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
9900000219	MATHEMATICS - II	Compulsory	1	2	4

Level of Course Unit

First Cycle

Objectives of the Course

The aim of this course is; to explain the functions to introduce more detailed functions, increasing and decreasing functions, to teach the functions and their graphs, to teach the limit and continuity of the function, to describe the derivative of the function, to explain the geometric and physical meaning of the derivative, the higher order derivative, the derivatives of the commonly used functions, the uncertain shapes To define the differential, maximum and minimum problems, uncertain integrals, integration techniques, to teach certain integral applications.

Name of Lecturer(s)

Learning Outcomes

1	Example solutions of plotting graphs by using properties of Description and Value sets of highly used functions
2	Derivation rules, Derivatives of commonly used functions
3	Application of derivative: maximum-minimum problems, calculation of uncertain limits-Application of hospital rule
4	Calculation of specific and uncertain integrals
5	Disclosure of applications

Mode of Delivery

Daytime Class

Prerequisites and co-requisities

None

Recommended Optional Programme Components

None

Course Contents

To increase the level of knowledge about functions To show and teach derivatives of function To give detailed information about the subject of derivative in applications and to gain the ability of solving problems of machines. To give information about limit of functions and uncertain limit calculation. To define the definite and definite integrals, to teach integration techniques and definite integral applications

Weekly Detailed Course Contents

Week	Theoretical	Practice	Laboratory
1	Majorly Used Functions, Classification of Functions: - Algebraic (Force, Fully rational, Fractional and Irrational) Functions and Their Graphs - Transcendental (Exponential, Logarithmic, Trigonometric, Inverse Trigonometric, Hyperbolic) Functions and Their Graphs Exercises
2	Function Limit - Right and Left (One-Way) Limits - Limits of the Function in the Case of Variable - Algebraic Operations on Functions with Limit Very Important Used Limits - Limits of Fractional Rational Functions - Limits of Trigonometric Functions - Irrational Number and Limits Associated with This Number - Uncertainty in Limit Accounts Exercises
3	Function Continuity - Concept of Continuity, Some Theorems About Continuity - Right and Left Continuity at the point, Continuity in open and closed intervals - Discontinuity and Types of Functions
4	Derivation of Function - Function's Derivative - Left and Right Derivatives of Function - On and Off Range Derivative of Function Geometric and Physical Meaning of Derivatives - The Tangent Line of the Curve - Sudden Speed and Acceleration - Density of the Bar Differential of Function - Definition and Geometric Meaning - Characteristics and Rules of Differential - Derivative and Differential Table Exercises
5	Rules of Derivation - Multiplication and Division of Derivatives - Derivative of Compound Function - Derivative of Inverse Function - High Order Derivative - Derivative of the Parametrically Given Function - Derivative of Closed Function Exercises Derivatives of Most Used Functions - Derivative of Force and General Force Function - Derivative of Exponential Function - Derivative of logarithmic function - Derivative of General Force-Exponential Function - Derivative of Trigonometric Function - Derivative of Inverse Trigonometric Function - Derivative of Hyperbolic Function Exercises
6	Applications of Derivatives Geometric Applications of Derivatives - Equations of Tangent and Normal at any point in the curve - Tangent and Normal Six Lengths - Intersecting Angle of Intersecting Two Curves Investigation of Functions - Ascending and Descending Functions - Concavity of the Curve - Twist Points of the Curve
7	Uncertainties, Lopital Theorem Exercises Maximum and Minimum Functions (Extreme) - Local extremes in the vicinity - Local and Absolute Extreme in December - The Rule of Finding the Function's Extreme Exercises
8	Midterm
9	Application of Derivatives to Economic Problems - Total, Average and Marginal Cost Functions - Total, Average and Marginal Income Functions - Total, Average and Marginal Profit Functions - Profit Maximization
10	Unıque Integral - Primitive Function and Indefinite Integral - Properties of Indefinite Integral - Indefinite Integrals Table - Application of Uncertain Integral in the Fields of Economics and Business
11	Methods of Integration - Integration with simple elements - Variable Replacement Method - Partial Integration Method - Integration of Rational Functions - Integration of trigonometric functions - Integration of Binomial Expressions - Integration of irrational functions
12	Specific Integral - Area of Curvilinear Slope as the Limit of a Total - Properties of definite integral - Calculation Methods of Specific Integrals
13	Applications of Integral Integral - Area Account - Length of Curved Spring - Volume Account - Calculation of Areas of Rotary Surfaces - Calculation of Consumer and Producer Rent by Specific Integrals. Consumer Benefit
14	Exercises for the general subject, Review of the term subjects for the Final Exam