Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
INTEGRAL EQUATIONS MAT 464 8 2 + 0 2 5
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. YALÇIN YILMAZ Dersi Verenler Dersin Yardımcıları Research assistants in Department of Applied Mathematics Dersin Kategorisi Dersin Amacı Defining and solving problems in integral equations arising in applied mathematics. Dersin İçeriği Volterra integral equations, Fredholm integral equations, Boundary value problems with one parameter, Singular integral equations.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - One identifies Volterra integral equation and solves it. 1 - 4 - A - 2 - Identifies the kernel of Volterra integral equation and solves the equation by aid of it. 1 - 4 - A - 3 - Finds the solutions using successive approxiamations. 1 - 4 - A - 4 - Identifies Abel integral equation and solves it. 1 - 4 - A - 5 - Finds the solutions of integro-differential equation by use of Laplace transformation. 1 - 4 - A - 6 - Uses methods of Fredholm determinants for second type Fredholm integral equations. 1 - 4 - A - 7 - States the integral equations with degenerate kernel and finds the solutions. 1 - 4 - A -
 Öğretim Yöntemleri: 1:Lecture 4:Drilland Practice Ölçme Yöntemleri: A:Testing

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Relation between linear differential equations and Volterra integral equations.
2 Solvent kernel of Volterra integral equation.
3 Successive approxiamations method.
4 Convolution type integral equations.
5 Solutions of integro-differential equation by use of Laplace transformation
6 First kind Volterra integral equation, Euler integral and Abel problem.
7 Convolution type First kind Volterra integral equations
8 Midterm exam
9 Second kind Volterra integral equations, Methods of Fredholm Determinants.
10 Successive kernels, Occurence of resolvent kernel by use of successive kernel.
11 Integral equations with degenerate kernel.
12 Characteristic numbers and eigenfunctions
13 Fredholm integral equations whose kernels is functions of (x-t)
14 Solutions to homogen integral equations with degenerate kernel.

#### Kaynaklar

Ders Notu Integral Equations, C. Cerit (translator) 1976
Ders Kaynakları 1] Introduction to integral equations with applications, Abdul J. Jerri; 1999.
[2] Principle of differential and integral equations, C. Corduneanu; 1977.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs.
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 70
KisaSinav 1 10
Odev 1 10
KisaSinav 2 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 1 16
Mid-terms 1 15 15
Assignment 1 5 5
Final examination 1 15 15
Toplam İş Yükü 99
Toplam İş Yükü /25(s) 3.96
Dersin AKTS Kredisi 3.96
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