| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematics I | MTH101 | English | Compulsory | 1. Semester | 4 + 0 | 4.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Face to Face |
| Course Coordinator | Doç. Dr. Nejla ÖZMEN, Dr. Öğr. Üyesi Esra KORKMAZ |
| Instructor(s) | Dr. Öğr. Üyesi Esra KORKMAZ (Güz) |
| Goals | This course aims to provide a solid foundation in calculus by introducing the fundamental concepts of functions, limits, and derivatives, enabling students to analyze and model real-world phenomena. |
| Course Content | Functions, Limits and Continuity, Derivative and its Applications |
| # | Öğrenme Kazanımı |
| 1 | Uses transcendental functions including logarithms, exponentials and inverse trigonometric functions effectively |
| 2 | Computes limits and carry out some basic proofs about limits and continuity. |
| 3 | Computes derivatives and use it in applications such as computing rates of change, finding extreme values. |
| 4 | Solves optimization problems in the field using the concepts of first and second derivatives |
| 5 | Analyzes the behavior of functions by determining intervals of increase/decrease, concavity, and asymptotes, and sketches graphs of functions. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Precalculus: Pre-Calculus Real numbers, Equations and Inequalities | |
| 2. Week | Pre-Calculus: Functions, Some Special Functions (Polynomial, Absolute Value, Trigonometric, Inverse Trigonometric, Exponential, Logarithmic, Hyperbolic) | |
| 3. Week | The Concept of Limit, One-Sided Limits, Squeeze Theorem | |
| 4. Week | Infinite Limits, Limits at Infinity, Continuity, Intermediate Value Theorem | |
| 5. Week | Slope, Tangent Lines, Definition of Derivative, Derivative as a Function | |
| 6. Week | Higher Derivatives, Derivatives of Inverse Functions, Derivatives of trigonometric functions | |
| 7. Week | Chain rule, Implicit derivative, Tangent and Normal lines | |
| 8. Week | Midterm | |
| 9. Week | Logarithmic differentiation, Indeterminate Forms, L'Hôpital's rule | |
| 10. Week | Mean Value Theorem, Rolle's Theorem, Local extremum, Absolute extremum, 1st derivative test | |
| 11. Week | Concavity, Inflection points, Second derivative test, Asymptotes | |
| 12. Week | Curve Sketching | |
| 13. Week | Taylor formula, Big-O Notation | |
| 14. Week | Optimization problems |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Adequate knowledge of mathematics, science and related engineering disciplines; Ability to use theoretical and applied knowledge in these fields in complex engineering problems | ✔ | |||||
| 1 | Adequate knowledge of mathematics, science and related engineering disciplines; Ability to use theoretical and applied knowledge in these fields in complex engineering problems | ✔ | |||||
| 8 | Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering practice; Ability to use information technologies effectively | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 |
|---|---|---|---|---|---|
| PY1 | 3 | 4 | 4 | 5 | 4 |
| PY8 | 2 | 2 | 3 | 2 | 3 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| Güz Dönemi | |||
| Responsible Personnel | Grup | Evaluation Method | Percentage |
|---|---|---|---|
| Dr. Öğr. Üyesi Esra KORKMAZ | N.Ö | Vize | 40.00 |
| Dr. Öğr. Üyesi Esra KORKMAZ | N.Ö | Ders İçi Performans | 5.00 |
| Dr. Öğr. Üyesi Esra KORKMAZ | N.Ö | Final | 55.00 |
| Toplam | 100.00 | ||
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Sınavlar |
Midterm 1 | 1 | 2 | 2 |
| Homework 1 | 2 | 7 | 14 | |
| Homework 2 | 2 | 7 | 14 | |
| Quiz 1 | 1 | 5 | 5 | |
| Quiz 2 | 1 | 5 | 5 | |
| Final | 1 | 2 | 2 | |
| Practice | 11 | 2 | 22 | |
| Practice End-Of-Term | 3 | 12 | 36 | |
| Classroom Activities | 14 | 2 | 28 | |
| Total Workload | 128 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
