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| MAT1009 | Mathematics-I | 4+2+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures and 2 hours of practicals per week | | Lecturer | Doç. Dr. Pembe İPEK AL | | Co-Lecturer | Assist. Prof. Hüsnü Anıl ÇOBAN | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | This course aims to teach the basic mathematical techniques, introducing mathematical skills to analyzes problems. With many examples of math emphasis is on the practical usability. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn the concepts of limit and continuity of functions | | | | LO - 2 : | learn the concepts of derivatives of functions | | | | LO - 3 : | learn the concepts of integral of functions | | | | 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 | | | 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., Finney, R.L. 2001; Calculus ve Analitik Geometri (çeviri), Cilt 1, Beta Yayınları. | | | |
| 1 | Balcı, M. 2009; Genel Matematik 1, Balcı Yayınları, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 11/2021 | 1 | 50 | | End-of-term exam | 16 | 01/2022 | 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 | 10 | 1 | 10 | | Arasınav | 1 | 1 | 1 | | Uygulama | 2 | 14 | 28 | | Dönem sonu sınavı için hazırlık | 14 | 1 | 14 | | Dönem sonu sınavı | 1 | 1 | 1 | | Total work load | | | 180 |
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