Rapor Tarihi: 13.04.2026 03:10
| Course Title | Code | Language | Type | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|---|---|
| Mathematics I | MAT111 | Turkish | Compulsory | 1. Semester | 5 + 1 | 6.0 | 6.0 |
| Prerequisite Courses | |
| Course Level | Undergraduate |
| Mode of delivery | Lecturing |
| Course Coordinator | Prof. Dr. Emrah Evren KARA |
| Instructor(s) | Prof. Dr. Emrah Evren KARA (Güz) |
| Goals | The aim of this course is to equip students with analytical problem-solving skills based on the concepts of functions, limits, continuity, and derivatives. Throughout the course, students will learn to analyze trigonometric, logarithmic, exponential, and hyperbolic functions as well as inverse functions, and to solve problems such as maxima-minima, Taylor's theorem, indeterminate forms, and curve sketching using derivative and differential applications. The course aims to equip students with mathematical modeling and problem-solving skills. |
| Course Content | The course begins with sets, absolute value, inequalities, and an introduction to analytic geometry. Then, the concept of functions and special functions (power, polynomial, trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions) are addressed. Subsequently, limits and continuity, the Intermediate Value Theorem, and the maximum-minimum properties of functions are covered. A large portion of the course focuses on derivatives and derivative techniques, parametric and closed functions, the geometric meaning of the derivative, Rolle's and Mean Value Theorems, and maximum-minimum problems. Additionally, topics such as Taylor's Theorem, indeterminate forms (L'Hospital's Rule), differentials, polar coordinates, asymptotes, and curve sketching are covered. At the end of the course, students will develop their general problem-solving skills by using all these concepts. |
| # | Öğrenme Kazanımı |
| 1 | It defines and analyzes the concepts of function, limit, and continuity. |
| 2 | Applies and interprets the properties of trigonometric, inverse trigonometric, exponential, logarithmic, and hyperbolic functions. |
| 3 | He solves problems and conducts maximum-minimum analyzes using the concepts of derivatives and differentials. |
| 4 | Calculates and interprets the derivatives of parametric and closed functions. |
| 5 | He solves and analyzes indeterminate forms using Taylor's Theorem and L'Hôpital's Rule. |
| 6 | Curve sketching creates the graphs of functions using asymptotes and polar coordinates. |
| 7 | By performing mathematical modeling, he/she applies analytical problem-solving skills and interprets the results. |
| 8 | By comparing different types of functions and problems, he/she selects and applies the appropriate solution method. |
| Week | Topics/Applications | Method |
|---|---|---|
| 1. Week | Sets, Absolute Value and Properties, Inequalities, Analytical Analysis of Directness and Circle | Research, Other Activities, Interview, Practice |
| 2. Week | Function Concept, Some Special Functions (Force, Polynomial, Absolute Value Function), Trigonometric and Inverse Trigonometric Functions, Exponential, Logarithmic and Hyperbolic Functions | Research, Other Activities, Interview, Practice |
| 3. Week | Limit Concept, Right and Left Side Limits, Indeterminate Shapes, Limits of Trigonometric Functions | Research, Other Activities, Interview, Practice |
| 4. Week | Continuity in Functions, Properties of Continuous Functions (interpolate Theorem, Absolute Max, Min, Local Max, Min Definitions) | Research, Other Activities, Interview, Practice |
| 5. Week | Concept of derivative, rules of taking derivative | Research, Other Activities, Interview, Practice |
| 6. Week | Higher Order Derivative, Inverse Function Derivative, Trigonometric Functions derivative | Interview, Practice |
| 7. Week | Derivatives of Inverse Trigonometric Functions, Derivative of Logarithm Function, Derivative of Hyperbolic and Inverse Hyperbolic Functions | Research, Other Activities, Interview, Practice |
| 8. Week | Parametric Equations Derivatives of Functions Given, Derivative of Closed Functions | Interview |
| 9. Week | Parametric Equations Derivatives of Functions Given, Derivative of Closed Functions | Research, Other Activities, Interview, Practice |
| 10. Week | Geometric Meaning of Derivative, Rolle Theorem, The Mean Value Theorem, Increasing and Decreasing Functions, Concave and Convex Functions, | Interview |
| 11. Week | Maximum and Minimum Concepts, Maximum and Minimum Problems, Taylor Theorem, Indeterminate Shapes (L 'Hospital Rule) | Research, Other Activities, Interview, Practice |
| 12. Week | Indeterminate Shapes (L 'Hospital Rule) Continued, Differential Concept | Research, Other Activities, Interview, Practice |
| 13. Week | Polar Coordinates, Asymptotes | Research, Other Activities, Interview, Practice |
| 14. Week | Curve drawings | 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 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| PY4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY5 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY6 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| PY7 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY8 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| PY9 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 |
| Ders Kitabı veya Notu | Ders Kitabı veya Ders Notu bulunmamaktadır. |
|---|---|
| Diğer Kaynaklar |
|
| Güz Dönemi | |||
| Responsible Personnel | Grup | Evaluation Method | Percentage |
|---|---|---|---|
| Prof. Dr. Emrah Evren KARA | Vize | 40.00 | |
| Prof. Dr. Emrah Evren KARA | 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 | ||
