Ders Tanımı
Ders  Kodu  Yarıyıl  T+U Saat  Kredi  AKTS 

DIFFERENTIAL EQUATIONS  MAT 211  3  4 + 0  4  6 
Ön Koşul Dersleri  

Önerilen Seçmeli Dersler 
Dersin Dili  Türkçe 
Dersin Seviyesi  Lisans 
Dersin Türü  ZORUNLU 
Dersin Koordinatörü 
Prof.Dr. ŞEVKET GÜR 
Dersi Verenler 
Prof.Dr. UĞUR ARİFOĞLU Dr.Öğr.Üyesi MEHMET SANDALCI Doç.Dr. NEZAKET PARLAK Dr.Öğr.Üyesi ZEKERİYA PARLAK Prof.Dr. EKREM BÜYÜKKAYA Dr.Öğr.Üyesi ALPER KİRAZ Doç.Dr. YALÇIN YILMAZ Prof.Dr. ÖMER FARUK GÖZÜKIZIL Prof.Dr. ŞEVKET GÜR Dr.Öğr.Üyesi ÜNAL UYSAL Arş.Gör.Dr. ABDULLAH HULUSİ KÖKÇAM Dr.Öğr.Üyesi FARROKH MAHNAMFAR Öğr.Gör.Dr. EMİNE ÇELİK 
Dersin Yardımcıları  
Dersin Kategorisi  
Dersin Amacı 
The general pourpose of this course is to provide an understanding of ordinary differential equations (ODEs), and to give methods for solving them. Because differential equations express relationships between changing quantities, this material is applicable to many fields, and is essential for students of engineering and physical sciences. 
Dersin İçeriği 
Basic concepts and classifying differential equations, variable separated differential equations, Homogenous differential equations, exact differential equation, Integrator method, First order linear differential equations, finding solution for a linearized differential equations, Bernoulli differential equations, Ricatti differential equations, separation of variables, First order high degree differential equations, Singular solution of differential equations. Clairaut differential equation, Lagrange differential equation, Numeric solutions of differential equations, Taylor series method, Picard iteration method, RungeKutta method, High order linear differential equations, Criteria for linear independence, Solution of high order, one side, constant coefficient linear differential equation. Undetermined coefficients method, Exchange of Lagrange constants method. General solution of Euler differential equations. Decreasing the degree of a differential equation. Solution of constant coefficient differential equation with operator method. Linear differential equations. State equations. Solutions of differential equations with one side. Solution of differential equation systems with Eigen characteristic equation. Laplace conversion. Laplace transformation of derivatives. Methods of separation to basic fractions. Reverse Laplace transformation. Solution of constant coefficient linear differential equations with Laplace transformation. Convolution. Application of Convolution theorem to integral equations. Laplace transformation of periodic functions. Solution of partial derivative differential equations with Laplace transformation. Laplace transformation of step functions. Laplace transformation of impulse functions. Solution of differential equations with series. Bessel functions. Gamma function. 
Dersin Öğrenme Çıktıları  Öğretim Yöntemleri  Ölçme Yöntemleri 
1  Understands the terminology about the differential equations.  1  2  3  4   A  C  
2  Verify that a given function is solution of a differential equation  1  2  4   A  C  
3  Solve problems of ordinary differential equations and system of differential equations  1  2  3  4  15   A  C  
4  Apply knowledge of differential equations in order to solve realworld engineering problems  1  2  3  4  15   A  C  
5   1  2  3  4  15   A  C  
6   1  2  3  4  15   A  C  
7   1  2  3  4  15   A  C  
Öğretim Yöntemleri:  1:Lecture 2:QuestionAnswer 3:Discussion 4:Drilland Practice 15:Problem Solving 
Ölçme Yöntemleri:  A:Testing C:Homework 
Ders Akışı
Hafta  Konular  ÖnHazırlık 

1  Basic Concepts and Classifying Differential Equations. Obtaining differential equations. Separable differential equations. Engineering applications.  
2  Homogeneous functions, homogenous differential equations. Exact differential equations and engineering applications.  
3  NonLinear First Order linear Equations. Integration factor method. Change of variables method. Change of Lagrange variables method. Engineering Applications.  
4  Solution of differential equations by changing to the linear form. Bernoulli differential equation. Ricatti differential equation. Engineering applications.  
5  SecondOrder Linear Equations: Linear Independence, Homogeneous Equations with Constant Coefficients  
6  General solution of high order one sided, constant coefficient linear differential equations. Criteria of linear independence. Wronski determinant. Engineering applications.  
7  General solution of high order two sided, constant coefficient linear differential equations. Undetermined coefficients method. LSD method. Engineering applications.  
8  Euler differential equations. Decreasing the degree of a differential equation. Solution of constant coefficient differential equation with operator method.  
9  MidTerm Exam  
10  Introduction to differential equation systems. Linear differential equation systems. Solution of one sided linear differential equation systems. Eigen characteristic equation. Engineering applications.  
11  Solution of one sided linear differential equations. Undetermined coefficients method. Change of Lagrange constants method. Engineering applications.  
12  Laplace transformation, Laplace transformation of derivati.ve. Reverse Laplace transformation. Separation of basic fractions. Engineering applications.  
13  Laplace Transform Method  
14  Solution of differential equations with series. Bessel functions. Gamma function. 
Kaynaklar 


Ders Notu 
Çengel, Y. A. ve Palm, W. J. (Türkçesi: Tahsin Engin), 2012, Mühendisler ve Fen Bilimciler İçin Diferansiyel Denklemler, Güven Kitabevi, İzmir. 

Ders Kaynakları 
1. Türker, E. S. ve Başarır, M., 2003, Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Kitabevi, Sakarya. 
Döküman Paylaşımı 

Dersin Program Çıktılarına Katkısı
No  Program Öğrenme Çıktıları  KatkıDüzeyi  

1  2  3  4  5  
1  Engineering graduates with sufficient knowledge background on science and engineering subjects of their related area, and who are skillful in implementing theoretical and practical knowledge for modelling and solving engineering problems.  X  
2  Engineering graduates with skills in identifying, describing, formulating and solving complex engineering problems, and thus,deciding and implementing appropriate methods for analyzing and modelling.  X  
3  Engineering graduates with skills in designing a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; for this purpose, skills in implementing modern design methods.  
4  Engineering graduates with skills in developing, selecting and implementing modern techniques and tools required for engineering applications as well as with skills in using information technologies effectively.  
5  Engineering graduates with skills in designing and conducting experiments, collecting data, analyzing and interpreting the results in order to evaluate engineering problems.  
6  Engineering graduates who are able to work within a one discipline or multidiscipline team,as well as who are able to work individually  
7  Engineering graduates who are able to effectively communicate orally and officially in Turkish Language as well as who knows at least one foreign language  
8  Engineering graduates with motivation to lifelong learning and having known significance of continuous education beyond undergraduate studies for science and technology  
9  Engineering graduates with wellstructured responsibilities in profession and ethics  
10  Engineering graduates having knowledge about practices in professional life such as project management, risk management and change management, and who are aware of innovation and sustainable development.  
11  Engineering graduates having knowledge about universal and social effects of engineering applications on health, environment and safety, as well as having awareness for juridical consequences of engineering solutions. 
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  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  4  64 
Hours for offtheclassroom study (Prestudy, practice)  16  3  48 
Midterms  1  5  5 
Quiz  2  4  8 
Assignment  1  10  10 
Final examination  1  10  10 
Toplam İş Yükü  145  
Toplam İş Yükü /25(s)  5.8  
Dersin AKTS Kredisi  5.8 