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| MAT1005 | Analysis - I | 4+2+0 | ECTS:9 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face, Practical | | Contact Hours | 14 weeks - 4 hours of lectures and 2 hours of practicals per week | | Lecturer | Prof. Dr. Mehmet KUNT | | Co-Lecturer | PROF. DR. Bahadır Özgür GÜLER, | | 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 | 1,3,5,6,7 | 1 | | LO - 2 : | learn about limit, derivative and applications | 1,3,4,5,6 | 1 | | LO - 3 : | learn about integral and their applications | 2,3,5,6,7 | 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 | Definition of function, Introduction to function types, Summation, subtraction etc. properties of functions, | | | Week 2 | Graphs of basic functions and shifting graphs, Inverse functions | | | Week 3 | Trigonometric functions, Inverse trigonometric functions | | | Week 4 | Logarithmic, exponential and hyperbolic functions | | | Week 5 | Limit, limit computation rules. Formal definition of limit One-sided limits | | | Week 6 | Continuity, properties of continuous functions, Intermediate Value Theorem Limits at infinity and infinite limits, asymptotes of graphs | | | Week 7 | Derivative of a function, geometrical meaning of derivative, Differentiation rules, Derivatives of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions. | | | Week 8 | Chain rule, Implicit differentiation Higher order derivatives L?hospital?s rule | | | Week 9 | Mid-term exam | | | Week 10 | Applications of differentiation (maximum-minimum and Mean Value Theorem) First and second derivative tests | | | Week 11 | Sketching the graph of a function by analyzing changes. | | | Week 12 | Optimization problems | | | Week 13 | Indefinite integrals (Anti-derivatives) Methods of integration (change of variables, integration by parts) | | | Week 14 | Partial fractions, Integrals of trigonometric (rational) functions. | | | 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, 2009, Pearson, USA. | | | |
| 1 | Stewart, James, Calculus(Early transcendentals), 6th Edition, Thomson Brooks/Cole, 2008, USA. | | | 2 | Adams, R.A., Essex, C., Calculus a Complete Course, 2010, Pearson, USA. | | | 3 | Howie, John M. 2006; Real Analysis , Springer Verlag -Undergraduate Series in Mathematics ,3rd edition, | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 28/11/2020 | 2 | 50 | | End-of-term exam | 16 | 15/01/2021 | 2 | 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 | 10 | 14 | 140 | | Laboratuar çalışması | 0 | 0 | 0 | | Arasınav için hazırlık | 16 | 1 | 16 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Klinik Uygulama | 0 | 0 | 0 | | Ödev | 10 | 1 | 10 | | Proje | 0 | 0 | 0 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 16 | 1 | 16 | | Dönem sonu sınavı | 2 | 1 | 2 | | Diğer 1 | 0 | 0 | 0 | | Diğer 2 | 0 | 0 | 0 | | Total work load | | | 272 |
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