GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
LYAPUNOV TYPE INEQUALITIES I/5011305
Course Title: LYAPUNOV TYPE INEQUALITIES I
Credits 3 ECTS 7.5
Course Semester 1 Type of The Course Elective
COURSE INFORMATION
 -- (CATALOG CONTENT)
 -- (TEXTBOOK)
 -- (SUPPLEMENTARY TEXTBOOK)
 -- (PREREQUISITES AND CO-REQUISITES)
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- COURSE OBJECTIVES
 -- COURSE LEARNING OUTCOMES
To define a Lyapunov-type inequality.
To use Lyapunov’s inequalities in linear and non-linear problems.
To use Lyapunov’s inequalities in eigenvalue problems.
Lyapunov’s inequalities in n-dimensions.
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 --WEEKLY SCHEDULE
1. Week  Fundamental Definitions and Theorems
2. Week  Classical Lyapunov’s inequalities
3. Week  Quasilinear Problems
4. Week  Eigenvalue problems
5. Week  Nehari-Calogero-Cohn Inequality
6. Week  Calogero’s and Cohn’s Proofs
7. Week  Nehari’s proof for Second-Order Problems
8. Week  The Inequality for p-Laplacian problems
9. Week  Optimality of the bound
10. Week  Bargmann-type Bounds
11. Week  Comparison of Inequalities
12. Week  Lyapunov’s inequalities for Resonant Systems
13. Week  Lyapunov-type inequalities in dimensions
14. Week  Lyapunov –type inequalities and Orlicz Spaces
15. Week  
16. Week  
 -- TEACHING and LEARNING METHODS
 -- ASSESSMENT CRITERIA
 
Quantity
Total Weighting (%)
 Midterm Exams
1
40
 Assignment
0
0
 Application
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Percent of In-term Studies  
40
 Percentage of Final Exam to Total Score  
60
 -- WORKLOAD
 Activity  Total Number of Weeks  Duration (weekly hour)  Total Period Work Load
 Weekly Theoretical Course Hours
14
3
42
 Weekly Tutorial Hours
0
 Reading Tasks
12
4
48
 Searching in Internet and Library
11
3
33
 Material Design and Implementation
0
 Report Preparing
0
 Preparing a Presentation
0
 Presentation
0
 Midterm Exam and Preperation for Midterm Exam
1
12
12
 Final Exam and Preperation for Final Exam
1
12
12
 Other (should be emphasized)
12
3
36
 TOTAL WORKLOAD: 
183
 TOTAL WORKLOAD / 25: 
7.32
 Course Credit (ECTS): 
7.5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To be able to develop their knowledge of theory and applications at master degree depending on the competencies acquired in undergraduate level.X
2To be able to recognize different problems encountered in mathematics and to be able to make studies for their solutions.X
3To be able to formulate new solutions with scientific methods mostly based on analysis and synthesis.X
4To be able to carry out his/her works either independently or in groups within a project considering his/her knowledge on the field he/she works in a critical approach.X
5To be able to continue his/her works considering social, scientific and ethical values.X
6To be able to follow scientific and social developments related to his/her field.X
7To be able to carry out his/her works within the framework of quality management, workplace safety and environmental awareness and to be able to present systematically his/her works using various methods like written, oral or visual.X
8To be able to use methods of accessing knowledge effectively in accordance with ethical values.X
9To be able to use knowledge in other disciplines by combining it with mathematical information.X
10To be able to make activities in the awareness of need for lifelong learning.X
11To be able to make connections between mathematical and social concepts and produce solutions with scientific methods.X
12To be able to use his/her mathematical knowledge in technology.X
 -- NAME OF LECTURER(S)
   (Assoc. Prof. Dr. Mustafa Fahri AKTAŞ)
 -- WEB SITE(S) OF LECTURER(S)
   (http://websitem.gazi.edu.tr/site/mfahri/akademik)
 -- EMAIL(S) OF LECTURER(S)
   (mfahri@gazi.edu.tr)