| Course Title | Code | Semester | L+U Hour | Credits | ECTS |
|---|---|---|---|---|---|
| Mathematics I | MTH101 | 1. 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 |
Assoc. Prof. Dr. Nejla ÖZMEN Assist. Prof. Dr. Esra KORKMAZ |
| Instructors |
Esra KORKMAZ |
| Assistants | |
| Goals | This course aims to provide a solid foundation in calculus by introducing the fundamental concepts of functions, limits, and derivatives, enabling students to analyze and model real-world phenomena. |
| Course Content | Functions, Limits and Continuity, Derivative and its Applications |
| Learning Outcomes |
- Uses transcendental functions including logarithms, exponentials and inverse trigonometric functions effectively - Computes limits and carry out some basic proofs about limits and continuity. - Computes derivatives and use it in applications such as computing rates of change, finding extreme values. - Solves optimization problems in the field using the concepts of first and second derivatives - Analyzes the behavior of functions by determining intervals of increase/decrease, concavity, and asymptotes, and sketches graphs of functions. |
| Week | Topics | Learning Methods |
|---|---|---|
| 1. Week | Precalculus: Pre-Calculus Real numbers, Equations and Inequalities | |
| 2. Week | Pre-Calculus: Functions, Some Special Functions (Polynomial, Absolute Value, Trigonometric, Inverse Trigonometric, Exponential, Logarithmic, Hyperbolic) | |
| 3. Week | The Concept of Limit, One-Sided Limits, Squeeze Theorem | |
| 4. Week | Infinite Limits, Limits at Infinity, Continuity, Intermediate Value Theorem | |
| 5. Week | Slope, Tangent Lines, Definition of Derivative, Derivative as a Function | |
| 6. Week | Higher Derivatives, Derivatives of Inverse Functions, Derivatives of trigonometric functions | |
| 7. Week | Chain rule, Implicit derivative, Tangent and Normal lines | |
| 8. Week | Midterm | |
| 9. Week | Logarithmic differentiation, Indeterminate Forms, L'Hôpital's rule | |
| 10. Week | Mean Value Theorem, Rolle's Theorem, Local extremum, Absolute extremum, 1st derivative test | |
| 11. Week | Concavity, Inflection points, Second derivative test, Asymptotes | |
| 12. Week | Curve Sketching | |
| 13. Week | Taylor formula, Big-O Notation | |
| 14. Week | Optimization problems |
| Robert A. Adams, Christopher Essex, Calculus: A Complete Course, 8th edition, Pearson, 2013 |
| J. Stewart, Calculus: Early Transcentals, 8th edition, Brooks Cole, 2015 |
| 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 | Measurement Method |
|---|---|---|---|---|---|---|---|
| PY1 | 4 | 3 | 4 | 4 | 5 | 4 | - |
| PY8 | 2 | 2 | 2 | 3 | 2 | 3 | - |
| 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 | 2 | 2 |
| Homework 1 | 2 | 7 | 14 |
| Homework 2 | 2 | 7 | 14 |
| Quiz 1 | 1 | 5 | 5 |
| Quiz 2 | 1 | 5 | 5 |
| Final | 1 | 2 | 2 |
| Practice | 11 | 2 | 22 |
| Practice End-Of-Term | 3 | 12 | 36 |
| Classroom Activities | 14 | 2 | 28 |
| Total Workload | 128 | ||
| ECTS Credit of the Course | 5.0 | ||
