What is a Differential Equation? Applications And Examples.

In this video by Greg at ****** You'll learn what differential equations are, you'll see some examples of differential equations, and you'll gain an understanding of why their applications are so diverse. Specifically, you'll learn answers to the following questions. 1. What are some real-world applications of differential equations? 2. What is a differential equation? 3. Why might differential equations apply to so many real-world phenomena? 4. What are some examples of differential equations? Additional Resources To review the ideas in this video, try out the free "digital notecards" at the URL below. ****** I make one notecard for each video in the playlist. Each notecard contains a question or exercise that summarizes the content of the corresponding video. The notecards can help you rapidly review what you've learned, especially if you haven't watched the videos in a while. You'll also find them helpful if you want to test your understanding right after you watch a video. If you'd like to be notified when I post new videos in the playlist, just hit the subscribe button. Happy learning! Greg at Higher Math Help This video is part of a playlist: ******

Differential equations help us to understand phenomena that involve rates of change. [ENGINE BEING REVVED] For example, differential equations help us understand the spread of disease, weather and climate prediction, traffic flow, financial markets, population growth, water pollution, chemical reactions, suspension bridges, brain function, rockets, tumor growth, radioactive decay airflow across a plane's wing, electrical circuits, planetary motion, and the vibration of guitar strings. OK, but what is a differential equation? From calculus, we know the word differentiate means compute a derivative, and one definition of differential equation is an equation containing a derivative, and this actually explains to some extent the wide applicability of differential equations because remember that a derivative represents a rate of change, and that rate of change can be anything from a rate of population growth to a rate of radioactive decay. Let's take a look at some examples. Here's one. The derivative of y with respect to x plus xy equals e to the 2x. That's an equation containing a derivative, so it's a differential equation. Oh, and remember that dy/dx and y prime are two ways to write the derivative. Using the prime notation, here's an example involving a second order derivative. y double prime minus y prime plus y squared equals sine of x If the equation contains at least one derivative of any order, then it's a differential equation. Let's consider one more example. If you've taken multivariable calculus, then you'll have seen partial derivatives, and these come up in differential equations too. Here's a somewhat famous example: u xx plus u yy equals zero. Alright, now that you know what a differential equation is, the next step is to solve one. In the next video, we'll solve a simple differential equation, and we'll discuss how it's different from familiar algebraic equations. See you then!