| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Mathematics II | MTH102 | 2. Semester | 4 + 0 | 4.0 | 5.0 |
| Prerequisites | None |
| Language of Instruction | English |
| Course Level | Undergraduate |
| Course Type | |
| Mode of delivery | Face to face |
| Course Coordinator |
Assist. Prof. Dr. Umut SAYIN Assist. Prof. Dr. Esra KORKMAZ |
| Instructors |
Esra KORKMAZ |
| Assistants | |
| 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 |
| Learning Outcomes |
- Recognizes the concept of indefinite integral. - Applies the integrating methods. - Understands the applications of the definite integral. - Recognizes improper integrals. - Recognizes improper integrals. - Recognizes multivariable functions. - olves limit and continuity problems in multivariable functions. |
| Week | Topics | Learning Methods |
|---|---|---|
| 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 |
| J. Stewart, Calculus: Early Transcentals, 8th edition, Brooks Cole, 2015 |
| Robert A. Adams, Christopher Essex, Calculus: A Complete Course, 8th edition, Pearson, 2013 |
| M. D. Weir, J.Hass, F. R. Giordano, G. B. Thomas, Thomas' calculus : early transcendentals, 12th edition, Pearson Addison-Wesley, Boston, 2010 |
| Program Requirements | Contribution Level | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | 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) |
|---|---|---|---|
| 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 | ||
| ECTS Credit of the Course | 5.0 | ||
