Description of Individual Course Units
Course Unit CodeCourse Unit TitleType of Course UnitYear of StudySemesterNumber of ECTS Credits
20150102001100CALCULUS - ICompulsory115
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
1Defines the increasing and decreasing functions with tangent and normal equation.
2Defines the increasing and decreasing functions with tangent and normal equation.
3Calculates the limit of indeterminate states by using derivative.
4Calculates the limit of indeterminate states by using derivative.
5Defines asymptotes with maximum and minimum of functions.
6Defines asymptotes with maximum and minimum of functions.
7Explains the curve drawings.
8Explains the curve drawings.
9Solve engineering problems by using derivative. Calculates approximate using differential.
10Solve engineering problems by using derivative. Calculates approximate using differential.
11Define concepts of set and number sets. Explain the concepts of identity, equation and inequality.
12Define concepts of set and number sets. Explain the concepts of identity, equation and inequality.
13Defines the properties of functions and functions.
14Defines the properties of functions and functions.
15Defines trigonometric, inverse trigonometric and hyperbolic functions, Partial functions and specially defined functions (absolute value, exact value, sign functions).
16Defines trigonometric, inverse trigonometric and hyperbolic functions, Partial functions and specially defined functions (absolute value, exact value, sign functions).
17Explains the concept of limit and makes limit calculation with limit definition. Prove the rules used for limit calculation.
18Explains the concept of limit and makes limit calculation with limit definition. Prove the rules used for limit calculation.
19Defines right and left sided limits. He knows vague situations.
20Defines right and left sided limits. He knows vague situations.
21Defines the concept of continuity in functions and knows types of discontinuity.
22Defines the concept of continuity in functions and knows types of discontinuity.
23Explain the concept of derivative and make derivative calculations with the definition of derivative. Provides the rules of derivation with the definition of derivative.
24Explain the concept of derivative and make derivative calculations with the definition of derivative. Provides the rules of derivation with the definition of derivative.
25Defines the derivative of trigonometric and inverse trigonometric functions, exponential and logarithmic functions, hyperbolic and inverse hyperbolic functions.
26Defines the derivative of trigonometric and inverse trigonometric functions, exponential and logarithmic functions, hyperbolic and inverse hyperbolic functions.
27Calculates higher order derivatives. The parametric equations describe the derivatives of the given functions. Explain the derivative of closed functions.
28Calculates 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
WeekTheoreticalPracticeLaboratory
1Sets. Number Sets. Equations. Identities. Inequalities.
2Function concept. Function varieties (Polynomial function, rational function, exponential and logarithm function and the widest definition of these functions).
3Function types (Trigonometric, inverse trigonometric and hyperbolic functions. Partial functions, specially defined functions (Absolute value, exact value, sign functions)
4Limit concept and limit calculation. Proof of the rules used for limit calculation. Sandwich theorem. Limits of trigonometric functions.
5Right and left sided limits. Uncertain cases (0/0, infinite / infinite, 0.infinite, infinite-infinite, 1 ^ infinite)
6oncept of continuity in functions. Types of discontinuity. Properties of continuous functions (Intermediate theorem, absolute maximum and minimum, local maximum and minimum definitions)
7The concept of derivative and derivative calculus. Derivation of derivative with the definition of derivative rules. Derivative of inverse function.
8Midterm
9Derivative of trigonometric and inverse trigonometric functions. Derivative of exponential and logarithm functions. Derivative of hyperbolic and inverse hyperbolic functions.
10Higher order derivative. Derivatives of functions given parametric equations. Derivative of closed functions.
11Tangent and normal equation. Increasing and decreasing functions
12Indefinite cases (examination with L’Hopital Rule).
13Maximum and minimum functions, asymptotes, Curve drawings.
14Engineering problems. Approximate calculation with differential.
15Engineering problems. Approximate calculation with differential.
16Final 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
Term (or Year) Learning ActivitiesQuantityWeight
Midterm Examination1100
SUM100
End Of Term (or Year) Learning ActivitiesQuantityWeight
Final Examination1100
SUM100
Term (or Year) Learning Activities40
End Of Term (or Year) Learning Activities60
SUM100
Language of Instruction
Turkish
Work Placement(s)
Workload Calculation
ActivitiesNumberTime (hours)Total Work Load (hours)
Midterm Examination11010
Final Examination11515
Makeup Examination11010
Quiz11010
Attending Lectures14456
Question-Answer7321
Self Study14228
Homework4312
TOTAL WORKLOAD (hours)162
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High
 
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