DICLE UNIVERSITY

SCIENCE INSTITUTE

Department of Mathematics

COURSE INFORMATION PACKAGE

Course Code / Optic Code / Consultation Hours / T+A / Credit / ECTS
504064 / 10504064 / 3+0 / 3 / 8
Course Title / VARIATIONAL CALCULUS II
Year/Semester / SPRING
Status / SELECTİVE
Programme’s Name / MATHEMATICS
Language of Instruction / TURKISH
Prerequisites / NO
Disable Students / In case of need, Handicapped students, can request some facilities by giving information about herself.
Student Responsibilities / In order to content of course, to get ready, to participate, and responsibilities, which are homework, project, disputation, and reading the interested parts, about course have to be performed
Lecturer / Prof. Dr. H. İlhan TUTALAR, e-mail: , Phone: 3147
Course Assistant
Course Objectives / A general view to variational calculus and to teach some techniques of calculation
Special Quota for
Other Departments / The most 10 (ten) student
Learning Outcomes / At the end of this course the student;
-  Student through this course realizes that there is a need for a new point of view between this course and the previous analysis course from the aspect the meaning and the functioning.
-  Through this new understanding and this interpretation the student is to be equipped with enough knowledge of how the construction of the fundamentals of mathematics is achieved.
-  The student’s ability of thinking mathematically is to be improved in the case that he/she is being introduced with the processes, spaces and the models which he/she has never known before and probably never heard of.
-  May improve his/her ability of analyzing.
-  Improves the ability of self-motivation
-  May become competent of debating mathematics.
-  Acquires the enthusiasm for investigation, exploration of building strategies and reinforcing his/her intuitive approach.
504064 / 10504064 / VARIATIONAL CALCULUS II / 3+0 / 3 / 8
Contents, learning activities
Week / Topic / Learning Activities
1 / Some of The Basic Derivations of The Calculus of Variations / The student’s approaches to the subject are questioned under the light of the knowledge that is gained through the education process. The students are to be wanted to be ready after reminding them the subject of next week. A notice is made that the volunteers are free to make presentation.
2 / The Extremum of A Function of Many Variables / To reinforce the concepts. The students are wanted to be ready by reminding them the title of the next week.
3 / The Notions of Functional / To give examples about application area of the subject. Question is asked and answer provided.
4 / Variation of A Functional and İts Properties / To reinforce the concepts. Discussion with questions and answers.
5 / An Elementary Problem in The Calculus of Variations / To be given Homeworks / Term Paper / Presentation
6 / Euler’s Equation / Expressing their ideas before explaining the subject as controlling their information about subject. Examples are given. Questions are directed and answered. To be given research subject.
7 / Applications to Written exam / To work out the previous knowledge of students,
Discussing results of research subject.
8 / Midterm / Discussions on solution after midterm examination
9 / Euler-Lagrange Equation / Presentation and criticism of Homeworks / Term Paper / Presentation
10 / Restate The Elementary Problem of The Calculus of Variations / Presentation and criticism of Homeworks / Term Paper / Presentation
11 / Generalization of The Elementary Problem of The Calculus of Variations / Students will stimulate for next week's issue to be prepared. Students who wish to make presentations.
12 / Invariance of Euler’s Equation / Lecturing, Discussing, Questions-Answer
13 / Field of Extremals / To work out the previous knowledge of students, The students are wanted to be ready by reminding them the title of the next week.
14 / The Derivation and Pontrjagin Maximum Principle / The presentation of this subject by three different students is provided. Examples are given. Questions are directed and answered.
15 / Some Basic Applications of The Calculus of Variations and Applications to Written final exam / Summary of the semester will be done.
Assessment criteria / If any, mark as x / Percent (%) / Others
Midterm Exams / X / 30 / Will be given points to determine his marks of this course in certain percentages with respect to activities during the process have been realized by student in the class
Quizzes / X / 10
Homeworks / Term Paper / Presentation / X / 5
Projects / X / 10
Attendance & cover a subject / X / 5
Others
(in training, field survey, thesis preparation vb).
Final Exam / X / 40
Textbook / Material / Calculus of Variations, M. L. Krasnov, G. L. Makarenko, A. I. Kiselev; MIR Publishers, Moscow, 1975
Recommended Reading / Calculus of Variations, L. M. Gelfand, S.V. Fomin; Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1963, Copyright Material, 240 pp.
Regulating / Analysis and Theory of Functions Department