MATHEMATICS | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
MAT4071 | Inequalities | Fall Spring |
3 | 0 | 3 | 6 |
This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
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. |
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 |
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. |
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 |
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. |
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 |
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 |
No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
Program Outcomes | Level of Contribution |