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.
Course
Differential Equations
27 Lectures
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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!)
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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!
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Solving a Separable Differential Equation, Another Example #1. In this video, I solve a separable differential equation.
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Solving a Separable Differential Equation, Another Example #2. In this video, I solve a separable differential equation.
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Solving a Separable Differential Equation, Another Example #3. In this video, I solve an example of a separable differential equation.
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Solving a Separable Differential Equation, Another Example #4, Initial Condition. In this video, we solve a separable differential equation that has an initial condition.
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Solving a Separable Differential Equation, Another Example #5, Initial Condition. Just another example of solving a separable differential equation that has an initial condition.
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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!
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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!)
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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.
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Change of Variables / Homogeneous Differential Equation - Example 1. In this video, I solve a homogeneous differential equation by using a change of variables.
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Change of Variables / Homogeneous Differential Equation - Example 2. In this video, I solve a homogeneous differential equation by using a change of variables.
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Change of Variables / Homogeneous Differential Equation - Example 3. In this video, I solve a homogeneous differential equation by using a change of variables.
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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!
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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.
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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.
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The Laplace Transform - The Basic Idea of How We Use It. This video is the first of (what will be) many videos about the Laplace transform. In this video, I discuss the basic idea of how we will use the Laplace transform. There are no computations or anything heavy in this video! Just an outline of 'where we are going'.
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Laplace Transform is a Linear Operator - Proof. In this video I quickly prove the important property that the Laplace transform is a linear operator. This says that to take the Laplace transform of a linear combination of functions we take the Laplace transform of each term separately and add the result.
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The Laplace Transform, Basic Properties - Definitions and Derivatives. In this video, I give a few definitions and some results about basic properties of the Laplace Transform. I prove the result for the Laplace transform of derivatives. I do not solve any equations in this video; I am presenting a bit of the theory that justifies the way we do solve differential equations using the Laplace transform.
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The Laplace Transform - More Derivatives. In this video, I prove another result about laplace transforms of derivatives. Just some theory here and some important formulas to help solve problems!
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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.
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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.
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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!
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The Logistic Equation and the Analytic Solution. In this video, I find the analytic solution to the logistic differential equation.
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Exact Differential Equations - In this video I show what it means for a differential equation to be exact and then one solve one problem.
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Thanks for watching and please subscribe! Visit PatrickJMT.com and 'like' it! :) First Order Linear Differential Equations - In this video I outline the general technique to solve First Order Linear Differential Equations and do a complete example.