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Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
NONLINEAR PARTIAL DIFFERANTIAL EQUATIONS MAT 623 0 3 + 0 3 6
Ön Koşul Dersleri

Recommended course of undergraduate education has received partial differential equations.

Önerilen Seçmeli Dersler
Dersin Dili Türkçe
Dersin Seviyesi Doktora
Dersin Türü SECMELI
Dersin Koordinatörü Prof.Dr. ÖMER FARUK GÖZÜKIZIL
Dersi Verenler
Dersin Yardımcıları
Dersin Kategorisi
Dersin Amacı

It is useful for graduate students in mathematics and engeneering.

Dersin İçeriği

Adomian Decomposition Method , Solution of Nonlinear PDEs by Adomian Method, Solution of Nonlinear PDEs Systems by Adomian Method. Linear and Nonlinear Physical Models. The Goursat Problem. The Telegraph Equation .Schrodinger Equation. Fourth-order Parabolic Equation. The Pad´e Approximants. Solitons and Compactons.

Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri
1 - To learn the details of partial differential equations. 1 - 2 - 3 - 4 - 6 - 8 - 14 - 15 - A - C - F -
2 - To recognize the non-linear partial differential equations. 1 - 2 - 3 - 4 - 6 - 8 - 14 - 15 - A - C - F -
3 - To learn methods of solution of nonlinear partial differential equations. 1 - 2 - 3 - 4 - 6 - 8 - 14 - 15 - A - C - F -
4 - To learn the methods of numerical solution of nonlinear partial differential equations. 1 - 2 - 3 - 4 - 6 - 8 - 14 - 15 - A - C - F -
5 - To learn to linear and nonlinear physical models. 1 - 2 - 3 - 4 - 6 - 8 - 14 - 15 - A - C - F -
6 - To solve to the Goursat problem, telegraph equation and the Schrodinger equation. 1 - 2 - 3 - 4 - 6 - 8 - 14 - 15 - A - C - F -
Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 6:Motivations to Show 8:Group Study 14:Self Study 15:Problem Solving
Ölçme Yöntemleri: A:Testing C:Homework F:Performance Task

Ders Akışı

Hafta Konular ÖnHazırlık
1 Adomian decomposition method.
2 Solution of nonlinear partial differential equations by using adomian method.
3 Solution of nonlinear partial differential equations by using adomian method.
4 Linear and Nonlinear Physical Models.
5 The Goursat Problem.
6 The Telegraph Equation.
7 Schrodinger Equation.
8 Fourth-order Parabolic Equation.
9 Midterm
10 The Pad´e Approximants.
11 The Pad´e Approximants.
12 Solitons
13 Solitons
14 Compactons

Kaynaklar

Ders Notu
Ders Kaynakları

1.Nonlinear Partial Differential Equations for Scientist and Engineers,Debnath L., Boston , 1997.
2. Partial Differential Equations and Solitary Waves Theory, Abdul-Majid Wazwaz,Springer, 2009.


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. X
2 Student completes the missing or limited knowledge by using the scientific methods. X
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
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
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
9 Student knows enough foreign language to do a collaborative work with the scientists studying on the same field as him/her abroad. X
10 Student follows the necessary technological developments in his/her field, and s/he uses them. X
11 Student looks out for the scientific and ethic values while gathering, interpreting and publishing data. X

Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 60
KisaSinav 1 20
Odev 1 20
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
Quiz 1 10 10
Assignment 1 10 10
Final examination 1 15 15
Toplam İş Yükü 151
Toplam İş Yükü /25(s) 6.04
Dersin AKTS Kredisi 6.04
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