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Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | DUM1012022252 | | Compulsory | 1 | 1 | 3 |
| | Level of Course Unit | | First Cycle | | Objectives of the Course | | To provide concepts of functions, limits, continuity, differentiation and integration.
To provide the applications of differentiation and integration.
To give an ability to apply knowledge of mathematics on engineering problems. | | Name of Lecturer(s) | | | Learning Outcomes | | 1 | Compute the limit of various functions, use the concepts of continuity, use the rules of differentiation to differentiate functions. | | 2 | Sketch the graph of a function using asymptotes, critical points and the derivative test for increasing/decreasing and concavity properties. | | 3 | This course is designed to give the fundamental concepts of analysis. |
| | Mode of Delivery | | Formal Education | | Prerequisites and co-requisities | | | Recommended Optional Programme Components | | | Course Contents | | Natural numbers, rational numbers, irrational numbers and real number sets, the properties of linear points-phrases and completeness axiom, Extented real numbers and complex numbers. Sequences, sub-sequences, convergent sequences, the lower limit and upper limit, Cauchy sequences. Limit of functions. Continuty of functions. Trigonometric, exponential, logaritmic and hyperbolic functions. Unifom contunuity, properties of continuity functions. Derivatives, derivative rules. Parametric and implicit differentiation, higher-order derivatives. Geometrical and physical meaning of the derivative. Extrema, the derivative theorems. Uncertain limits and differential forms. Cartesian and polar coordinates, curve sketching. | | Weekly Detailed Course Contents | |
| 1 | Natural numbers, rational numbers, irrational numbers and real number sets | | | | 2 | The properties of linear points-phrases and completeness axiom | | | | 3 | Extented real numbers and complex numbers. | | | | 4 | Sequences, sub-sequences, convergent sequences, the lower limit and upper limit, Cauchy sequences | | | | 5 | Limit of functions. | | | | 6 | Continuty of functions | | | | 7 | Trigonometric, exponential, logaritmic and hyperbolic functions | | | | 8 | Midterm Exam | | | | 9 | Unifom contunuity, properties of continuity functions. | | | | 10 | Derivatives, derivative rules | | | | 11 | Parametric and implicit differentiation, higher-order derivatives. | | | | 12 | Geometrical and physical meaning of the derivative | | | | 13 | Extrema, the derivative theorems | | | | 14 | Uncertain limits and differential forms | | | | 15 | Final Exam | | |
| | Recommended or Required Reading | | Thomas, G.B., Finney, R.L.. (Çev: Korkmaz, R.), 2001. Calculus ve Analitik Geometri, Cilt I, Beta Yayınları, İstanbul. Balcı, M. 2009. Genel Matematik 1, Balcı Yayınları, Ankara | | Planned Learning Activities and Teaching Methods | | | 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) | |
| | Workload Calculation | |
| Midterm Examination | 1 | 1 | 1 | | Final Examination | 1 | 1 | 1 | | Attending Lectures | 14 | 4 | 56 | | Individual Study for Mid term Examination | 2 | 2 | 4 | | Individual Study for Final Examination | 2 | 3 | 6 | | 5 | 2 | 10 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 5 | 2 | 5 | 3 | 4 | 2 | 2 | 1 | 2 | 3 | 2 | 2 | | LO2 | 4 | 5 | 5 | 3 | 3 | 2 | 2 | 2 | 1 | 2 | 2 | 1 | | LO3 | 3 | 5 | 5 | 4 | 3 | 3 | 3 | 3 | 2 | 3 | 2 | 3 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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