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NİĞDE ÖMER HALİSDEMİR UNIVERSITY
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HRT2001 / Diferantial Equations
GENERAL INFORMATION ABOUT THE COURSE
Course Code
Semester
Course Type
Course Level
Course Language
Course Title
Theoretical
Practical
ECTS
Turkish Name of the Course
Course Coordinator
E Mail
Assistant Staff of the Course
E Mail
Course Objective
Develop mathematical thinking. Mathematics, physics and engineering to solve problems encountered in.
Brief Content of the Course
Differential Equations, The Definition and Classification, Order and Degree of Differential Equations, Solutions of Differential Equations: The Integral Curve, İmplicit-Explicit Solution, Particular Solution, The General Solution, Singular Solution, İnitial Value Problem. Derivation of Differential Equations. First Order Differantial equations: Separable Differential Equations, Variables that can be converted Separable Differential Equations Differential Equations, Homogeneous Functions, Homogeneous Differential Equations, Becomes homogeneous differential equations that can be converted. Linear Equations, Method of Integrating Factors, Method of Variation Parameters, Bernoulli Equations, Exact Equations and Integrating Factors , Exact Equtions, The Method of İntegrating Factors Based on a Single Variable, Riccati Equations. First Order Higher Degree Differential Equations: Clairaut and Lagrange's Equations. Second Order Linear Equations: Homogeneous Equations with Constant Coefficients, Characteristic Equation, Fundamental Solutions of Linear Homogeneous Equations, Linear independence and Wronskian Determinant, Complex Roots of The Characteristic Equation, Real Valued Solutions, Repeated Roots, Reduction of Order. Nonhomogeneous Equations Method of Undetermined Coefficients, Method of Variation Parameters. Higher Order Linear Equations: General Theory of nth Order Linear Equations, The Homogeneous Equation and its solution. The Nonhomogeneous Equation, Particiluar Solutions, General Solutions, Linear İndependence and Wronskian Determinant, Homogeneous Equations with Constant Coefficients. Characteristic Polynomial ,Characteristic Equation, Real and Unequal Roots, Complex Roots , Repeated Roots, The Method of Undetermined Coefficients, The Method of Variation of Parameters. Some Special Second Order Equations: Equations with the Dependent Variable Missing, Equations with the Independent Variable Missing. Euler Differential Equation with Variable Coefficients. Series Solutions of Second Order Linear Equations: Review of Power Series, Series Solutions Near an Ordinary Point. The Laplace Transform: The Laplace Transform, Definition of Laplace Transform. The Inverse Laplace Transform, Definition of Inverse Laplace Transform. Solution of Initial Value Problems with the help of the Laplace Transformation. Systems of Linear Equation First Order Differential Equation: Elimination and Determinant Method
Prerequisites
None
Course Objectives
Course Objectives
1
Students will learn to develop mathematical thinking.
2
Students will learn to gain ability of solving differential equations
3
Students will learn mathematics, physics and engineering to solve problems encountered in
4
Students will learn a method to be used to gain scientific research
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Course Category
Course Category
Percentage
Mathematics and Basic Sciences
Basic Vocational Courses