Course Name Code Semester T+U Hours Credit ECTS
Variational Calculus MAT 610 0 3 + 0 3 6
Precondition Courses
Recommended Optional Courses
Course Language Turkish
Course Level Doctorate Degree
Course Type Optional
Course Coordinator Prof.Dr. MUSTAFA ERÖZ
Course Lecturers
Course Assistants
Course Category
Course Objective Fiding extremum. To present optimization problems as the minimization of functionals in function spaces and demonstrate the solution methods.
Course Content The extremum of functions with multi variables. The extemums of functionals. Euler equation and its solution. Constrained exremums. The methods of finite dfifferences, Ritz nd Kantorovich. The solution of eigenvalue problems with variational approximation.
# Course Learning Outcomes Teaching Methods Assessment Methods
1 Students will have defined the extremum of a multi-variable function. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
2 Students will have explained the notion of a functional and the problem of finding the extremums of a functional. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
3 Students will have derived the Euler equation of a variational problem. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
4 Students will explained the sufficiency conditions for extremums. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
5 Students will be able to compute constrained extremums. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
6 Students will have constructed the approximate solutions with Ritz, Kantorovich and finite difference methods. Lecture, Question-Answer, Drilland Practice, Testing, Homework,
Week Course Topics Preliminary Preparation
1 The extremum of functions with multi variables
2 The extremums of functionals.
3 The basic theorem of variational calculus.
4 Euler equations
5 Field of extremalls
6 Sufficiency conditions
7 Constrained extremums.
8 Hamilton Jacobi theory
9 Variational principle in mechanics
10 Variational principle in mechanics
11 Direct methods
12 Finite difference method
13 Ritz method
14 Kantorovich method. Finding eigen values.
Resources
Course Notes
Course Resources
Order Program Outcomes Level of Contribution
1 2 3 4 5
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application.
1 At a master´s degree level, student reaches new knowledge via scientific researches, the use of knowledge of the same field as him/her or of different field from him/her, and the use of knowledge based on the competence in his/her field; s/he interprets the knowledge and prospects for the fields of application. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
2 Student completes the missing or limited knowledge by using the scientific methods.
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result.
3 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field. X
4 Student conveys, orally or in writing, his/her studies or the current developments in his/her field to the people in or out of his/her field.
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches.
5 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity. X
6 At a doctorate degree level, student prepares at least one scientific article of his/her field to be published in an international indexed journal, and s/he extends its popularity.
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters.
7 Student analyzes the works that have been published before, approaches the same subjects with different proof methods, or determines the open problems about the current subject matters. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work. X
8 Student looks for the scientists studying on the same field as him/her, and s/he gets in touch with them for a collaborative work.
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them.
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data.
Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 50
1. Ödev 50
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100
ECTS - Workload Activity Quantity Time (Hours) Total Workload (Hours)
Course Duration (Including the exam week: 16x Total course hours) 16 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 20 20
Assignment 1 20 20
Final examination 1 20 20
Total Workload 156
Total Workload / 25 (Hours) 6.24
dersAKTSKredisi 6