We begin in earnest our study of differential equations. These tremendously useful tools for science and engineering end up being rather pesky in terms of the ways we go about solving them. In this unit, we will be introduced to two types of DEs, as well as a numerical method for approximating solutions.
- Section 8.2: While direction fields and Euler's method are optional for this course, they will definitely come back to help you later in your undergrad. Take the time to look at them and understand them. Direction fields are an excellent visual aid and Euler's method is a powerful numeric tool. Between them, they will help you estimate solutions to unsolvable problems, much as numerical integration helps out with unsolvable integrals.
- Section 8.3: The easiest variant of Differential Equations (other than y' = f(x)) is the separable equation. In the future, when you are taking a course that is heavy on DEs, always remember that when a differential equation looks more terrible than anything you've ever seen - it can probably be factored and separated...or else you have to use Laplace Transforms.
- Section 8.4: The linear DEs done in Section 8.4 are a little boring - they actually reduce to separable equations. We will take them a little farther and look at the general case, which is a lot more fun.
|Euler's Method - Direction Fields and Euler's Method | Euler's Method - Direction Fields and Euler's Method||Shai Cohen|
|Separable Differential Equations | Separable Differential Equations||Shai Cohen|
|Separable Differential Equations Example | Separable Differential Equations Example||Shai Cohen|
|Separable Differential Equations Example - Hidden DEs | Separable Differential Equations Example - Hidden DEs||Shai Cohen|
|Linear DEs - Easy First Order Linear DEs | Linear DEs - Easy First Order Linear DEs||Shai Cohen|
|Linear DEs - General First Order Linear Des | Linear DEs - General First Order Linear Des||Shai Cohen|
|Linear DEs Example - Basics | Linear DEs Example - Basics||Shai Cohen|
|Linear DEs Example - Some Work | Linear DEs Example - Some Work||Shai Cohen|
|Linear DEs Example - Mixtures | Linear DEs Example - Mixtures||Shai Cohen|
|Linear DEs Example - More Mixtures | Linear DEs Example - More Mixtures||Shai Cohen|