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| MAT1011 | Mathematics - I | 4+0+0 | ECTS:5 | | Year / Semester | Fall 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 | Dr. Öğr. Üyesi Seda ÖZTÜRK | | Co-Lecturer | Other instructor assigned for the course | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn how to model with functions | 1,2 | 1 | | LO - 2 : | learn about limit, derivative and applications | 1,2 | 1 | | LO - 3 : | learn about integral and their applications | 1,2 | 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 | | |
| Functions (polynomials, rational, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions) graphs of basic functions, shifting and scaling graphs, limit, continuity, differentiation and applications (Intermediate Value Theorem, L'hopital's rule, Mean Value Theorem, Optimization problems, sketching the graph of a function), integration techniques |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Functions and their graphs, composite functions, polynomial and rational functions, transcendental functions | | | Week 2 | Inverse functions, exponential and logarithmic functions, functions derived from verbal expressions, applications | | | Week 3 | Limits-an intuitive approach, limit theorems, continuity, trigonometric limits | | | Week 4 | limits at infinity, limits-a mathematical approach, tangent line problem, application | | | Week 5 | Derivative, power and sum rules, product and division rules, trigonometric functions | | | Week 6 | Chain rule, implicit differentiation, derivative of inverse functions, exponential functions | | | Week 7 | Logarithmic functions, hyperbolic functions, rectilinear motion, related rates | | | Week 8 | Extrema of functions, mean value theorem, limits with L'Hopital rule, drawing graphs, first and second derivative test | | | Week 9 | Midterm exam | | | Week 10 | Optimization, linearization and differentials, applications | | | Week 11 | Indefinite integral, integration by a change of variable, area, definite integral | | | Week 12 | Main theorem of calculus, rectilinear motion, area, volumes of solids: slicing method | | | Week 13 | Volumes of solids: cylindirical shells, arch length, area of a surface of revolution, mean value of a function(work, fluid pressure and force, mass and center of weight) | | | Week 14 | Integral, integration by a change of variable, integration by parts, powers of trigonometric functions | | | Week 15 | Trigonometric change of variables, simple fractions, improper integrals | | | Week 16 | Final exam | | | |
| 1 | Zill, D.G, Wright, W.S., 2012; Matematik Cilt I (Calculus Early Transcendentals), Çeviri Editörü Prof. Dr. İsmail Naci Cangül, Nobel Yayıncılık, Ankara. | | | |
| 1 | Thomas, G.B., Weir, M.D., Hass, J., 2009; Thomas' Calculus, 12th Edition, Pearson, USA. | | | 2 | Adams, R.A., Essex, C., Calculus a Complete Course, 2012, Pearson, USA. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 28.11.2023 | | 50 | | End-of-term exam | 16 | 22.01.2024 | | 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 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 12 | 1 | 12 | | Arasınav | 2 | 1 | 2 | | Uygulama | 0 | 0 | 0 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 0 | 0 | 0 | | Proje | 0 | 0 | 0 | | Kısa sınav | 0 | 0 | 0 | | Dönem sonu sınavı için hazırlık | 15 | 1 | 15 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 157 |
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