Rapor Tarihi: 13.04.2026 03:08
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematics I | MAT111 | Turkish | Compulsory | 1. Semester | 5 + 1 | 6.0 | 6.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | face to face |
| Course Coordinator | Prof. Dr. İlhame AMİRALİ |
| Instructor(s) | Prof. Dr. İlhame AMİRALİ (Güz) |
| Goals | To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions |
| Course Content | Course Content (in English): Sets (Set operations, open set, closed set, accumulation point, etc.), Number Sets (Natural Numbers, Integers, Real Numbers and their Properties), Concepts of Supremum and Infimum, Concept and Properties of Functions, Some Special Functions, Limits in Functions, Continuity, Uniform Continuity, Sequences of Real Numbers, Boundedness and Convergence in Sequences of Real Numbers, Bolzano-Weierstrass Theorem, Concept of Derivative, General Rules for Differentiation, Methods of Derivatives, Higher Order Derivatives, Geometric and Physical Meaning of the Derivative, Theorems Related to Derivatives, Indeterminate Forms, Differential and Curve Sketching. |
| # | Öğrenme Kazanımı |
| 1 | Describe the concepts of set and number sets. It explains the concepts of identity, equation and inequality |
| 2 | Defines the properties of functions and functions |
| 3 | Defines trigonometric, inverse trigonometric and hyperbolic functions, partial functions and special defined functions (absolute value, exact value, sign functions) |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Sets. Number sets. Equations. Equality and inequality. | |
| 2. Week | Concept of function. Types of functions (Polynomial sets, rational function, exponential and logarithmic functions and the definition set of these functions) | |
| 3. Week | Function types (Trigonometric, reverse trigonometric and hyperbolic functions, Partial functions , special defined functions (Absolute value, exact value, sign functions) . | |
| 4. Week | Concept of limit and limit calculation with the definition of limit. Proof of the rules used for limit rule. Sandwich theorem. Limit of trigonometric functions. | |
| 5. Week | Right and left limit. Undetermined conditions (0/0,infinity/infinity, 0.infinity, infinity-infinity,1^infinity) | |
| 6. Week | Continuity concept in functions. Types of discontinuity and characteristics of continuous functions (Mid value theorem, absolute maximum and minimum, concept of local maximum and minimum.. ) | |
| 7. Week | Concept of derivative, and calculation with derivative rule. Proof of derivate with derivative rule. Derivative of reverse function. | |
| 8. Week | High order derivatives. Derivatives of functions with parametric equations. Derivative of implicit functions. | |
| 9. Week | Midterm | |
| 10. Week | Equation of tangent and normal. Increasing and decreasing functions | |
| 11. Week | Undetermined conditions ( Analyses of 8 condition with L’hopital Rule ) | |
| 12. Week | Maximum, minimum and asymptote of functions. | |
| 13. Week | Curve plotting. | |
| 14. Week | Engineering problems. Approximation with differential |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Sufficient knowledge in mathematics, science, and discipline-specific engineering topics; the ability to apply theoretical and practical knowledge in these areas to solve complex engineering problems. | ✔ | |||||
| 1 | Sufficient knowledge in mathematics, science, and discipline-specific engineering topics; the ability to apply theoretical and practical knowledge in these areas to solve complex engineering problems. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 |
|---|---|---|---|
| PY1 | 1 | 1 | 1 |
| Ders Kitabı veya Notu |
|
|---|---|
| Diğer Kaynaklar |
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| 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 | 4 | 56 |
|
Ders Dışı |
Preparation, After Class Study | 1 | 55 | 55 |
| Research | 1 | 15 | 15 | |
| Other Activities | 1 | 25 | 25 | |
|
Sınavlar |
Midterm | 1 | 1 | 1 |
| Final | 1 | 1 | 1 | |
| Total Workload | 153 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 6.0 | ||
