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Language of Instruction
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English
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Level of Course Unit
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Bachelor's Degree
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Department / Program
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ENGINEERING SCIENCES
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Type of Program
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Formal Education
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Type of Course Unit
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Compulsory
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Course Delivery Method
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Face To Face
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Objectives of the Course
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The main goals of the course are as follows:
• To realize the need for applications of differential equation methods to global challenges in natural and engineering sciences.
• To understand the features of their application to engineering problems;
• To practice mathematical symbolic and numerical skill.
• learn how to apply the studied mathematical methods to real-life engineering problems.
• To learn how to apply the studied mathematical methods to real-life engineering problems.
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Course Content
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This course covers classifying and solving the differential equations. Especially, the differential equations related to Electrical-Electronics Engineering are studied. Various methods are covered for first and higher order differential equations such as Laplace Transform, Fourier Transform, Euler’s Method. Beside these, two-point boundary value problems, heat conduction, the wave equation: the occurrence of' two-point boundary value problems are also covered.
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Course Methods and Techniques
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In this course, theoretical knowledge is provided first, followed by problem-solving to reinforce the material.
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Prerequisites and co-requisities
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( MATH154 )
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Course Coordinator
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None
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Name of Lecturers
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Dr. MAHMUT BÜYÜKBAŞ
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Assistants
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None
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Work Placement(s)
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No
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Recommended or Required Reading
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Resources
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Introduction, Direction Fields, First Order Differential Equations, Separable Equations. Modeling with First Order Differential Equations in Electrical Engineering.
Method of Integrating Factor. Introduction to Laplace Transform for First Order Differential Equations.
Second Order Linear Homogeneous Equations with Constant Coefficients and Their Fundamental Solutions. Complex Roots of the Characteristic Equation, Repeated Roots. Applications to Electrical Engineering.
Second Order Linear Nonhomogeneous Equations. Laplace Transform Method for Second Order Linear Nonhomogeneous Equations.
Numerical Approach to ODEs. Euler's Method, The Existence and Uniqueness Theorem. Matlab for First and Second Order Differential Equations and Laplace Method.
Method of Undetermined Coefficients, Variation of Parameters.
n-th Order Homogeneous Differential Equations with Constant Coefficients: The Method of Undetermined Coefficients, The Method of Variation of Parameters. Laplace Method for Higher Order Linear Differential Equations; Differential Equations with Discontinuous Forcing Functions.
Introduction to Difference Equations for Electrical Engineering.
Introduction to Systems of First Order Linear Equations. Homogeneous Linear Systems with Constant Coefficients, Complex Eigenvalues, Fundamental Matrices, Repeated Eigenvalues.
Two-Point Boundary Value Problems, Fourier Series, The Fourier Convergence Theorem.
Introduction to Partial Differential Equations and Fourier Series: Heat Conduction in a Rod.
The Wave Equation.
The Occurrence of' Two-Point Boundary Value Problems.
Final Review: Modeling Engineering Problems with Differential Equations.
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https://books.google.com.tr/books/about/Elementary_Differential_Equations_and_Bo.html?id=SyaVDwAAQBAJ&redir_esc=y
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Course Category
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Mathematics and Basic Sciences
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%70
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Engineering
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%20
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Engineering Design
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%10
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