| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematics II | MTH102 | English | Compulsory | 2. Semester | 4 + 0 | 4.0 | 5.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Face to face |
| Course Coordinator | Dr. Öğr. Üyesi UMUT SAYIN, Dr. Öğr. Üyesi Esra KORKMAZ |
| Instructor(s) | |
| Goals | The primary objective of this course is to comprehensively present students with the theoretical foundations and practical application methods of integral calculus. By also encompassing various applications of integrals and the fundamental concepts of multivariable calculus, it aims to develop students' analytical thinking skills and enable them to effectively use mathematical tools to solve problems in diverse fields. |
| Course Content | Introduction to Integral Calculus, Definite Integral and its Properties, Integration Techniques, Improper Integrals, Applications of Integrals, Introduction to Multivariable Functions, Multivariable Differentiation |
| # | Öğrenme Kazanımı |
| 1 | Recognizes the concept of indefinite integral. |
| 2 | Applies the integrating methods. |
| 3 | Understands the applications of the definite integral. |
| 4 | Recognizes improper integrals. |
| 5 | Recognizes improper integrals. |
| 6 | Recognizes multivariable functions. |
| 7 | olves limit and continuity problems in multivariable functions. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | General Introduction to Integrals, Riemann Sums, Definite Integral | |
| 2. Week | Properties of the Definite Integral, Antiderivative, Indefinite Integral | |
| 3. Week | Fundamental Theorem of Calculus, Substitution Method | |
| 4. Week | Integration by Parts, Trigonometric Integrals | |
| 5. Week | Trigonometric Substitution, Integration by Partial Fractions | |
| 6. Week | Improper Integrals | |
| 7. Week | Convergence Tests for Improper Integrals | |
| 8. Week | Midterm | |
| 9. Week | Applications of Integrals, Area, Volume | |
| 10. Week | Applications of Integrals, Arc Length, Area of a Surface of Revolution | |
| 11. Week | Domain of Multivariable Functions | |
| 12. Week | Limits and Continuity in Multivariable Functions | |
| 13. Week | Partial Derivatives, Higher-Order Derivatives | |
| 14. Week | Chain Rule, Gradient and Directional Derivative |
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 |
|---|
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Sınavlar |
Midterm 1 | 1 | 15 | 15 |
| Homework 1 | 1 | 16 | 16 | |
| Homework 2 | 1 | 16 | 16 | |
| Final | 1 | 25 | 25 | |
| Classroom Activities | 14 | 4 | 56 | |
| Total Workload | 128 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 5.0 | ||
