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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 | | 20150102001100 | CALCULUS - I | Compulsory | 1 | 1 | 5 |
| | Level of Course Unit | | First Cycle | | Objectives of the Course | | To give basic concepts about mathematics, to give the concepts of limit, continuity, derivative in single variable functions. | | Name of Lecturer(s) | | Dr.Öğr.Üyesi Hasan KARA | | Learning Outcomes | | 1 | Defines the increasing and decreasing functions with tangent and normal equation. | | 2 | Calculates the limit of indeterminate states by using derivative. | | 3 | Defines asymptotes with maximum and minimum of functions. | | 4 | Explains the curve drawings. | | 5 | Solve engineering problems by using derivative. Calculates approximate using differential. | | 6 | Define concepts of set and number sets. Explain the concepts of identity, equation and inequality. | | 7 | Defines the properties of functions and functions. | | 8 | Defines trigonometric, inverse trigonometric and hyperbolic functions, Partial functions and specially defined functions (absolute value, exact value, sign functions). | | 9 | Explains the concept of limit and makes limit calculation with limit definition. Prove the rules used for limit calculation. | | 10 | Defines right and left sided limits. He knows vague situations. | | 11 | Defines the concept of continuity in functions and knows types of discontinuity. | | 12 | Explain the concept of derivative and make derivative calculations with the definition of derivative. Provides the rules of derivation with the definition of derivative. | | 13 | Defines the derivative of trigonometric and inverse trigonometric functions, exponential and logarithmic functions, hyperbolic and inverse hyperbolic functions. | | 14 | Calculates higher order derivatives. The parametric equations describe the derivatives of the given functions. Explain the derivative of closed functions. |
| | Mode of Delivery | | Daytime Class | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | Preliminaries, Functions, Limits and Continuity, Derivatives, Applications of Derivatives. | | Weekly Detailed Course Contents | |
| 1 | Sets. Number Sets. Equations. Identities. Inequalities. | | | | 2 | Function concept. Function varieties (Polynomial function, rational function, exponential and logarithm function and the widest definition of these functions). | | | | 3 | Function types (Trigonometric, inverse trigonometric and hyperbolic functions. Partial functions, specially defined functions (Absolute value, exact value, sign functions) | | | | 4 | Limit concept and limit calculation. Proof of the rules used for limit calculation. Sandwich theorem. Limits of trigonometric functions. | | | | 5 | Right and left sided limits. Uncertain cases (0/0, infinite / infinite, 0.infinite, infinite-infinite, 1 ^ infinite) | | | | 6 | oncept of continuity in functions. Types of discontinuity. Properties of continuous functions (Intermediate theorem, absolute maximum and minimum, local maximum and minimum definitions) | | | | 7 | The concept of derivative and derivative calculus. Derivation of derivative with the definition of derivative rules. Derivative of inverse function. | | | | 8 | Midterm | | | | 9 | Derivative of trigonometric and inverse trigonometric functions. Derivative of exponential and logarithm functions. Derivative of hyperbolic and inverse hyperbolic functions. | | | | 10 | Higher order derivative. Derivatives of functions given parametric equations. Derivative of closed functions. | | | | 11 | Tangent and normal equation. Increasing and decreasing functions | | | | 12 | Indefinite cases (examination with L’Hopital Rule). | | | | 13 | Maximum and minimum functions, asymptotes, Curve drawings. | | | | 14 | Engineering problems. Approximate calculation with differential. | | | | 15 | Engineering problems. Approximate calculation with differential. | | | | 16 | Final Exam | | |
| | Recommended or Required Reading | | 1-Matematik Analiz ve Analitik Geometri, Edwards ve Penney, Çeviri Editörü Prof.Dr. Ömer Akın
2-Genel Matematik, Prof. Dr. Mustafa Balcı Calculus, Robert Ellis-Denny Gulick
3-Genel Matematik, Prof. Dr. Ekrem Kadıoğlu, Prof. Dr. Muhammet Kamalı | | Planned Learning Activities and Teaching Methods | | | Assessment Methods and Criteria | |
| Midterm Examination | 1 | 100 | | SUM | 100 | |
| Final Examination | 1 | 100 | | SUM | 100 | | Term (or Year) Learning Activities | 40 | | End Of Term (or Year) Learning Activities | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | |
| | Workload Calculation | |
| Midterm Examination | 1 | 10 | 10 | | Final Examination | 1 | 15 | 15 | | Makeup Examination | 1 | 10 | 10 | | Quiz | 1 | 10 | 10 | | Attending Lectures | 14 | 4 | 56 | | Question-Answer | 7 | 3 | 21 | | Self Study | 14 | 2 | 28 | | Homework | 4 | 3 | 12 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 3 | 3 | 3 | 2 | 3 | 4 | 3 | 3 | 4 | 3 | 3 | | LO2 | 3 | 3 | 3 | 3 | 2 | 3 | 3 | 3 | 2 | 4 | 4 | | LO3 | 4 | 4 | 4 | 3 | 3 | 4 | 2 | 3 | 3 | 3 | 3 | | LO4 | 3 | 4 | 4 | 3 | 4 | 4 | 4 | 3 | 4 | 3 | 3 | | LO5 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 4 | | LO6 | 3 | 4 | 3 | 2 | 3 | 4 | 3 | 4 | 4 | 3 | 4 | | LO7 | 3 | 3 | 3 | 4 | 3 | 3 | 4 | 4 | 3 | 4 | 3 | | LO8 | 3 | 4 | 3 | 2 | 3 | 3 | 3 | 3 | 3 | 4 | 3 | | LO9 | 3 | 3 | 3 | 3 | 3 | 4 | 3 | 2 | 3 | 3 | 3 | | LO10 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | | LO11 | 3 | 4 | 3 | 3 | 4 | 3 | 3 | 3 | 3 | 3 | 3 | | LO12 | 3 | 2 | 3 | 2 | 3 | 3 | 4 | 4 | 4 | 4 | 3 | | LO13 | 2 | 3 | 3 | 3 | 3 | 3 | 4 | 3 | 2 | 4 | 3 | | LO14 | 3 | 2 | 3 | 2 | 3 | 4 | 2 | 3 | 3 | 2 | 3 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
226 13 14 • e-mail: info@igdir.edu.tr
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