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| MATH1000 | Mathematics II | 4+0+0 | ECTS:5 | | Year / Semester | Spring Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of ELECTRICAL and ELECTRONICS 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 | | | 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 : | apply the integration to some engineering problems and to some applications
| 1,2 | 1, | | LO - 2 : | analyze convergence of improper integrals. | 1,2 | 1 | | LO - 3 : | analyze convergence of sequences and series. | 1,2 | 1 | | LO - 4 : | know the concepts of limit and continuity of functions of two variables | 1,2 | 1 | | LO - 5 : | compute mass and density, and center of mass by using double integrals in multivariable functions. | 1,2 | 1 | | LO - 6 : | know the concepts of derivative of functions of two variables and apply it to engineering problems | 1,2 | | | LO - 7 : | know the concepts of integration of functions of two variables 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, matrices, linear equation systems, elementary matrix operations, Gauss elimination, eigenvalues and eigenvectors. Sequences and convergence, infinite series, convergence tests for infinite series (the integral test, the comparison test and limit comparison tests, the ratio and root tests, the alternating series and its 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, Lagrange multipliers. 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), curves and parametrization, vector and scalar fields, parametrizing curves, line integrals.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Vectors in plane and in three dimensional space, vector algebra, lines and planes in space
| | | Week 2 | Linear Equation Systems and Matrices, Matrix Operations | | | Week 3 | Solution by Gauss elimination,eigenvalues and eigenvectors
| | | Week 4 | Squences, series, integral test
| | | Week 5 | Comparison test, power series
| | | Week 6 | Series represenatation of functions, Taylor series, Binomial series, applications
| | | Week 7 | Conics, parametric equations, polar coordinat system
| | | Week 8 | Vector functions and their calculus, motion along a curve, curvature and acceleration
| | | Week 9 | Midterm Exam | | | Week 10 | Limit and continuity for functions of multiple variables, partial derivative
| | | Week 11 | Chain rule, directional derivative, tangent plane, extrema of functions of multiple variables
| | | Week 12 | Least squares method, Lagrange multipliers, applications
| | | Week 13 | Double integrals and applications(center of mass and moment)
| | | Week 14 | Double integrals in polar coordinate system, area of a surface, triple integrals
| | | Week 15 | Change of variables in multiple integral, line integrals, applications
| | | Week 16 | Final Exam | | | |
| 1 | C. Henry Edwards, David E. Penney: Calculus, Matrix Version (6th Edition), Prentice Hall, 2003.
| | | 2 | Robert A. Adams, Christopher Essex: Calculus, A Complete Course, 7th Ed., Pearson, 2010. | | | |
| 1 | P. V. O'Neil: Advanced Engineering Mathematics, 7th. Ed., Cengage Learning, 2011. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 18/04/2022 | 1 | 50 | | End-of-term exam | 16 | 08/06/2022 | 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 | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 12 | 1 | 12 | | Arasınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 1 | 1 | 1 | | Total work load | | | 155 |
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