Differential equations

• 
  

  Differential equations

• First order differential equations
• Second order linear equations
• Laplace transform

Click On & Wait For Five Seconds Then Press

First order differential equations

Differential equations with only first derivatives.

Subscribe

Intro to differential equations

How is a differential equation different from a regular one? Well, the solution is a function (or a class of functions), not a number. How do you like me now (that is what the differential equation would say in response to your shock)!

• What is a differential equation
• Simple Differential Equations

Separable equations

Arguably the 'easiest' class of differential equations. Here we use our powers of algebra to "separate" the y's from the x's on two different sides of the equation and then we just integrate!

• Separable Differential Equations
• Separable differential equations 2

Exact equations and integrating factors

A very special class of often non-linear differential equations. If you know a bit about partial derivatives, this tutorial will help you know how to 'exactly' solve these!

• Exact Equations Intuition 1 (proofy)
• Exact Equations Intuition 2 (proofy)
• Exact Equations Example 1
• Exact Equations Example 2
• Exact Equations Example 3
• Integrating factors 1
• Integrating factors 2

Homogeneous equations

In this equations, all of the fat is fully mixed in so it doesn't collect at the top. No (that would be homogenized equations). Actually, the term "homogeneous" is way overused in differential equations. In this tutorial, we'll look at equations of the form y'=(F(y/x)).

• First order homegenous equations
• First order homogeneous equations 2

Click On & Wait For Five Seconds Then Press

Second order linear equations

Linear differential equations that contain second derivatives

Subscribe

Linear homogeneous equations

To make your life interesting, we'll now use the word "homogeneous" in a way that is not connected to the way we used the term when talking about first-order equations. As you'll see, second order linear homogeneous equations can be solved with a little bit of algebra (and a lot of love).

• 2nd Order Linear Homogeneous Differential Equations 1
• 2nd Order Linear Homogeneous Differential Equations 2
• 2nd Order Linear Homogeneous Differential Equations 3
• 2nd Order Linear Homogeneous Differential Equations 4

Complex and repeated roots of characteristic equation

Thinking about what happens when you have complex or repeated roots for your characteristic equation.

• Complex roots of the characteristic equations 1
• Complex roots of the characteristic equations 2
• Complex roots of the characteristic equations 3
• Repeated roots of the characteristic equation
• Repeated roots of the characteristic equations part 2

Method of undetermined coefficients

Now we can apply some of our second order linear differential equations skills to nonhomogeneous equations. Yay!

• Undetermined Coefficients 1
• Undetermined Coefficients 2
• Undetermined Coefficients 3
• Undetermined Coefficients 4

Click On & Wait For Five Seconds Then Press

Laplace transform

Transforms and the Laplace transform in particular. Convolution integrals.

Subscribe

Laplace transform

We now use one of the coolest techniques in mathematics to transform differential equations into algebraic ones. You'll also learn about transforms in general!

• Laplace Transform 1
• Laplace Transform 2
• L{sin(at)}) - transform of sin(at)
• Part 2 of the transform of the sin(at)

Properties of the Laplace transform

You know how to use the definition of the Laplace transform. In this tutorial, we'll explore some of the properties of the transform that will start start to make it clear why they are so useful for differential equations. This tutorial is paired well with the tutorial on using the "Laplace transform to solve differential equations". In fact you might come back to this tutorial over and over as you solve more and more problems.

• Laplace as linear operator and Laplace of derivatives
• Laplace Transform of cos t and polynomials
• "Shifting" transform by multiplying function by exponential
• Laplace Transform of : L{t}
• Laplace Transform of t^n: L{t^n}
• Laplace Transform of the Unit Step Function
• Inverse Laplace Examples
• Dirac Delta Function
• Laplace Transform of the Dirac Delta Function

Laplace transform to solve a differential equation

You know a good bit about taking Laplace transform and useful properties of the transform. You are dying to actually apply these skills to an actual differential equation. Wait no longer!

• Laplace Transform to solve an equation
• Laplace Transform solves an equation 2
• Using the Laplace Transform to solve a nonhomogeneous eq
• Laplace/Step Function Differential Equation

The convolution integral

This tutorial won't be as convoluted as you might suspect. We'll see what multiplying transforms in the s-domain give us in the time domain.

• Introduction to the Convolution
• The Convolution and the Laplace Transform
• Using the Convolution Theorem to Solve an Initial Value Prob

Get paid to share your links!