Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
INTRODUCTİON TO PARTİAL DİFFERENTİAL EQUATİON THEO MAT 510 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. METİN YAMAN Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı It’s aiming to solve partial differential equations arising in engineering and science. Dersin İçeriği Sobolev spaces, sobolev inequality, fonction spaces, second order eliptik equations, second order evolution equations,
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She recognizes sobolev spaces. 1 - 4 - 14 - 15 - A - C - F - 2 - He/She defines concept of weak derivative. 1 - 4 - 14 - 15 - A - C - F - 3 - He/She investigates existence of weak and classical solutions. 1 - 4 - 14 - 15 - A - C - F - 4 - He/She learns evolution equations. 1 - 4 - 14 - 15 - A - C - F - 5 - He/She comprehends parabolic and hyperbolic equations. 1 - 4 - 14 - 15 - A - C - F - 6 - He/She applies these to some examples. 1 - 4 - 14 - 15 - A - C - F -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework F:Performance Task

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Introduction to PDE
2 Clasiccal solution, weak solution
3 Sobolev spaces
4 Sobolev inequalities
5 Function spaces, spaces, spaces with time
6 Second order eliptik equation
7 Existence of weak solution, Lax-Milgram theorem
8 Regularity, maximum principle
9 Linear evolution equation
10 Second order parabolic equation
11 Midterm
12 Weak solution and maximum principle
13 Second order hyperbolic equation
14 Existence of weak solution

Ders Notu
Ders Kaynakları

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Student follows the current journals in his/her field and puts forward problems.
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
5 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
6 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
7 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
8 Student uses different proof methods to come to a solution by analyzing the problems encountered.
9 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
10 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
11 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
12 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
13 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
14 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
15 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
16 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research.
17 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
18 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
19 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
20 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
KisaSinav 2 10
Odev 1 10
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 10 10
Assignment 1 30 30
Final examination 1 10 10
Toplam İş Yükü 146
Toplam İş Yükü /25(s) 5.84
Dersin AKTS Kredisi 5.84
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