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| MAT1011 | Mathematics - I | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of PHYSICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Mehmet KUNT | | Co-Lecturer | Staff | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide comprehensive information on functions, limits, derivatives, integrals and their applications and to develop students' ability to apply related concepts to physical, biological and engineering problems.
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| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | They gain knowledge about modeling with functions
| 1 - 2 - 3 | 1, | | LO - 2 : | They learn about limits, derivatives and their applications and develop their skills in solving related problems. | 1 - 2 - 3 | 1, | | LO - 3 : | They will have knowledge about integrals and their applications and will develop their ability to solve related problems. | 1 - 2 - 3 | 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, algebraic, trigonometric, hyperbolic, exponential, logarithmic and inverse trigonometric functions), limit, continuity, derivative and its applications (Intermediate Value Theorem, L'Hospital's rule, Mean Value Theorem, Optimization problems, drawing the graph of the function), integration techniques |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | The concept of function, introduction of types of functions, addition, subtraction and properties of functions. | | | Week 2 | Graphing simple functions and shifting graphs, Inverse functions | | | Week 3 | Trigonometric functions, Inverse trigonometric functions
| | | Week 4 | Logarithmic, exponential and hyperbolic functions | | | Week 5 | Limit, limit calculation rules, precise definition of limit, one-way limits | | | Week 6 | Continuity, properties of continuous functions, the intermediate value theorem, limits involving infinity, and asymptotes of graphs | | | Week 7 | Derivative of a function, geometric meaning of derivative, rules of derivative, trigonometric functions, inverse trigonometric functions, derivatives of logarithmic and exponential functions | | | Week 8 | Chain rule, Differentiation of implicit function, Higher order derivatives, L'Hospital's rule | | | Week 9 | Midterm Exam | | | Week 10 | Derivative applications (Maximum-minimum, Mean value theorem), First and Second derivative tests | | | Week 11 | Examining the changes in functions and drawing their graphs. | | | Week 12 | Optimization problems | | | Week 13 | Indefinite integrals (antiderivatives) Integral calculation methods (change of variables, integration by parts) | | | Week 14 | Decomposition of simple fractions, integrals of trigonometric (rational) functions.
| | | Week 15 | Elimination of deficiencies and general evaluation | | | Week 16 | Final 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. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 17/11/2025 | 1,5 | 50 | | End-of-term exam | 16 | 05/01/2026 | 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 | 6 | 14 | 84 | | Arasınav için hazırlık | 4 | 4 | 16 | | Arasınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 4 | 5 | 20 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 180 |
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