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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 537ANALYSIS ON TIME SCALES II3 + 01st Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective The aim of this course is to examine existence of solutions for boundary value problems on time scales.
Course Content Alpha ve nabla derivatives, Positive solutions of boundary value problems , The Avery-Henderson fixed point theorem and applications , The Legget-Williams fixed point theorem and applications.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.
Mode of Delivery Face to Face

COURSE LEARNING OUTCOMES
1Learns the rules of Alpha and nabla derivations.
2Finds the positive solutions of Boundary value problems.
3Learns the proof and application areas of Avery-Henderson fixed point theorem.
4Proves the Legget-Williams fixed point theorem and learns the application areas of the theorem.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 00154 54   
LO 0024 45    
LO 00354 45   
LO 00444 45   
Sub Total181241814   
Contribution53154000

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course






195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2022-2023 Spring1İSMAİL YASLAN
Details 2019-2020 Spring1İSMAİL YASLAN
Details 2017-2018 Spring1İSMAİL YASLAN
Details 2013-2014 Spring1İSMAİL YASLAN
Details 2011-2012 Spring1İSMAİL YASLAN
Details 2010-2011 Spring1İSMAİL YASLAN
Details 2009-2010 Spring1İSMAİL YASLAN


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester
MAT 537 ANALYSIS ON TIME SCALES II 3 + 0 1 Turkish 2022-2023 Spring
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. İSMAİL YASLAN iyaslan@pau.edu.tr FEN A0205 %
Goals The aim of this course is to examine existence of solutions for boundary value problems on time scales.
Content Alpha ve nabla derivatives, Positive solutions of boundary value problems , The Avery-Henderson fixed point theorem and applications , The Legget-Williams fixed point theorem and applications.
Topics
WeeksTopics
1 Alpha Derivatives
2 Nabla Derivatives
3 Left-Dense Continuous Functions, Nabla Integral
4 The Method of Upper and Lower Solutions in Separated Boundary Value Problems
5 Quasilinearization Method in Separated Boundary Value Problems
6 Mixed Derivative Problems
7 The Method of Upper and Lower Solutions in Periodic Boundary Value Problems
8 Quasilinearization Method in Periodic Boundary Value Problems
9 Midterm Exam
10 Examples
11 Cones, u0-Positive Operators and Krein-Rutman Theory
12 Eigenvalue Problems
13 Fixed Point Theory and Topological Transversality Methods
14 Existence of at Least One Solution
Materials
Materials are not specified.
Resources
ResourcesResources Language
Advances in Dynamic Equations on Time Scales, Martin Bohner and Allan PetersonEnglish
Advances in Dynamic Equations on Time Scales, Martin Bohner and Allan PetersonEnglish
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes