Before we get started, it is best to know a few things that will helps deal with theses differential equations. These concepts are quickly covered in class though not guranteed, so it is best to discuss it here first.
Linearity and principle of superposition are two concepts that is thrown around in differential equation and physics and so this video will explain what they are and give you a better understanding about them.
Solving differential equations is not as hard as you think. This lecture will show you how to solve and ODE using the algebra you learned way back... the quadratic equation ;-;This lecture will discuss about using the characteristic equation to solve for homogeneous equations with constant coefficients.
Using what was discussed in the previous video, we will solve ODEs using the characteristic equation.
Nothing new here, other than the specific solution of homogeneous ODEs with constant coefficient.
Some more examples with finding our c1 and c2 :D
We know how to solve for ODE's that homogeneous... what if they are nonhomogeneous?? Hmmmm it turns out that its just like solving for homogeneous ODEs (mostly) but with extra steps :D
Solving nonhomogenenous equations is the same as solving a homogeneous equation, but it has one extra step which is what the video is about.
Now it's time to find the specific solution for a nonhomogeneous equation.
Same thing as the previous examples except this is a bit more challenging.
Even though this is a "new" method, we will still be using the other 2 methods that were taught. What makes this new is the type of ODE that we will be looking at!
These examples about to "catch these hands." Solving homogeneous Cauchy-Euler equations will be a breeze as you will see by the length of the video lol.
We all know the homogeneous ODEs are the easiest, so let's add a little spice and do some nonhomogeneous ODEs :D
In this video we will discuss another method to solve ODEs which involves guessing our solution to being the product of 2 functions.
In this example/lecture hybrid I will discuss about a new method of solving an ODE that takes in the same form as the previous lecture/example hybrid and do one example that uses this method.
Systems of equations?!?! This isn't linear algebra... well... there are some things in linear algebra that can be used in ODE such as having a linear system of differential equations.
Baby steps. Starting small by creating first-order systems before we start solving these systems :)
Still taking baby steps as we solve a linear system by converting it into a 2nd order differential equation, which we know how to solve so it shouldn't be too hard.
Skipping massive steps, this video will show you how to check if the set of solutions are linearly independent.
Ayo?!?! I thought we did this already?!?!?! Well... yes.... kind of... This lecture will show the holistic version of solving linear systems of differential equations and not just the 2-by-2 that we previously discussed.
Well... they are easier than the other types of systems. We are going to start solving basic linear ODE systems before we get into the more challenging ones.
Before we get into actually solving systems containing defective eigenvalues, we will first see how we write the genereal solution for such system to get a sense of what we are dealing with.
Hopefully you saw the previous video, if not its up there ^^ >:( Now we are going ot solve a system of ODE that has defective eigenvalues and paint a clear picture on how the solutions are written.
Taking a step back in examples, it is best to understand why is it that we can obtain real solutions to a complex case of defective eigenvalues. One reason is the eigenvalue must have a conjugate pair. Additionally, this will cover the general steps to solving these types of systems.
Now that we know where the solutions comes from, we are now going to solve a system of ODEs that containes complex eigenvalues!
Are we conducting academic dishonesty here?!?! Of course not!! This series will help you conduct a universal cheat sheet for your PDE exam (assuming they allow you to have one). This section will focus on showing the work on certain problems that frequently show up when solving PDEs. Some of this can also help you in your ODE class too ;)
In this first video, I will be showing you a much faster way to solve 2nd order ODE without using the characteristic equation ;-;
Sometimes the Cauchy-Euler method can get confusing and so this video will show you a much faster way to solving ODEs that use the Cauchy-Euler method.
This video will find the particualr solution of a very common Sturm-Liouville Problem.
Picking up where we left off, this video will finsih the last 2 parts of the problem.
In this lecture will learn a concept that will help us make solving PDEs easier.
This series will have a different approach in teaching you by doing examples of the methods. In this example video, we will solve a simple PDE problem using the separation of variables method.
In this example we will be solving a wave eqaution with a Direchlet boundary conditions using the method of characteristics
This video will show the process of evaluating any periodic function and creating the Fourier series of the periodic function
After finding the Fourier series, we can actually now use this to find the summation of infinite series. Additionally, this video will discuss Parseval's identity.