MATHEMATICS
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT4071	Inequalities	Fall	3	0	3	6

This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

Basic information

Language of instruction:	English
Type of course:	Departmental Elective
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Hybrid
Course Coordinator :	Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Objectives:	The aim of this course is providing students to understand and to consolidate the basic concepts, theory and solution methods of introductory inequalities such as Jordon, Young, Bernoulli, Nesbitt, Jensen, Minkowski, Hadwiger-Finsler, Weizenbock, Hilbert inequality, integral inequalities and their discrete analogies.

Learning Outcomes

The students who have succeeded in this course;
1. Can solve elementary inequalities
2. Have an understanding of rearrangement inequality and its applications
3. Have a comprension and discussion of inequalities for integral and differential operators and their applications
4. Have a comprension and discussion of integral inequalities and their applications
5. Have a comprension and discussion of differential inequalities and their applications
6. Have a comprension and discussion of discrete analogies of integral inequalities and their applications
7. Have a comprension and discussion of first and second order differential inequalities and their applications

Course Content

In this course basic concepts of inequalities will be covered. The solution techniques for elementary inequalities will be given. Inequalities for real numbers, inequalities for sequences, geometric inequalities, inequalities for integral and differential operators, integral inequalities and their discrete analogies will be discussed. Finally, first and second order differential inequalities will be taught.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	A Sum formula. Solving inequalities
2)	Arithmetic Mean-Geometric Mean inequality. Jordan’s inequality
3)	Young’s inequality. Bernoulli’s inequality. Nesbitt’s inequality
4)	The rearrangement inequality.The general means inequality.Jensen’s inequality
5)	Minkowski inequality. Holder’s inequality
6)	Hadwiger-Finsler inequality. Weizenbock's inequality
7)	Carlson’s inequality
8)	Wirtinger's inequality. Hardy's inequality
9)	Hilbert's inequality - MIDTERM
10)	Inequalities involving a function and its first and second derivatives
11)	Gronwall's inequalities for integrals
12)	Wendroff's inequalities for integrals
13)	Discrete analogy of integral inequalities
14)	First and second orders differential inequalities

Sources

Course Notes / Textbooks:	Edwin F. Beckenbach and Richard Bellman. Inequalities. Springer Verlag: Berlin, Heidelberg, New York, 1965, 188 p. Ravi P. Agarwal. Difference equations and inequalities: Marcel Dekker,Inc. New York, Basel, 2000, 963p.
References:	Edwin F. Beckenbach and Richard Bellman. Inequalities. Springer Verlag: Berlin, Heidelberg, New York, 1965, 188 p. Ravi P. Agarwal. Difference equations and inequalities: Marcel Dekker,Inc. New York, Basel, 2000, 963p.

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Study Hours Out of Class	14	8	112
Midterms	1	2	2
Final	1	2	2
Total Workload			158

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

Program Outcomes

Level of Contribution