| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | PM1012016954 | MATHEMATICS I | Compulsory | 1 | 1 | 5 |
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| Level of Course Unit |
| First Cycle |
| Objectives of the Course |
| This lecture deals with limit, continuity, derivative and applications of derivative. |
| Name of Lecturer(s) |
| Yrd.Doç.Dr. Tolga AKTÜRK |
| Learning Outcomes |
| 1 | Recognizes basic elementary functions | | 2 | Knows the definitions of limit, continuity and derivative and evaluates limits | | 3 | Obtains the derivatives of elementary functions. Finds the derivative of the composition of functions | | 4 | Uses the applications of the derivative in the areas of maximum-minimum problems and engineering. Explains the mean value theorem | | 5 | Decides some properties of the functions such as increasing, decreasing, convexity concavity by using derivative. Sketch their graphs |
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| Mode of Delivery |
| Formal Education |
| Prerequisites and co-requisities |
| None |
| Recommended Optional Programme Components |
| None |
| Course Contents |
| Function, limit, continuity, derivative, applications of the derivative |
| Weekly Detailed Course Contents |
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| 1 | Definition of function. Trigonometric functions | | | | 2 | Inverse Trigonometric functions, Exponential and Logarithmic functions | | | | 3 | The least integer function, Signum function, Scaling and Reflecting a Graph of a function | | | | 4 | Definition of the limit, one sided limits. | | | | 5 | Basic trigonometric limits. The concept of continuity. | | | | 6 | Properties of continuous functions on the closed interval. Intermediate value theorem, Bolzano's theorem, local and absolute maxima and minima. | | | | 7 | Derivative. | | | | 8 | Midterm | | | | 9 | Basic differentiation rules. Derivative of inverse function. Derivative of trigonometric functions. | | | | 10 | Derivative of inverse trigonometric functions. Derivatives of Logaritmic and exponential functios. | | | | 11 | Logarithmic differentiation. Derivative of parametric equations, Implicit differentiation. | | | | 12 | Higher derivatives. Geometric interpretation of derivative. | | | | 13 | Increasing, decreasing function. First and second derivative tests for local extrema. | | | | 14 | Applied maximum-minimum problems. Mean value theorem, Rolle's Theorem. | | | | 15 | Final Exam | | | | 16 | | | |
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| Recommended or Required Reading |
| Mustafa Balcı Genel Matematik I |
| Planned Learning Activities and Teaching Methods |
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| Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
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| Workload Calculation |
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| Midterm Examination | 1 | 3 | 3 |
| Final Examination | 1 | 4 | 4 |
| Attending Lectures | 14 | 5 | 70 |
| Self Study | 14 | 5 | 70 |
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| Contribution of Learning Outcomes to Programme Outcomes |
| LO1 | 4 | 4 | | | 3 | 5 | | | | | | | | | | | | | | | | | | | | | | | | | LO2 | 4 | 4 | | | 3 | 5 | | | | | | | | | | | | | | | | | | | | | | | | | LO3 | 4 | 4 | | | 3 | 5 | | | | | | | | | | | | | | | | | | | | | | | | | LO4 | 4 | 4 | | | 3 | 5 | | | | | | | | | | | | | | | | | | | | | | | | | LO5 | 4 | 4 | | | 3 | 5 | | | | | | | | | | | | | | | | | | | | | | | |
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| * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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