Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
NUMERİCAL METHODS FOR DİFFERENTİAL EQUATİONS MAT 565 0 3 + 0 3 6
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MUSTAFA ERÖZ Dersi Verenler Dersin Yardımcıları Dersin Kategorisi Dersin Amacı Since most problems arise in applied mathematics and engineering have no analytical solutions, the theory of numerical solutions of these problems is investigated. The complexity of these equations which represent the natural phenomenon bring us to study the approximate solutions. Dersin İçeriği Existence and uniqueness of the solutoin of differential equations, Tayloer series method, Runge-Kutta methods, Multistep methods, System of equations, Boundary-value problems, Shooting methods, Finite difference methods, Collocation, Linear differential equations, Stiff equations, Introduction to numerical solution of partial differential equations.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - Students will have explained the need of a numerical solution of a differential equation. 1 - 2 - 4 - A - C - 2 - Students will have constructed the numerical solutions of differential equations 1 - 2 - 4 - A - C - 3 - Students will have constructed the numerical solutions of differential equations of higher order and systems. 1 - 2 - 4 - A - C - 4 - Students will have composed an alghorithm for the numerical solutions of DEs. 1 - 2 - 4 - A - C - 5 - Students will have demonstrated how to reach more accurate numerical solutions. 1 - 2 - 4 - A - C - 6 - Students will have summarized the numerical solutions of PDEs. 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 existence and the uniquness of the solutions of differential equations
2 Taylor series method
3 Runge-Kutta methods
4 Multistep methods
5 Equations and systems of higher order
6 Boundary value problems
7 Shooting methods
8 Finite difference method
9 Collocation
10 Linear differential equations
11 Stiff equations
12 Introduction to numerical solution of PDEs
13 Parabolic equations: Explicit and implicit methods
14 Finite difference method for PDEs

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. X
2 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
3 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
4 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
5 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
6 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
7 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
8 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
9 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
10 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 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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