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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 GEOLOGICAL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Fatma GÜLTEKİN | | Co-Lecturer | DOCTOR LECTURER Sema DİKMENOĞLU, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The aim of the course is to teach the basic mathematical techniques. Analyzing the two and three dimensional problems in engineering sciencies and introducing a number of mathematical skills which can be used for the analysis of problems. The emphasis is on the practical usability of mathematics; this goal is mainly pursued via a large variety of examples and applications from these disciplines. |
| 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 | 1 | | LO - 2 : | Analize convergence of improper integrals. | 1 | 1 | | LO - 3 : | Analize convergence of sequences and series. | 1 | 1 | | LO - 4 : | understand functions of two and three variables and their properties | 1 | | | LO - 5 : | know the concepts of limit and continuity of functions of two variables | 1 | 1 | | LO - 6 : | know the concepts of derivative of functions of two variables and apply it to engineering problems | 1 | 1 | | LO - 7 : | know the concepts of integration of functions of two variables and apply it to engineering problems | 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), LO : Learning Outcome | | |
| Riemann sums, definite integrals and their properties, Fundamental Theorem of Calculus.Change of variables in definite integrals
Applications of definite integrals: areas of plane regions,Applications of definite integrals: Volume computations (disk and cross-section methods) length of parametric curves, areas of surfaces of revolution.Improper integrals (Type 1 and Type 2).Sequences and infinite series, (definitions of convergence and divergence, geometric series, n-th term test, p-series, alternating series).Series(absolute convergence, ratio and root tests) Power series and their convergence, Taylor and Maclaurin series.
Multivariable functions, limit, continuity and partial derivatives.Chain rule, directional derivatives,
Maximum and minimum, Lagrange Multipliers (Single constraint case) Double integrals and their applications (Area). Polar Coordinates ,Double integrals in Polar Coordinates and their applications (mass and density, center of mass ). |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Riemann sums, definite integrals and their properties, Fundamental Theorem of Calculus | | | Week 2 | Change of variables in definite integrals and Area Between Curves | | | Week 3 | Applications of definite integrals: Volume computations (disk and cross-section methods) | | | Week 4 | Arc length of a parametric curve, areas of surfaces of revolution | | | Week 5 | Improper integrals (Type 1 and Type 2) | | | Week 6 | Sequences and infinite series, (definitions of convergence and divergence, geometric series, n-th term test, p-series, comparision, ratio and root tests) | | | Week 7 | Alternating series, Conditional and absolute convergences, Power series and their convergence, | | | Week 8 | Taylor and Maclaurin series | | | Week 9 | Mid-term | | | Week 10 | Multivariable functions, limit, continuity and partial derivatives.
| | | Week 11 | Chain rule, directional derivatives, the gradient vector | | | Week 12 | Maximum and minimum, 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 | Elimination of incomplete parts, general assessment | | | Week 16 | End-of-term exam | | | |
| 1 | Thomas, G.B., Weir, M.D., Hass, J., Thomas Calculus, 12th Edition, Pearson, USA. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 06/04/2020 | 1,50 | 50 | | End-of-term exam | 16 | 04/06/2020 | 1,50 | 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 | 9 | 1 | 9 | | Uygulama | 1.5 | 1 | 1.5 | | Dönem sonu sınavı için hazırlık | 12 | 1 | 12 | | Dönem sonu sınavı | 1.5 | 1 | 1.5 | | Total work load | | | 150 |
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