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| IMMT201 | Analysis - I | 4+2+0 | ECTS:8 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT OF MATHEMATICS AND SCIENCE TEACHING | | 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 | -- | | Co-Lecturer | None | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | Examining one real-variable and real-value functions and interpreting their diagrams, reinforcing the concepts of limit, continuity and derivative and making applications and interpretations on them, transfering the knowledge obtained in this cource to other cources, setting a background knowledge for the course Analysis-II. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | define limit of univalent functions in one point and find the limits of univalent functions with using limit computing methods. | 1,9,22,23,24 | 1,4 | | LO - 2 : | define a function's continuity in a point | 1,9,17,22,23,24 | 1,4 | | LO - 3 : | define discontinuity and determining different varieties of discontinuity | 1,3,9,17,22,23,24 | 1,4 | | LO - 4 : | define a function's derivative in this point | 1,9,17,22,23,24 | 1,4 | | LO - 5 : | say relationship between a function's extremum points and derivative of it in this point. | 1,9,17,22,23,24 | 1,4 | | 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 | | |
| The concept of limit and its applications in single-variable functions. Continuity in single-variable functions and its applications, sorts of transitoriness. The concept of derivative in single-variable functions and the rules of taking a derivative. Trigonometric, logarithmic, exponential and hiperbolic functions, and the derivatives of their opposites and the closed functions. High-level derivatives. Extremum and absolute extremum points of functions, extremum problems and their applications in differents areas. Rolle and Average Value Theorems. Finite Taylor Theorem. L?Hospital Theory and limit calculations by the help of this theory. Differential and linear increase. The concept of integral, indefinite integrals, integral-taking techniques, definite integrals, area and volume calculations with a certain integral and its applications in various fields. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | The concept of limit and its applications in single-variable functions.
| | | Week 2 | The concept of limit and its applications in single-variable functions.
| | | Week 3 | Continuity in single-variable functions and its applications, sorts of transitoriness.
| | | Week 4 | The concept of derivative in single-variable functions and the rules of taking a derivative.
| | | Week 5 | The concept of derivative in single-variable functions and the rules of taking a derivative.
| | | Week 6 | Trigonometric, logarithmic, exponential and the derivatives of their opposites and the closed functions.
| | | Week 7 | Hiperbolic functions, and the derivatives of their opposites and the closed functions
| | | Week 8 | Extremum and absolute extremum points of functions, extremum problems and their applications in differents areas.
| | | Week 9 | Mid-term exam | | | Week 10 | Rolle and Average Value Theorems. Finite Taylor Theorem.
| | | Week 11 | L' Hospital Theory and limit calculations by the help of this theory.
| | | Week 12 | Differential and linear increase.
| | | Week 13 | The concept of integral, indefinite integrals, integral-taking techniques, definite integrals, area and volume calculations with a certain integral and its applications in various fields.
| | | Week 14 | The concept of integral, indefinite integrals, integral-taking techniques, definite integrals, area and volume calculations with a certain integral and its applications in various fields.
| | | Week 15 | The concept of integral, indefinite integrals, integral-taking techniques, definite integrals, area and volume calculations with a certain integral and its applications in various fields.
| | | Week 16 | End-of-term exam | | | |
| 1 | Demir, H. 2008; Teori ve Problemleri ile Analiz I, Pegem, Ankara. | | | |
| 1 | Balcı, M. 2008; Matematik Analiz I, Balcı Yayınları, Ankara. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 18/11/2013 | 2 | 50 | | End-of-term exam | 16 | 07/01/2014 | 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 | 4 | 14 | 56 | | Arasınav için hazırlık | 4 | 7 | 28 | | Arasınav | 2 | 1 | 2 | | Uygulama | 2 | 14 | 28 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 4 | 7 | 28 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 201 |
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