Table of Laplace Transforms. In this video, I show the Laplace transform for a few common functions. No theory or derivations here, just a quick reference that I will refer to in other videos.
Logistic Differential Equation. In this video we look at the logistic differential equation and its solution. We use the solution to determine when a population will reach a certain size.
Euler's Method - Another Example #1. In this video, I show another example of using Euler's method to solve a differential equation. (Ok, we do not find an exact solution when doing this method; rather we are approximating the solution!)
Euler's Method - Another Example #2. In this video, I show another example of using Euler's method to solve a differential equation. (Ok, we do not find an exact solution when doing this method; rather we are approximating the solution!
Solving a Separable Differential Equation, Another Example #1. In this video, I solve a separable differential equation.
Solving a Separable Differential Equation, Another Example #2. In this video, I solve a separable differential equation.
Solving a Separable Differential Equation, Another Example #3. In this video, I solve an example of a separable differential equation.
Solving a Separable Differential Equation, Another Example #4, Initial Condition. In this video, we solve a separable differential equation that has an initial condition.
Solving a Separable Differential Equation, Another Example #5, Initial Condition. Just another example of solving a separable differential equation that has an initial condition.
Basic Differential Equation with an Initial Condition. In this video, I solve a basic differential equation with an initial condition (that means we must solve for C). You should have seen these problems when you first started integration in calculus!
Differential Equations - Basic Idea of What It Means to be a Solution. Ok, nothing heavy at all here! What does it mean to be a solution of a differential equation? Let's looks and see! Ya just take a derivative, plug it in, see if it works! (Basically!)
First Order Linear Differential Equations / Integrating Factors - Ex 2. In this video, I show another example of using integrating factors to find the solution of a first order linear differential equation.
Change of Variables / Homogeneous Differential Equation - Example 1. In this video, I solve a homogeneous differential equation by using a change of variables.
Change of Variables / Homogeneous Differential Equation - Example 2. In this video, I solve a homogeneous differential equation by using a change of variables.
Change of Variables / Homogeneous Differential Equation - Example 3. In this video, I solve a homogeneous differential equation by using a change of variables.
Change of Variables / Homogeneous Differential Equation - Example 4. In this video, I solve a homogeneous differential equation by using a change of variables. This example is looooong, requiring partial fractions to integrate! So much fun though!
The Inverse Laplace Transform. In this video, I give an important theorem related to the inverse Laplace transform, give a definition about the inverse Laplace transform and find the inverse Laplace transform of a function.
Table of Laplace Transforms. In this video, I show the Laplace transform for a few common functions. No theory or derivations here, just a quick reference that I will refer to in other videos.
The Logistic Equation and Models for Population - Example 1, part 1. In this video, we have an example where biologists stock a lake with fish and after one year the population has tripled. Knowing the carrying capacity, I find a formula for the the population at time ' t ' using the analytic solution.
The Logistic Equation and Models for Population - Example 1, part 2. In this video, I find how long it actually takes for the population of fish to reach a total of 4,000.
Power Series Solutions of Differential Equations - In this video, I show how to use power series to find a solution of a differential equation. This is a SIMPLE example and the final solution is very NICE compared to what would normally happen with a more complicated differential equation, so please be aware of that!
The Logistic Equation and the Analytic Solution. In this video, I find the analytic solution to the logistic differential equation.
Exact Differential Equations - In this video I show what it means for a differential equation to be exact and then one solve one problem.