School of Humanities \ Mathematics
Course Credit
ECTS Credit
Course Type
Instructional Language
Programs that can take the course
Faculty of Engineering Departments
This course includes the following topics:
First order differential equations, linear equations, separable, homogeneous and Bernouilli equations, exact differential equations, second and higher order differential equations, constant coefficient equations. Systems of linear equation and eigenvalues methods , Laplace transforms and solution of differential equations, Power series and solutions of differential equations, Fourier series.
Textbook and / or References
Course Book:
Elementary Differential Equations and Boundary Value Problems (9th Ed.), W.E. Boyce and R.C. DiPrima, Wiley, USA, 2010, ISBN: 978-0-470-39873-9.
References:
Ömer Akın, Bilgisayar Destekli,Matematiksel Modellemeli Diferensiyel Denklemler ve Sınır Değer Problemleri, Palme Yayıncılık, 2008 (Çeviri).
To give basic differential equations and their solutions. To develop mathematical thinking and modeling techniques. To express and find solutions to problems in different fields with the help of differential equations.
1. Understand the basic concepts of differential equations and mathematical modeling processes and apply them to real-world problems.
2. Solve first order equations and analyze second and higher order differential equations.
3. Solve systems of differential equations, initial value problems and step functions.
4. Construct series solutions of differential equations.
1. Hafta: Diferensiyel Denklemler ve Matematiksel Modelleme. Değişkenlerine Ayrılabilen Diferensiyel Denklemler
2. Hafta: Birinci Mertebeden Lineer Denklemler
3. Hafta: Homogen, Tam, Bernoulli ve Riccati Diferensiyel Denklemleri
4. Hafta: kinci Mertebeden Homogen Denklemler. İkinci Mertebeden Homogen Olmayan Denklemler
5. Hafta: n. Mertebeden Lineer Denklemler. Homogen Olmayan Denklemler ve Çözüm Metotları
6. Hafta: Diferensiyel Denklem Sistemlerine Giriş. Yok Etme (Eliminasyon) Yöntemi
7. Hafta: Homogen Sistemler için Özdeğer Yöntemi
8. Hafta: Temel Matrisler ve Lineer Sistemler. Homogen Olmayan Lineer Sistemler
9. Hafta: Laplace Dönüşümleri ve Özellikleri. Ters Laplace Dönüşümleri ve Özellikleri
10. Hafta: Başlangıç Değer Problemlerine Uygulamaları
11. Hafta: Konvolüsyon. Adım Fonksiyonları ve uygulamaları
12. Hafta: Kuvvet Serilerine Giriş ve Genel Bakış. Noktaların sınıflandırılması ve seri çözümleri
Tentative Assesment Methods
• Midterm 40 %
• Final 60 %
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