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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
VARIATIONAL CALCULUS MAT 610 0 3 + 0 3 6
Ön Koşul Dersleri
Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Doktora
Dersin Türü SECMELI
Dersin Koordinatörü Doç.Dr. MUSTAFA ERÖZ
Dersi Verenler
Dersin Yardımcıları
Dersin Kategorisi
Dersin Amacı
Fiding extremum. To present optimization problems as the minimization of functionals in function spaces and demonstrate the solution methods.
Dersin İçeriği
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.
Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - Students will have defined the extremum of a multi-variable function. 1 - 2 - 4 - A - C -
2 - Students will have explained the notion of a functional and the problem of finding the extremums of a functional. 1 - 2 - 4 - A - C -
3 - Students will have derived the Euler equation of a variational problem. 1 - 2 - 4 - A - C -
4 - Students will explained the sufficiency conditions for extremums. 1 - 2 - 4 - A - C -
5 - Students will be able to compute constrained extremums. 1 - 2 - 4 - A - C -
6 - Students will have constructed the approximate solutions with Ritz, Kantorovich and finite difference methods. 1 - 2 - 4 - A - C -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice
Ölçme Yöntemleri: A:Testing C:Homework

Ders Akışı

Hafta Konular ÖnHazırlık
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.

Kaynaklar

Ders Notu
Ders Kaynakları

Döküman Paylaşımı


Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
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.
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.
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.
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.
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.
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.
12 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
13 Student completes the missing or limited knowledge by using the scientific methods. X
14 Student freely poses a problem of his/her field, develops a solution method, solves the problem, and evaluates the result. X
15 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
16 Student finds a solution to the unforeseen complex problems in his/her studies by developing new approaches. X
17 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
18 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
19 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
20 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad.
21 Student follows the necessary technological developments in his/her field, and s/he uses them. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 50
Odev 1 50
Toplam 100
Yıliçinin Başarıya Oranı 50
Finalin Başarıya Oranı 50
Toplam 100

AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
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
Toplam İş Yükü 156
Toplam İş Yükü /25(s) 6.24
Dersin AKTS Kredisi 6.24
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