| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Analysis I | MAE103 | Turkish | Compulsory | 1. Semester | 4 + 0 | 4.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Face to face |
| Course Coordinator | Dr. Öğr. Üyesi Duygu ARABACI |
| Instructor(s) | Dr. Öğr. Üyesi Duygu ARABACI (Güz) |
| Goals | The aim of this course is to enable students to develop a good understanding of some univariate analysis concepts and to gain the ability to apply these concepts. |
| Course Content | Sets and number systems; types of functions, exponential functions and logarithmic functions; concepts of limit, continuity; derivative, applications of derivative and graphing. - Knows functions and graphs. - Knows the concepts of limit, continuity and discontinuity. - Makes applications of the limit. - Knows derivatives and derivatives rules. - Makes applications of derivative. - Knows the concept of differential. - Knows the concepts of integral, indefinite integral and definite integral. - Makes the applications of the integral. |
| # | Öğrenme Kazanımı |
| 1 | Knows the axioms of the real number system. |
| 2 | Knows the basic types of functions and draws their graphs. |
| 3 | Interpret the formal definitions of limit and continuity concepts in both algebraic and graphical dimensions and comprehend the difference between these two definitions. |
| 4 | Apply the concepts of limit and continuity in problem solving. |
| 5 | Knows different interpretations of derivative concept (instantaneous rate of change, slope of tangent) and can adapt the concept of derivative to optimization problems. |
| 6 | It establishes the connection between the sign of the first and second order derivative functions of a function and the increasing/decreasing convex/concave characteristics of the graph of the function. |
| 7 | Can construct rational numbers and some irrational numbers on the number line with the Euclidean method. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Sets | Interview Class Hours |
| 2. Week | Number systems | Interview Class Hours |
| 3. Week | Concept of function and types of functions | Class Hours Interview |
| 4. Week | Exponential and logarithmic functions | Class Hours Interview |
| 5. Week | Trigonometric Functions | Class Hours Interview |
| 6. Week | Inverse Trigonometric Functions | Interview Class Hours |
| 7. Week | Hyperbolic and Parametric Functions; Implicitly Defined Functions | Interview Class Hours |
| 8. Week | Limits | Class Hours Interview |
| 9. Week | Continuity of Functions | Interview Class Hours |
| 10. Week | Derivative, basic differentiation rules | Interview Class Hours |
| 11. Week | Derivatives of Trigonometric and Inverse Trigonometric Functions | Class Hours Interview |
| 12. Week | Derivatives of Logarithmic, Exponential, and Hyperbolic Functions | Interview Class Hours |
| 13. Week | Derivatives of Parametric and Implicit Functions, Higher-Order Derivatives | Interview Class Hours |
| 14. Week | Applications of the Derivative | Interview Class Hours |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 27 | By using mathematical language and terminology correctly and effectively, the student has knowledge about the nature, source, historical development and limits of basic concepts and approaches and interprets their reflections in the field. | ✔ | |||||
| 30 | The student knows the context of technological pedagogical content knowledge for mathematics and has knowledge about how to use information and communication technologies in mathematics education and training. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 |
|---|---|---|---|---|---|---|---|
| PY27 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY30 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| 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 | 4 | 56 |
|
Ders Dışı |
Research | 14 | 2 | 28 |
| Interview | 14 | 2 | 28 | |
| Other Activities | 11.5 | 1 | 11.5 | |
|
Sınavlar |
Midterm 1 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 | |
| Total Workload | 127.5 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
