Mechanical Engineering

Definition and Classification of Differential Equations, Derivative of Differential Equations and Derivatives, Solution of Differential Equations: Integral Curve, Closed-Open Solution, Special Solution, General Solution, Unique Solution, Initial Value Problem. Obtaining of Differential Equations. First Order Differential Equations: Differentiable Differential Equations in Variables, Differential Equations Converting to Differential Equations Which Can Separate into Their Variables. Homogeneous Differential Equations, Homogeneous Differential Equations, Homogeneous Differential Equations, Linear Equations, Integral Factor Method, Variation Method of Parameters, Bernoulli Differential Equations, Exact Differential Equations and Integral Factors, Integral Factors Including One Variable, Riccati Differential Equations, First Order Higher Order Clairaut and Lagrange Equations from Differential Equations. Second Order Linear Differential Equations: Constant Coefficient Homogeneous Differential Equations, Characteristic Equation, General Solutions of Linear Homogeneous Equations, Linear Independence and Wronskian Determinancy. Complex Roots of the Characteristic Equation, Real Valuable Solutions, Repeating Roots, Order Dropping, Nonhomogeneous Equations. Indefinite Coefficients Method, Variation of Parameters (Steady Change-Lagrange) Method. High Order Linear Differential Equations: General Theory of Nth Order Linear Differential Equations, Homogeneous Equation and Solution, Homogeneous Equation (Second Sided Equation), Special Solutions, General Solutions, Linear Independence and Wronxian Determinants, Constant Coefficient Homogeneous Equations , Characteristic Polynomial, Characteristic Equation, Real and Different Roots, Complex Roots, Repeating Roots, Indeterminate Coefficients Method, Parameter (Static) Change Method. Some Special Second Order Differential Equations: Differential Equations without Dependent Variables, Differential Equations without Independent Variables. Variable Coefficient Euler Differential Equation. Solution of Second Order Linear Differential Equations by Series: Short Turn of Force Series, Solution by Series of One Add Point. Definition of Laplace Transformation, Definition of Laplace Transformation, Inverse Laplace Transformation, Definition of Inverse Laplace Transformation, Solution of Initial Value Problems with Laplace Transformation. First order linear differential equations systems: Elimination and Determinant method.

Develop mathematical thinking. To be able to solve problems in mathematics, physics and engineering.