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Differential Equation Inverse Transforms And Transforms Of Derivatives

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Syllabus
Videos

Introduction 48:19

Introduction To Differential48:19

First Order Differential Equation 81:30

Linear And Nonlinear Differential Equation81:30
A Numerical Method
Exact Equations and Integrating Factors
Solution by Substitutions

Second Order Linear Equation

Homogeneous Equations with Constant Coefficients
Solutions Of Linear Homogeneous Equation
Complex Roots Of The Characteristic Equation
Repeated Roots; Reduction Of Order
Non Homogeneous Equations; Method Of Undetermined Coefficients
Variation Of Parameters
Cauchy – Euler Equation25:15
Greens Functions40:32
Reduction Of Order48:55
Solving Systems Of Linear DE By Elimination57:53
Preliminary Theory-Linear Equations52:15

Higher order linear equation

General Theory Of Nth Order Linear Equations
Homogeneous equations with constant coefficients

Series solutions of second order linear equations

Review of power series
Series Solutions Near An Ordinary Point57:04
Series Solutions Near a Regular Singular Point31:04
Special Functions34:42

The Laplace Transform

Laplace Transform
Inverse Transforms And Transforms Of Derivatives30:25
Opertional Properties71:21
The Dirac Delta Function18:17

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Notes
Comments & Questions

اذا كان Laplace transform ل f(t) هوF(s) فانf(t) هتساوي Laplace inverse ل F(s)
مثال :

نظرية :

الـ Linearityاو الخاصية الخطية : هي خاصية تنطبق على Laplace transform و Inverse Laplace transform هذه الخاصية تجعل ال transformاو ال inverse transformيتقسموا على الجمع ولو في ثابت نقدر نخليه خارج او داخل ال transform ولايوثر على الناتج النهائي
Transforms of Derivatives Theorem :

اذا كان

اذن

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