Rapor Tarihi: 13.04.2026 03:07
| 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.) | |
| 2. Week | Number Sets (Natural Numbers, Integers, Real Numbers and Their Properties) | |
| 3. Week | Supremum and Infimum Concepts | |
| 4. Week | Function Concept and Its Properties, Some Special Functions | |
| 5. Week | Limits, Continuity and Uniform Continuity in Functions. | |
| 6. Week | Sequences of Reel Numbers, Boundedness and Convergence Sequences of Reel Numbers,, Bolzano-Weierstrass Theorem | |
| 7. Week | Sequences of Reel Numbers, Boundedness and Convergence Sequences of Reel Numbers,, Bolzano-Weierstrass Theorem | |
| 8. Week | Sequences of Reel Numbers, Boundedness and Convergence Sequences of Reel Numbers,, Bolzano-Weierstrass Theorem | |
| 9. Week | Derivative, Derivative Rules | |
| 10. Week | Derivative Methods, Higher Order Derivatives. | |
| 11. Week | Geometric and Physical Meaning of the Derivative. | |
| 12. Week | Derivative Theorems. | |
| 13. Week | Indefinite Forms. | |
| 14. Week | Diferantial and Drawing Curves. |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 1 | Possesses theoretical and applied knowledge of the fundamental areas of mathematics (Analysis and Function Theory, Algebra and Number Theory, Geometry, Applied Mathematics, Topology and Foundations of Mathematics, and Mathematical Logic). | ✔ | |||||
| 2 | Explains the historical development of mathematical concepts, their relationship with other branches of science, and their application areas. | ✔ | |||||
| 3 | Defines mathematical problems, selects appropriate methods, and solves them using analytical/numerical techniques. | ✔ | |||||
| 4 | Constructs mathematical expressions with logical integrity and reaches conclusions using proof methods. | ✔ | |||||
| 5 | Formulates and interprets real-life problems by performing mathematical modeling. | ✔ | |||||
| 6 | Effectively uses information technologies and mathematical software in data analysis and computation processes. | ✔ | |||||
| 7 | Takes responsibility in individual or team work; plans and executes projects. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 8 | Follows current developments in their field; improves themselves with a lifelong learning awareness. | ✔ | |||||
| 9 | Expresses mathematical ideas verbally and in writing clearly and in accordance with academic rules. | ✔ | |||||
| 10 | Acts in accordance with professional and academic ethical values; acts with a sense of social responsibility. | ✔ | |||||
| 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 |
|
| Güz Dönemi | |||
| Responsible Personnel | Grup | Evaluation Method | Percentage |
|---|---|---|---|
| Prof. Dr. İlhame AMİRALİ | Vize | 40.00 | |
| Prof. Dr. İlhame AMİRALİ | Final | 60.00 | |
| Toplam | 100.00 | ||
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 6 | 84 |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Homework | 14 | 1 | 14 | |
| Homework Preparation | 10 | 1 | 10 | |
| Quiz | 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 | ||
