#FreeEducationForAll. Doing Bachelor's(3rd Year) from BHU. Inspire Scholar. 64 Rank IIT JAM Physics. TIFR GS 2020 QUALIFIED. 

Siddharth Sahu

"Since Newton, mankind has come to realize that the laws of physics are always expressed in the language of differential equations." -Steven Strogatz 
In This Course Our task will be to learn different mathod of solving ODE.

IIT-JAM 

English

Ordinary Differential Equation: IIT-JAM

First Order Equations

Mathematical Methods

Physics

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Test Preparation

Since Newton mankind come to realize that the law of physics can always express as Differential Equations.

Overview to Course

In this video we discuss the concept of ODE, some of the basic definition Order of ODE ,Degree of ODE, Homogeneous ODE and Some of Examples.

Introduction

The solution of differential equation is a family of curve that satisfy the differential equation. Order of derivative is equals to no of constant appear on the solution.

Solution Of Differential Equation

For first order differential equation you can plot the slope field. We know that first order derivative is a slope of tangent to the curve and thus if we plot small line with that slope we can plot a field in space.

Direction Field

After this lesson you will able to :Define first order ODE, Solve separable equation,  Define and Solve Exact equation, Integrating factor.

First Order Differential Equations

First order Linear differential equation,  Bernoulli equation and Examples

First Order Linear Differential Equation & Bernaulli Equation

In this video we talk about Homogeneous Differential equations and look at some problems.

Homogeneous First Order ODE

In this video we discuss Second order linear differential equation. And see How to solve the special case where there constant coefficient and zero on RHS. Harmonic oscillator problem.

Second Order ODE (Constant Coefficients)

After This lesson you will able to:
1.Define Second order ODE with constant coefficient and Non zero RHS 2.Superposition Principle 3. Related Preposition 4.Particular Solution 5.way to find them

Second Order Linear Differential Equation With Constant Coefficient & Non-Zero RHS

After this lesson you will able to:
Evaluate the particular solution for exponential function on RHS.Write down the general solution of Differential equation with constant coefficient and Exponential on RHS.

Second Order ODE (Constant Coefficient) With Exponential On RHS

After This lesson you will able to find out particular solution for second order ODE constant coefficient with Sine or Cosine Function On RHS

Second Order ODE (Constant Coefficient) Sine/Cosine On RHS

After This lesson you will able to solve second order differential equations with constant coefficient and Polynomial on Right hand Side, also Exponential multiple with some function.

Second Order ode With Constant Coefficient Polynomial On RHS

In this lesson we will learn another method called Method of Undermined coefficient to Find Particular Solution Of Linear Second order differential equations with constant coefficient.

Method Of Undetermined Coefficient

Using Principal of Superposition, Finding particular solution of differential equation where There is sum of function of function on RHS with known Particular solution.

Principal of Superposition

In this lesson we learn some special form of Differential equation namely : Dependent variable is missing,  Independent variable is missing.

Special Forms:Second Order Ordinary Differential Equations

In this lesson we learn How to solve Cauchy Euler equation.

Cauchy-Euler Equation: Second Order Ordinary Differential Equations

In this lesson we see How to find general solution of given second order differential equations knowing one solution with the help of Order of reduction method.

Order Of Reduction: Second Order Ordinary Differential Equations

After this lesson you will able to Define The Laplace transform, compute the laplace transform of functions.

The Laplace Transform

After This lesson you will able to compute the solution of ODE with the help of Laplace transform.

Solution Of Differential Equations By Laplace Tranforms

In this lesson we define convolution of two functions ,Convolution Theorem and Finding Laplace inverse with the help of Convolution theorem.

Lessons

20 lessons • 3h 3m

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Overview to Course

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Introduction

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Solution Of Differential Equation

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Direction Field

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First Order Differential Equations

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First Order Linear Differential Equation & Bernaulli Equation

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Homogeneous First Order ODE

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Second Order ODE (Constant Coefficients)

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Second Order Linear Differential Equation With Constant Coefficient & Non-Zero RHS

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Second Order ODE (Constant Coefficient) With Exponential On RHS

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