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
The course opens with the approval of the Department at the beginning of each semester

Basic information

Language of instruction: En
Type of course: Departmental Elective
Course Level: Bachelor
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 Outputs

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: 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
Attendance % 0
Laboratory % 0
Application % 0
Field Work % 0
Special Course Internship (Work Placement) % 0
Quizzes % 0
Homework Assignments % 0
Presentation % 0
Project % 0
Seminar % 0
Midterms 1 % 40
Preliminary Jury % 0
Final 1 % 60
Paper Submission % 0
Jury % 0
Bütünleme % 0
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
Laboratory 0 0 0
Application 0 0 0
Special Course Internship (Work Placement) 0 0 0
Field Work 0 0 0
Study Hours Out of Class 14 8 112
Presentations / Seminar 0 0 0
Project 0 0 0
Homework Assignments 0 0 0
Quizzes 0 0 0
Preliminary Jury 0 0 0
Midterms 1 2 2
Paper Submission 0 0 0
Jury 0 0 0
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