Rapor Tarihi: 13.04.2026 03:11
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematics II | MAT112 | Turkish | Compulsory | 2. Semester | 5 + 1 | 6.0 | 6.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | This course is conducted through lectures, question–answer sessions, and worked examples in order to help students understand and apply the fundamental concepts of the subject. During the course, the instructor explains the topics using the board or presentations, and then works through examples together with the students. When necessary, short activities and discussions are included to enhance student participation. |
| Course Coordinator | Prof. Dr. Emrah Evren KARA, Doç. Dr. İzzettin DEMİR |
| Instructor(s) | Doç. Dr. İzzettin DEMİR (Bahar) |
| Goals | The aim of this course is to teach students the concepts and application techniques of indefinite and definite integrals; to equip them with the ability to use methods such as substitution, partial integration, partial fraction decomposition, and integration of trigonometric and irrational expressions. Additionally, it aims to provide proficiency in analytical problem-solving and mathematical modeling by using generalized integrals, area, volume, and surface area calculations, as well as the topics of limits and continuity in multivariable functions. |
| Course Content | The course begins with indefinite integrals and the rules of integration, applying basic methods such as substitution and integration by parts. Next, techniques such as partial fraction decomposition and the integration of trigonometric and irrational expressions are covered. The course progresses with the definition and properties of definite integrals, generalized integrals, and convergence criteria. Within the scope of practical examples, calculations of area, arc length, volume, and surface area of revolution are performed. In the final section of the course, multivariable functions, domains, limits, and continuity concepts are addressed. Throughout the course, students develop their problem-solving and analytical thinking skills by using these concepts. |
| # | Öğrenme Kazanımı |
| 1 | Explains and applies the definition and basic rules of indefinite and definite integrals. |
| 2 | He solves integral problems using the methods of substitution and partial integration. |
| 3 | Partial fraction decomposition makes trigonometric and irrational expressions integrable and solves them. |
| 4 | Analyzes and comments on the convergence of generalized integrals. |
| 5 | Applies and interprets the calculations for area, arc length, volume, and surface of revolution. |
| 6 | Determines the domains of multivariable functions and conducts limit and continuity analyzes. |
| 7 | By establishing mathematical models, they develop solution strategies and report the results. |
| 8 | Compares different integral and multivariable problem-solving methods and selects the appropriate one. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Indefinite Integral, Indefinite Integral Rules, Variable Change Method, Partial Integral Method. | Research, Other Activities, Interview, Practice |
| 2. Week | Simple fractional separation method, Integration of Trigonometric Expressions | Research, Other Activities, Interview, Practice |
| 3. Week | Integration of Irrational Algebraic Expressions, Binomial Integrals. | Research, Other Activities, Interview, Practice |
| 4. Week | Calculation of Some Original Integrals, Definition of Definite Integrals | Research, Other Activities, Interview, Practice |
| 5. Week | Problems in the Concept of Definite Integral, Definition of Definite Integral and Its Properties. | Research, Other Activities, Interview, Practice |
| 6. Week | Problems in the Concept of Definite Integral, Definition of Definite Integral and Its Properties. | Research, Other Activities, Interview, Practice |
| 7. Week | Genelleştirilmiş integraller, Özel Olmayan İntegraller, Karışık Örnekler | Research, Other Activities, Interview, Practice |
| 8. Week | Convergence Criteria of Generalized Integrals | Interview, Practice |
| 9. Week | area account, curve arc length | Research, Other Activities, Interview, Practice |
| 10. Week | area account, curve arc length | Interview, Practice |
| 11. Week | volume account | Research, Other Activities, Interview, Practice |
| 12. Week | Rotary Surface Area Account. | Research, Other Activities, Interview, Practice |
| 13. Week | Definition Clusters in Multivariable Functions. | Research, Other Activities, Interview, Practice |
| 14. Week | Limit and Continuity in Two and More Variable Functions. | Research, Other Activities, Interview, Practice |
| 15. Week | General problem solutions | Research, Other Activities, Interview, Practice |
| No | Program Requirements | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | To have theoretical and / or practical knowledge in the field of mathematics, science, social sciences, engineering and / or industrial engineering, and the ability to use this knowledge to model and solve engineering problems | ✔ | |||||
| 2 | Gaining the ability to work actively in projects and projects aimed at professional development in both individual and multidisciplinary groups and taking responsibility in situations that may arise in this process | ✔ | |||||
| 3 | Knowledge of at least one foreign language at a level that will enable communication with colleagues in the field and follow current developments; ability to write and understand written reports effectively, prepare design and production reports, make effective presentations, and give and receive clear and understandable instructions. | ✔ | |||||
| 4 | To be individuals who are sensitive to universal and social values, have knowledge of professional and ethical responsibilities and standards used in engineering practices. | ✔ | |||||
| 5 | The ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions; the ability to apply modern design methods for this purpose. | ✔ | |||||
| 6 | Ability to design and conduct experiments, collect data, analyze and interpret results to investigate complex engineering problems or discipline-specific research topics. | ✔ | |||||
| 7 | Ability to select and use modern techniques and tools necessary for the identification, formulation, analysis and solution of complex problems encountered in engineering applications; ability to use information technologies effectively. | ✔ | |||||
| 8 | Knowledge of business practices such as project management, risk management and change management; awareness of entrepreneurship and innovation; knowledge of sustainable development. | ✔ | |||||
| 9 | Knowledge of the universal and societal impacts of engineering practices on health, environment and safety, and contemporary issues reflected in the field of engineering; awareness of the legal consequences of engineering solutions, the necessity of lifelong learning and the ability to continuously renew oneself. | ✔ | |||||
| Program Requirements | DK1 | DK2 | DK3 | DK4 | DK5 | DK6 | DK7 | DK8 |
|---|---|---|---|---|---|---|---|---|
| PY1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY5 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY6 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY7 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY8 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY9 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| Bahar Dönemi | |||
| Responsible Personnel | Grup | Evaluation Method | Percentage |
|---|---|---|---|
| Doç. Dr. İzzettin DEMİR | Vize | 40.00 | |
| Doç. Dr. İzzettin DEMİR | Final | 60.00 | |
| Toplam | 100.00 | ||
| ECTS credits and course workload | Quantity | Duration (Hour) | Total Workload (Hour) | |
|---|---|---|---|---|
|
Ders İçi |
Class Hours | 14 | 6 | 84 |
|
Ders Dışı |
Research | 4 | 2 | 8 |
| Practice | 10 | 1 | 10 | |
|
Sınavlar |
Midterm | 1 | 1.5 | 1.5 |
| Homework | 4 | 2 | 8 | |
| Homework Preparation | 4 | 2 | 8 | |
| Final | 1 | 1.5 | 1.5 | |
| Practice | 14 | 1 | 14 | |
| Practice End-Of-Term | 6 | 2 | 12 | |
| Classroom Activities | 6 | 1 | 6 | |
| Total Workload | 153 | |||
| *AKTS = (Total Workload) / 25,5 | ECTS Credit of the Course | 6.0 | ||
