| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Mathematics I | MAT111 | 1. Semester | 5 + 1 | 6.0 | 6.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | face to face |
| Course Coordinator |
Prof. Dr. İlhame AMİRALİ |
| Instructor(s) |
İlhame AMİRALİ |
| Assistants | |
| Goals | To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions |
| Course Content | |
| Learning Outcomes |
- Describe the concepts of set and number sets. It explains the concepts of identity, equation and inequality - Defines the properties of functions and functions - Defines trigonometric, inverse trigonometric and hyperbolic functions, partial functions and special defined functions (absolute value, exact value, sign functions) |
| Week | Topics | Learning Methods |
|---|---|---|
| 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 |
| Thomas, G.B., Thomas Calculus, 11.baskı, çeviri:Recep Korkmaz, Beta Basım, 2010. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | Measurement Method |
|---|
| 0 | 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|---|
| Course's Level of contribution | None | Very Low | Low | Fair | High | Very High |
| Method of assessment/evaluation | Written exam | Oral Exams | Assignment/Project | Laboratory work | Presentation/Seminar |
| Event | Quantity | Duration (Hour) | Total Workload (Hour) |
|---|---|---|---|
| Course Hours | 14 | 4 | 56 |
| Preparation, After Class Study | 1 | 55 | 55 |
| Research | 1 | 15 | 15 |
| Other Activities | 1 | 25 | 25 |
| Midterm 1 | 1 | 1 | 1 |
| Final | 1 | 1 | 1 |
| Total Workload | 153 | ||
| ECTS Credit of the Course | 6.0 | ||
