Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
DIFFERENTIAL EQUATIONS MAT 211 3 4 + 0 4 6
 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, Runge-Kutta 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 real-world 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:Question-Answer 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 Non-Linear 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 Second-Order 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 Mid-Term 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.
2. Bronson, R.,1993, Differantial Equations, Schaum´s Outlines, Nobel Kitabevi, Ankara.
3. Edwards, C. H.ve Penney, D. E., (Türkçesi: Ömer Akın) 2008, Diferansiyel Denklemler ve Sınır Değer Problemleri,Palme Yayıncılık.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. X
2 Ability to identify formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. X
3 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues, according to the nature of the design.)
4 Ability to devise, select, and use modem techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
5 Ability to design and conduct experiments, gather data analyze and interpret results for investigating complex engineering problems or discipline specific research questions.
6 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
9 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11 Knowledge about the global and social effects of engineering practice on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal 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 off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 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
; ;