Rapor Tarihi: 13.04.2026 03:09
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Analytical Geometry II | MAT132 | Turkish | Compulsory | 2. Semester | 3 + 0 | 3.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Doç. Dr. GÜLHAN AYAR |
| Instructor(s) | Doç. Dr. GÜLHAN AYAR (Bahar) |
| Goals | The aim of this course is to teach the fundamental topics of analytic plane geometry; to enable the ability to transform between polar and Cartesian coordinate systems, classify conics using their general equations, and examine the analytic properties of circles, ellipses, hyperbolas, and parabolas. Additionally, it is aimed that students will be able to analyze the relationships between lines and conics and mathematically derive the equations of tangents and normals. |
| Course Content | Polar coordinate system, Conics, Analytic examination of the circle, Ellipse, Hyperbola, Parabola, Coordinate transformations, General equation of conics |
| # | Öğrenme Kazanımı |
| 1 | Learns the Polar Coordinate System, Coordinate Transformations |
| 2 | 2) Learns the analytical examination of the circle. |
| 3 | 3) Learns the analytical examination of the ellipse. |
| 4 | 4) Learns the analytical examination of the Parabola and Hyperbola. |
| 5 | 5) Makes the General Conic Classification |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Translate from: Polar Coordinate System | Preparation, After Class Study, Research, Other Activities, Interview |
| 2. Week | Coordinate Transformations, Translation of Points, Translation of Axs | Preparation, After Class Study, Research, Other Activities, Interview |
| 3. Week | Conics, General Conic Classification | Preparation, After Class Study, Research, Other Activities |
| 4. Week | Analytical Examination of the Circle, Circle Equation | Preparation, After Class Study, Research, Other Activities, Interview |
| 5. Week | Equations of the Tangent and Normal to a Circle | Preparation, After Class Study, Research, Other Activities, Interview |
| 6. Week | The States of the Circle According to Each Other The States of the Circles According to Each Other | |
| 7. Week | Ellipse, Elements of the Ellipse | Preparation, After Class Study, Research, Other Activities, Interview |
| 8. Week | The Relative Positions of an Ellipse and a Line, the Equations of the Tangent and Normal to the Ellipse | Preparation, After Class Study, Research, Other Activities, Interview |
| 9. Week | Equations of Tangents and Normals to an Ellipse, Non-Central Horizontal and Vertical Ellipses | Preparation, After Class Study, Research, Other Activities, Interview |
| 10. Week | Hyperbola, Elements of the Hyperbola, Hyperbola Equations | Preparation, After Class Study, Research, Other Activities, Interview |
| 11. Week | The Situations of a Line and a Hyperbola Relative to Each Other, Non-Central Hyperbola Equations | Preparation, After Class Study, Research, Other Activities, Interview |
| 12. Week | Equations of Tangents and Normals to a Hyperbola | Preparation, After Class Study, Research, Other Activities, Interview |
| 13. Week | Parabola, Elements of a Parabola, Parabola Equation | Preparation, After Class Study, Research, Other Activities, Interview, Presentation (Preparation) |
| 14. Week | The Relationship Between a Line and a Parabola, the Equation of the Tangent and Normal to the Parabola | Preparation, After Class Study, Research, Other Activities, Interview |
| 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). | ✔ | |||||
| 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. | ✔ | |||||
| 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 | 1 | 1 | 2 | 2 | 2 |
| PY3 | 4 | 4 | 5 | 5 | 5 |
| PY4 | 3 | 4 | 4 | 4 | 5 |
| PY5 | 3 | 4 | 5 | 5 | 5 |
| PY6 | 1 | 2 | 2 | 2 | 2 |
| PY7 | 2 | 2 | 2 | 2 | 2 |
| PY8 | 2 | 3 | 3 | 3 | 3 |
| PY9 | 2 | 3 | 3 | 3 | 3 |
| PY10 | 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 | 3 | 42 |
|
Sınavlar |
Midterm | 1 | 2 | 2 |
| Homework | 5 | 1.5 | 7.5 | |
| Final | 1 | 2 | 2 | |
| Practice End-Of-Term | 15 | 4 | 60 | |
| Classroom Activities | 14 | 1 | 14 | |
| Total Workload | 127.5 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
