## Activities for Meetings 16-17, Tues-Thurs 3/26-28/19  1

Newman Ch. 8: Ordinary differential equations:

8.1 First-order differential equations with one  variable.

8.2 Differential equations with more than one variable.

8.3 Second-order differential equations.

These three sections cover the material we will use in P281. You should take a look at the remaining sections of Ch. 8 to get an idea of some more advanced methods for solving ODEs.

Section “Solving ordinary differential equations” in handout Summary of numerical methods.

# In-Class Activities

Completing all of the non-starred activities will count as A-level work. To receive credit, these activities must be checked off in class or office hours within three weeks (by Fri 4/19).

1. Solving an ODE with odeint: The low-pass filter. The circuit shown in the figure below built from a resistor R and a capacitor C is called a “low-pass filter”. The input voltage Vin(t) is specified. Then the output voltage Vout(t) is determined by the following first-order ODE:

This is called a low-pass filter because low-frequency sine waves with angular frequencies ω 1/RC pass through this circuit nearly un- changed, while high frequency sine waves with ω 1/RC are (imper- fectly) blocked. For this problem use R = 10 kΩ, C = 1 µF which gives 1/RC = 100 rad/s.

12019-03-27 P281 W9ab.tex §c 2019 Donald Candela