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.
Week 1: Differential Equations and Mathematical Models. Separable Equations
Week 2: First Order Linear Equations
Week 3: Homogeneous, Exact, Bernoulli and Riccati Differential Equations
Week 4: Second Order Homogeneous Equations. Second Order Non-Homogeneous Equations
Week 5: n. Order Linear Equations. Non-Homogeneous Equations and Solution Methods
Week 6: Introduction to Differential Equation Systems. Elimination Method
Week 7: Eigenvalue Method for Homogeneous Systems
Week 8: Fundamental Matrices and Linear Systems. Non-Homogeneous Linear Systems
Week 9: Laplace Transforms and Properties. Inverse Laplace Transforms and Properties
Week 10 Applications to Initial Value Problems
Week 11: Convolution Step Functions and applications
Week 12: Introduction and Overview of Power Series. Classification of points and series solutions
Tentative Assesment Methods
• Midterm 40 %
• Final 60 %
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