| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Analysis I | MAE103 | 1. Semester | 4 + 0 | 4.0 | 5.0 |
| Prerequisites | None |
| Language of Instruction | Turkish |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Face to face |
| Course Coordinator |
Assoc. Prof. Dr. EMİNE NUR ÜNVEREN BİLGİÇ |
| Instructor(s) |
EMİNE NUR ÜNVEREN BİLGİÇ |
| Assistants | |
| Goals | The aim of this course is to enable students to develop a good understanding of some univariate analysis concepts and to gain the ability to apply these concepts. |
| Course Content | - Knows functions and graphs. - Knows the concepts of limit, continuity and discontinuity. - Makes applications of the limit. - Knows derivatives and derivatives rules. - Makes applications of derivative. - Knows the concept of differential. - Knows the concepts of integral, indefinite integral and definite integral. - Makes the applications of the integral. |
| Learning Outcomes |
- Knows the axioms of the real number system. - Knows the basic types of functions and draws their graphs. - Interpret the formal definitions of limit and continuity concepts in both algebraic and graphical dimensions and comprehend the difference between these two definitions. - Apply the concepts of limit and continuity in problem solving. - Knows different interpretations of derivative concept (instantaneous rate of change, slope of tangent) and can adapt the concept of derivative to optimization problems. - It establishes the connection between the sign of the first and second order derivative functions of a function and the increasing/decreasing convex/concave characteristics of the graph of the function. - Can construct rational numbers and some irrational numbers on the number line with the Euclidean method. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Functions (trigonometric, exponential, logarithmic, hyperbolic functions) | Course Hours Verbal Expression |
| 2. Week | Functions (custom defined functions and graphs) | Verbal Expression Course Hours |
| 3. Week | The concept of limit/continuity in functions of one variable and its applications | Course Hours Verbal Expression |
| 4. Week | Types of discontinuities | Course Hours Verbal Expression |
| 5. Week | The concept of derivatives and the rules of differentiation in functions of one variable | Verbal Expression Course Hours |
| 6. Week | Higher order derivatives, extreme and absolute extreme points of functions | Course Hours Verbal Expression |
| 7. Week | Extreme problems and their applications in various fields | Course Hours Verbal Expression |
| 8. Week | Mid Term Exam | Other Activities |
| 9. Week | Role and Mean Value Theorems | Course Hours Verbal Expression |
| 10. Week | L'Hospital Rule and limit calculations with the help of this rule | Course Hours Verbal Expression |
| 11. Week | Differential and linear increment | Course Hours Verbal Expression |
| 12. Week | Concept of integral, indefinite integrals | Verbal Expression Course Hours |
| 13. Week | Integration techniques | Course Hours Verbal Expression |
| 14. Week | Integration techniques | Course Hours Verbal Expression |
| Analiz1, Ahmet Dernek, Nobel Yayın Dağıtım. |
| Çoker, D, Özer, O. ve Taş, K. (2009). Genel Matematik I, Seçkin Yayıncılık. |
| Finney, T. (2011), Thomas Kalkülüs, Çeviri: Recep Korkmaz, Beta yayınları. |
| Bizim O., Tekcan, A., Gezer, B. (2009), Genel Matematik I, Dora Yayıncılık. |
| Stewart, J. (2010), Kalkülüs: Kavram ve Kapsam, Seçkin Yayıncılık. |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | Measurement Method |
|---|---|---|---|---|---|---|---|---|---|
| PY27 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 40,60 |
| PY30 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 40,60 |
| 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 |
| Research | 14 | 2 | 28 |
| Other Activities | 11.5 | 1 | 11.5 |
| Verbal Expression | 14 | 2 | 28 |
| Midterm 1 | 1 | 2 | 2 |
| Final | 1 | 2 | 2 |
| Total Workload | 127.5 | ||
| ECTS Credit of the Course | 5.0 | ||
