Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
DIFFERENTIAL EQUATIONS I MAT 205 3 2 + 1 3 5
Ön Koşul Dersleri Calculus I, calculus II
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü ZORUNLU Dersin Koordinatörü Prof.Dr. ÖMER FARUK GÖZÜKIZIL Dersi Verenler Prof.Dr. ÖMER FARUK GÖZÜKIZIL Doç.Dr. METİN YAMAN Dersin Yardımcıları Research Assistants in Applied Mathematics Dersin Kategorisi Dersin Amacı To introduce differential equations and to have knowledge about the methods of solution. Dersin İçeriği Classification of Differential Equations and Their Solutions, First Order Equations, High Order Equations, The Homogeneous Linear Equations with Constant Coefficients.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/She recognizes differential equation 1 - 2 - 4 - 15 - A - C - 2 - He/She classifies differential equations 1 - 2 - 4 - 15 - A - C - 3 - He/She Finds equation which solution is known 1 - 2 - 4 - 15 - A - C - 4 - He/She Recognizes and solves first order equation 1 - 2 - 4 - 15 - A - C - 5 - He/She Finds a curve which cuts another curve 1 - 2 - 4 - 15 - A - C - 6 - He/She Recognizes high order equation 1 - 2 - 4 - 15 - A - C - 7 - He/She Finds a solution linear homogenous equation with constant coefficient 1 - 2 - 4 - 15 - A - C - 8 - He/She Finds a solution linear nonhomogenous equation with constant coefficient 1 - 2 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Definition and Classification of Differential quations.
2 Seperable Equations and Equations Reducible to This Form.
3 Homogeneous Differential Equations
4 Exact Differential Equations and Integrating Factors
5 Linear Equations
6 Bernoulli Equations
7 Riccati Equations
8 First Order Higher Degree Differential Equations.Clairaut Equations
9 Midterm
10 Lagrange Equations, Orthogonal and Oblique Trajectories
11 The Homogeneity of a Linear Equation with Constant Coefficients
12 The Homogeneity of a Linear Equation with Constant Coefficients
13 The Method of Undetermined Coefficients
14 The Method of Variation of Parameters

#### Kaynaklar

Ders Notu [1] Adi diferansiyel denklemler, Prof.Dr.Mehmet Çağlıyan, Y.Doç.Dr.Nisa Çelik, Y.Doç.Dr.Setenay Doğan, Dora yayınları.
Ders Kaynakları [2] Differential Equations, Shepley L. Ross
[3] Diferansiyel Denklemler, Eyüp Sabri Türker, Metin Başarır
[4] Diferensiyel Denklemler ve Sınır Değer Problemleri, Edwards&Penney (Çeviri Editörü: Ömer Akın )

#### 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.
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 75
KisaSinav 1 10
KisaSinav 2 10
Odev 1 5
Toplam 100
Yıliçinin Başarıya Oranı 55
Finalin Başarıya Oranı 45
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
Quiz 2 5 10
Assignment 1 5 5
Final examination 1 10 10
Toplam İş Yükü 131
Toplam İş Yükü /25(s) 5.24
Dersin AKTS Kredisi 5.24
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