| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Analysis I | MAT123 | Turkish | Compulsory | 1. Semester | 4 + 2 | 5.0 | 6.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. İlhame AMİRALİ |
| Instructor(s) | Prof. Dr. İlhame AMİRALİ (Güz) |
| Goals | To give students information about the limit, continuity, derivative, indefinite of single variable functions and their applications. |
| Course Content | Sets (Operations on sets, open sets, closed sets, accumulation point, vb.), Number Sets (Natural Numbers, Integers, Real Numbers and Their Properties), Supremum and Infimum Concepts, Function Concept and Its Properties, Some Special Functions , Limits, Continuity and Uniform Continuity in Functions, Sequences of Reel Numbers, Boundedness and Convergence Sequences of Reel Numbers,, Bolzano-Weierstrass Theorem, Derivative, Derivative Rules, Derivative Methods, Higher Order Derivatives, Geometric and Physical Meaning of the Derivative, Derivative Theorems, Indefinite Forms, Diferantial and Drawing Curves. |
| # | Öğrenme Kazanımı |
| 1 | 1.This course will enable one to:Know basic rules about subject of limit and practice on single variable functions |
| 2 | 2.Have information about concept of continuity, discontinuity and make geometrical commet on single variable functions |
| 3 | 3.Have information about derivative and basic theorems related derivative, calculate and practice derivative of polynomial, trigonometric, logarithmic, exponentional and composite and inverse functions |
| 4 | 4.Calculate limit by the help of L’Hospital Rule on single variable functions |
| 5 | 5.Know indefinite integral and integral methods and apply to problems on single variable functions |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Sets (Operations on sets, open sets, closed sets, accumulation point, vb.) | Class Hours |
| 2. Week | Number Sets (Natural Numbers, Integers, Real Numbers and Their Properties) | Class Hours |
| 3. Week | Supremum and Infimum Concepts | Class Hours |
| 4. Week | Function Concept and Its Properties, Some Special Functions | Class Hours |
| 5. Week | Limits, Continuity and Uniform Continuity in Functions. | Class Hours |
| 6. Week | Sequences of Reel Numbers, Boundedness and Convergence Sequences of Reel Numbers,, Bolzano-Weierstrass Theorem | Class Hours |
| 7. Week | Sequences of Reel Numbers, Boundedness and Convergence Sequences of Reel Numbers,, Bolzano-Weierstrass Theorem | Class Hours |
| 8. Week | Mid-term Exam | Class Hours |
| 9. Week | Derivative, Derivative Rules | Class Hours |
| 10. Week | Derivative Methods, Higher Order Derivatives. | Class Hours |
| 11. Week | Geometric and Physical Meaning of the Derivative. | Class Hours |
| 12. Week | Derivative Theorems. | Class Hours |
| 13. Week | Indefinite Forms. | Class Hours |
| 14. Week | Diferantial and Drawing Curves. | Class Hours |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Acquiring knowledge on theories and practice of education in general, subject teaching in particular, and the basic concepts and theories of the related disciplines, | ✔ | |||||
| 1 | Acquiring knowledge on theories and practice of education in general, subject teaching in particular, and the basic concepts and theories of the related disciplines, | ✔ | |||||
| 2 | Knowing how to obtain information geared towards lifelong learning, | ✔ | |||||
| 3 | Doing effective educational planning, organizing and evaluating based on theoretical and practical content matter and in relation to the needs of the learners, | ✔ | |||||
| 4 | Utilizing educational technologies in a variety of educational settings, | ✔ | |||||
| 5 | Analyzing studies in the field with a scientific perspective, assessing the findings and offering solutions, | ✔ | |||||
| 6 | Acquiring academic literacy and minimum B1 level competence at a foreign language in order to pursue the global developments in the area of study, | ✔ | |||||
| 7 | Pursuing the scientific discussions in the field and interpreting them through scientific examination, | ✔ | |||||
| 8 | Forming scientific study platforms in order to solve the problems in practice, | ✔ | |||||
| 8 | Forming scientific study platforms in order to solve the problems in practice, | ✔ | |||||
| 9 | Preparing and conducting solution-based projects in response to social problems in an effort to contribute to the School-Society collaboration | ✔ | |||||
| 10 | Following the developments in the field through professional activities such as literature reviews, seminars, conferences and workshops, and sharing them with other expert and non-expert individuals, | ✔ | |||||
| 11 | Being an innovative and self-confident intellectual with a sense of society, environment, social justice and respect for ethical values. | ||||||
| 12 | To be able to analyse the notions and ideas in the field by using scientific methods, to identify problems, and to develop solutions based on proofs and researches | ✔ | |||||
| 13 | To be able to gain ability of doing academic research | ✔ | |||||
| 14 | To be able to work interactively | ✔ | |||||
| 15 | To be able gain necessary computer software for further studies | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 |
|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 |
| PY2 | 5 | 5 | 5 | 5 | 5 |
| PY3 | 4 | 4 | 4 | 4 | 4 |
| PY4 | 5 | 5 | 5 | 5 | 5 |
| PY5 | 4 | 4 | 4 | 4 | 4 |
| PY6 | 1 | 1 | 1 | 1 | 1 |
| PY7 | 5 | 5 | 5 | 5 | 5 |
| PY8 | 2 | 2 | 2 | 2 | 2 |
| PY9 | 3 | 3 | 3 | 3 | 3 |
| PY10 | 5 | 5 | 5 | 5 | 5 |
| PY11 | 0 | 0 | 0 | 0 | 0 |
| PY12 | 5 | 5 | 5 | 5 | 5 |
| PY13 | 4 | 4 | 4 | 4 | 4 |
| PY14 | 2 | 2 | 2 | 2 | 2 |
| PY15 | 1 | 1 | 1 | 1 | 1 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 6 | 84 |
|
Sınavlar |
Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 14 | 1 | 14 | |
| Homework 2 | 10 | 1 | 10 | |
| Quiz 1 | 1 | 1.5 | 1.5 | |
| Final | 1 | 3 | 3 | |
| Practice | 14 | 1.5 | 21 | |
| Practice End-Of-Term | 14 | 1 | 14 | |
| Classroom Activities | 14 | 1 | 14 | |
| Total Workload | 163.5 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 6.0 | ||
