The Logistic Equation and the Analytic Solution. In this video, I find the analytic solution to the logistic differential equation.
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.