| 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 |
| 2. Week | Number systems | Interview |
| 3. Week | Concept of function and types of functions | Interview |
| 4. Week | Exponential and logarithmic functions | Interview |
| 5. Week | Trigonometric Functions | Interview |
| 6. Week | Inverse Trigonometric Functions | Interview |
| 7. Week | Hyperbolic and Parametric Functions; Implicitly Defined Functions | Interview |
| 8. Week | Limits | Interview |
| 9. Week | Continuity of Functions | Interview |
| 10. Week | Derivative, basic differentiation rules | Interview |
| 11. Week | Derivatives of Trigonometric and Inverse Trigonometric Functions | Interview |
| 12. Week | Derivatives of Logarithmic, Exponential, and Hyperbolic Functions | Interview |
| 13. Week | Derivatives of Parametric and Implicit Functions, Higher-Order Derivatives | Interview |
| 14. Week | Applications of the Derivative | Interview |
| 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 | ||
