Introduction, and a brief review of differential equations

First, we need to go over the structure of this course.

This course, like many of those in the Physics major, combines both math and physics. The pattern you'll see over and over again is

• introduce an interesting and common situation
• apply physics to derive equations which will describe the behavior of objects
• explain the mathematical techniques which are particularly useful to solve those equations

The "big" topics this course will cover are

1. the mathematical description of vibrations, including simple harmonic motion (SHM), but also damped and forced harmonic motion
2. the behavior of coupled oscillators
3. representing periodic motion with Fourier series
4. the mathematical description of waves: 1-D, 2-D, stationary and travelling
5. a tiny bit about the interaction of waves with boundaries and obstacles

You may have seen some of this material back in University Physics II, but we will probably go into somewhat greater detail than you did in that class.

There will be math. Bring your calculator, paper, and pen/pencil to class.

At times, I may ask students to search for specific information on the Internet. Bring an internet-enabled device to class.

Review of differential equations

This is a very brief review of differential equations. I hope you have some textbooks to fill in all the details.

Suppose we have a variable x -- it could represent time, or distance, or any other property. We discover that there's a connection between this variable and another quantity: the other quantity depends on x. We can call it a function of x: f(x).

There are many ways that we can connect two quantities mathematically. Let's start with simple ones and work our way up to more complex ones. Your job is to provide an example of the function f(x) which satisfies the differential equation. The more general your solution, the better.

Let's make the next question into a quick little quiz for today. Please take out a pencil and piece of paper. Write your name on the top of the paper, and then write your answer to the following differential equation on the paper.

You will have three minutes to complete this task.

For more information

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.