 |
Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | MT409.4B | Field Education and Research | Elective | 4 | 7 | 5 |
| | Level of Course Unit | | First Cycle | | Objectives 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. | | Name of Lecturer(s) | | Prof. Dr. Rabil AYAZOĞLU | | Learning Outcomes | | 1 | 1. define limit of univalent functions in one point and find the limits of univalent functions with using limit computing methods. | | 2 | 2. define a function's continuity in a point | | 3 | 3. define discontinuity and determining different varieties of discontinuity | | 4 | 4. define a function's derivative in this point | | 5 | 5. say relationship between a function's extremum points and derivative of it in this point. |
| | Mode of Delivery | | Normal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | 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 | | Weekly Detailed Course Contents | |
| 1 | The concept of limit and its applications in single-variable functions | | | | 2 | The concept of limit and its applications in single-variable functions. | | | | 3 | Continuity in single-variable functions and its applications, sorts of transitoriness | | | | 4 | The concept of derivative in single-variable functions and the rules of taking a derivative. | | | | 5 | The concept of derivative in single-variable functions and the rules of taking a derivative. | | | | 6 | Trigonometric, logarithmic, exponential and the derivatives of their opposites and the closed functions. | | | | 7 | Hiperbolic functions, and the derivatives of their opposites and the closed functions | | | | 8 | Extremum and absolute extremum points of functions, extremum problems and their applications in differents areas. | | | | 9 | Mid-term exam | | | | 10 | Rolle and Average Value Theorems. Finite Taylor Theorem | | | | 11 | L' Hospital Theory and limit calculations by the help of this theory. | | | | 12 | Differential and linear increase. | | | | 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. | | | | 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. | | | | 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. | | | | 16 | End-of-term exam | | |
| | Recommended or Required Reading | | Demir, H. 2008; Teori ve Problemleri ile Analiz I, Pegem, Ankara.Balcı, M. 2008; Matematik Analiz I, Balcı Yayınları, Ankara.Özdeğer, A, 1996 Çözümlü Analiz Problemleri Cilt 1, İstanbulÖzdeğer, A, 1996 Çözümlü Analiz Problemleri Cilt 2, İstanbulHacısalihoğlu, H,H, 2003 Temel ve Genel Matematik, Cilt 1, Ankara | | Planned Learning Activities and Teaching Methods | | | Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 1 | 1 | | Attending Lectures | 14 | 6 | 84 | | Problem Solving | 1 | 1 | 1 | | Self Study | 14 | 2 | 28 | | Individual Study for Mid term Examination | 7 | 4 | 28 | | Individual Study for Final Examination | 1 | 7 | 7 | |
| Contribution of Learning Outcomes to Programme Outcomes | | | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
 |
| |
|
|