| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Analysis II | MAE104 | 2. Semester | 3 + 0 | 3.0 | 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 | To learn multivariable functions, limit, continuity and derivative concepts and applications in multivariable functions, double integral concept and applications. |
| Course Content | Makes applications of definite integral. Knows the concept of multivariable function. Knows the concepts of limit and derivative in functions of two variables. Makes applications of limit and derivative in functions of two variables. Knows the concept of double integral. Makes the applications of double integral. |
| Learning Outcomes |
- Will be able to make sense of complex numbers and perform defined operations on these numbers. - Will be able to understand how trigonometric functions are defined in the context of real numbers. - Will be able to understand the Riemann sum. - Will be able to understand the relationship between the indefinite integral and the definite integral. - Will be able to apply integration methods. - will be able to examine the convergence of the series using convergence tests. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Area and volume calculations with definite integral, applications in various fields | Course Hours Verbal Expression |
| 2. Week | Area and volume calculations with definite integral, applications in various fields | Verbal Expression Course Hours |
| 3. Week | Multivariable function concept, function definition and value sets, function plots | Course Hours Verbal Expression |
| 4. Week | The concept of limit and its applications in functions of two variables, the concept of continuity | Course Hours Verbal Expression |
| 5. Week | The concept of limit and its applications in functions of two variables, the concept of continuity | Verbal Expression Course Hours |
| 6. Week | Partial derivative and geometric interpretation of functions of two variables | Course Hours Verbal Expression |
| 7. Week | Chain rule, differential increment and linearization, local extreme values | Course Hours Verbal Expression |
| 8. Week | Mid Term Exam | Other Activities |
| 9. Week | Chain rule, differential increment and linearization, local extreme values | Course Hours Verbal Expression |
| 10. Week | Absolute extreme values and applications | Course Hours Verbal Expression |
| 11. Week | Lagrange multipliers | Verbal Expression Course Hours |
| 12. Week | İki katlı integral kavramı | Verbal Expression Course Hours |
| 13. Week | Volume calculations with double integral | Course Hours Verbal Expression |
| 14. Week | Volume calculations with double integral | Verbal Expression Course Hours |
| 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 | Measurement Method |
|---|---|---|---|---|---|---|---|---|
| PY27 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 40,60 |
| PY30 | 5 | 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 |
| Other Activities | 14 | 2 | 28 |
| Verbal Expression | 1 | 0.5 | 0.5 |
| Visual Presentation | 23 | 1 | 23 |
| Midterm 1 | 1 | 10 | 10 |
| Final | 1 | 10 | 10 |
| Total Workload | 127.5 | ||
| ECTS Credit of the Course | 5.0 | ||
