Math 125: Week 9
| Week 8 outline | Math 125 main page | Week 10 outline |
| What | Where | Link |
|---|---|---|
| Reading | Text -- 8.3, 9.1, 9.3 | |
| Worksheet | Website -- Newton's law of cooling |
DiffEQ.pdf Worksheet Solutions |
Student Guide:
From Section 8.3 we'll only cover a last application from Physics: Center of Mass -- the rest of that section will not be covered. The topic starts with a summation of the discrete data case and eventually replaces the summation with an integral. As always, a very important aspect of the process is understanding the process of modelling a problem with an integral, and how the Riemann Sums can provide the link from the simpler case to the more complex ones.
Then we are moving on to the last topic in the class, namely Differential Equations. The notation and terminology are introduced in Section 9.1. Building a differential equation from a written description of a situation is discussed. General Solutions and Initial Value Problems are contrasted. Population growth models may be discussed.
A large number of applied problems in Physics, Engineering, Economics and other areas can be modeled using Differential Equations. They are often very difficult to solve and we will focus on the just easiest cases.
In section 9.3 a method for solving a certain type of diff eqs is introduced, where one separates the variables and then integrates each side, using the integration techniques we have been studying this quarter. It is important to understand how one separates the variables correctly.
- Separable differential equations are discussed in Section 9.3.
WORKSHEET: Differential Equations have many interesting and useful applications. The worksheet DiffEQ.pdf will introduce you to two of these, Newton's Law of Cooling and a model for the spread of a rumor. Both involve differential equations that can be solved by the method of Separation of Variables. The worksheet gives a step-by-step introduction to this method.
| Week 8 outline | Math 125 main page | Week 10 outline |