Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH405VARIATIONAL ANALYSIS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course The variational analysis is concerned with finding optimal solutions (maximal and minimal values of functionals). This course provides an introduction to the classic ideas and techniques of the variational analysis, with emphasis on its applications in several scientific fields.
Course Content The Euler-Lagrange equation. First integrals. Geodesics. Minimal surface of revolution. Several dependent variables. Isoperimetric problems. Fermat’s principle. Dynamics of particles. The vibrating string. The Sturm-Liouville problem. The vibrating membrane. Theory of elasticity. Quantum mechanics. The principles of Feynman and Schwinger in Quantum mechanics. Variational principles in hydrodynamics.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Instructor İSMAİL ASLAN
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
Gelfand, I.M and Fomin, S.V., “Calculus of Variations”, Prentice-Hall, 1963
Brunt, B.V., “The Calculus of Variations”, Springer-Verlag, 2003

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 65 65
Exams and Exam Preparations 1 115 115
Total Work Load   Number of ECTS Credits 7 216

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 have knowledge of the classical problems of variational analysis
2 analyze the brachistochrone problem
3 study the problem of geodesics and the isoperimetric problem
4 use analytic methods for solving a variety of variational problems


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Euler-Lagrange equation. First integrals Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
2 Geodesics. Minimal surface of revolution Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
3 Several dependent variables Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
4 Isoperimetric problems. Fermat’s principle Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
5 Dynamics of particles Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
6 Midterm I Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
7 Vibrating string Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
8 Sturm-Liouville problem Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
9 Vibrating membrane Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
10 Theory of elasticity Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
11 Quantum mechanics Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
12 Midterm II Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
13 Principles of Feynman and Schwinger in Quantum mechanics Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
14 Variational principles in hydrodynamics Dacorogna, B., “Introduction To The Calculus of Variations”, Imperial College Press, 1992
15 Final 1st week
16 Final 2nd week


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3 4 3
C2 4 3 4 3
C3 4 3 4 3
C4 4 3 4 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163233&lang=en