Rapor Tarihi: 13.04.2026 03:07
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Analytical Geometry I | MAT131 | Turkish | Compulsory | 1. 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 (Güz) |
| Goals | The aim of this course is to ensure that students grasp the concept of vectors in the plane and space, operations on vectors, and the fundamental structures of analytical geometry. Within the scope of the course, topics such as equations of lines and planes, geometric relationships, distance problems, and projections are covered to enhance students' analytical thinking and problem-solving skills. |
| Course Content | Vectors in the plane and space, operations on vectors, scalar and vector multiplication, the concept of linear independence and basis, equations of lines, the relative positions of two lines, distance calculations, plane equations, the relative positions of a line and a plane, parallelism and distance problems, pencil of planes, projection, symmetry and reflection, and general problem-solving applications. |
| # | Öğrenme Kazanımı |
| 1 | Düzlem ve uzayda vektör kavramını ve vektörler üzerindeki işlemleri açıklar. |
| 2 | Calculates scalar and vector products and provides their geometric interpretations. |
| 3 | Explains and applies the concepts of linear independence and basis. |
| 4 | Creates and analyzes linear equations based on different scenarios. |
| 5 | Sets up plane equations and interprets geometric relationships in space. |
| 6 | Calculates the positional relationships and distances between lines and planes. |
| 7 | Explains and applies the concepts of projection, symmetry, and reflection. |
| 8 | Analyzes problems related to analytic geometry and develops solution methods. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Vectors in plane, operations on vectors | Preparation, After Class Study, Research, Other Activities, Interview |
| 2. Week | Parallel and orthogonal vectors, scalar product, linear independence, basis | Preparation, After Class Study, Research, Other Activities, Interview |
| 3. Week | The multiplication of vectors, applications of the Euclidean inner product, vector product, cross product, and geometric interpretations | Preparation, After Class Study, Research, Other Activities, Interview |
| 4. Week | Line equation in space | |
| 5. Week | line equation with two known points, line equations perpendicular to two vectors | Preparation, After Class Study, Research, Other Activities, Interview |
| 6. Week | The positions of two lines relative to each other, the distance of a point from a line | Preparation, After Class Study, Research, Other Activities, Interview |
| 7. Week | Plane equations in space | Preparation, After Class Study, Research, Other Activities, Interview |
| 8. Week | General question solving | |
| 9. Week | Plane equations in space | Preparation, After Class Study, Research, Other Activities, Interview |
| 10. Week | The position of a line relative to a plane, The position of two planes relative to each other | Preparation, After Class Study, Research, Other Activities, Interview |
| 11. Week | The distance from a point to a plane, the distance between a parallel line and a plane, the distance between two parallel planes | Preparation, After Class Study, Research, Other Activities, Interview |
| 12. Week | Plane Bundle | Preparation, After Class Study, Research, Other Activities, Interview |
| 13. Week | Projection-Symmetry-Reflection | Preparation, After Class Study, Research, Other Activities, Interview |
| 14. Week | Projection-Symmetry-Reflection | 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 | DK6 | DK7 | DK8 |
|---|---|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| PY3 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY5 | 3 | 4 | 5 | 4 | 4 | 4 | 4 | 4 |
| PY6 | 3 | 4 | 4 | 5 | 5 | 5 | 5 | 5 |
| PY7 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |
| PY8 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY9 | 2 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY10 | 1 | 1 | 1 | 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 |
|---|---|---|---|
| Doç. Dr. GÜLHAN AYAR | Vize | 40.00 | |
| Doç. Dr. GÜLHAN AYAR | Final | 60.00 | |
| Toplam | 100.00 | ||
| 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 | ||
