| 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 |
| # | 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 |
| Program Requirements | DK1 | DK2 | DK3 |
|---|
| 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 | 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 | 1 |
| Final | 1 | 1 | 1 | |
| Total Workload | 153 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 6.0 | ||
