Iğdır University Lifelong Learning Programme

Description of Individual Course Units

Course Unit Code	Course Unit Title	Type of Course Unit	Year of Study	Semester	Number of ECTS Credits
160103001100	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 and functions in univariate functions.

Name of Lecturer(s)

Learning Outcomes

1	Defines the increasing and decreasing functions with tangent and normal equation. Calculates the limit of indeterminate states by using derivative.
2	Defines asymptotes with maximum and minimum functions. Explains the curve drawings.
3	Solve engineering problems by using derivative. Calculates approximate using differential. Define concepts of cluster and number sets. Explain the concepts of identity, equation and inequality.
4	Defines the properties of functions and functions. Defines trigonometric, inverse trigonometric and hyperbolic functions, Partial functions and specially defined functions (absolute value, exact value, sign functions).
5	Explains the concept of limit and makes limit calculation with limit definition. Prove the rules used for limit calculation. Defines right and left sided limits. He knows vague situations.
6	Defines the concept of continuity in functions and knows types of discontinuity.
7	Explain the concept of derivative and make derivative calculations with the definition of derivative. Provides the rules of derivation with the definition of derivative.
8	Defines the derivative of trigonometric and inverse trigonometric functions, exponential and logarithmic functions, hyperbolic and inverse hyperbolic functions.
9	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

Functions. Limit. Continuity, Derivatives and Exercises. Limit values, average value theorem and applications. Graphics. Specific Integral. Area and volume integrals. Indefinite integral. Transandant Functions and Derivatives. L`Hopital` Rule. Methods of integration. Improper integrals. Exercises.

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Clusters. Number Sets. Equations. Identities. Inequalities.
2	Function concept. Function varieties (Polynomial function, rational function, supra and logarithm function and the widest definition of these functions).
3	Function types (Trigonometric, inverse trigonometric and hyperbolic functions.
4	Partial functions, specially defined functions (Absolute value, exact value, sign functions)
5	Limit concept and limit calculation. Proof of the rules used for limit calculation. Sandwich theorem. Limits of trigonometric functions.
6	Right and left sided limits. Uncertain cases (0/0, infinite / infinite, 0.sonless, infinite-infinite, 1 ^ infinite)
7	Concept of continuity in functions. Types of discontinuity. Properties of continuous functions (Intermediate theorem, absolute maximum and minimum, local maximum and minimum definitions, lar)
8	The concept of derivative and derivative calculus. Derivation of derivative with the definition of derivative rules. Derivative of inverse function.
9	Midterm
10	Derivative of trigonometric and inverse trigonometric functions.
11	Derivative of exponential and logarithm functions. Derivative of hyperbolic and inverse hyperbolic functions.
12	Higher order derivative. Derivatives of functions given parametric equations.
13	Derivative of closed functions. Tangent and normal equation. Increasing and decreasing functions.
14	Indefinite cases (examination with L’Hopital Rule). Maximum and minimum functions, asymptotes, Curve drawings. Engineering problems. Approximate calculation with differential.