Tahsin Öner)
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| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | | 1,5 | 50 | | End-of-term exam | 16 | | 1,5 | 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 | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 154.5 |
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