Download presentation

Presentation is loading. Please wait.

Published byBertha Stevens Modified over 2 years ago

1
More on Modeling 1.2: Separation of Variables January 18, 2007 HW change: 1.2 #38 is not due this week. Bring your CD-ROM to class Tuesday.

2
A mystery Here’s a new population model… Find the equilibrium solutions. For what values of P is the population increasing? decreasing? Sketch some solutions to the differential equation. Can you think of a situation in which this model makes sense? Be creative… From last time…

3
Spread of a rumor (group work) Quantities: (identify as indep var, dep var, or parameter) P = population of city N = people who have heard the rumor t = time k = proportionality constant Answers: 1.dN/dt 2.P - N 3.dN/dt = k(P - N) 4.dN/dt = k(350 - N) (N is in thousands, t could be days, weeks, etc. Your choice of units for t affects the value of k.) What should solutions look like? equilibrium solutions?

4
mmmm… Chocolate! Quantities: T = temp (degrees F) of hot chocolate at time t t = time in minutes, hours, etc. ( Why doesn’t it matter?) k = proportionality constant Equation: (Should k be positive or negative?)

5
HUH????? I asked you to look at the statement on p. 22: “So we should never be wrong.” What does that mean? Check this out: Paul says “y 1 (t) = 1 + t is a solution.” Glen says “y 2 (t) = 1 + 2t is a solution.” Bob says “y 3 (t) = 1 is a solution.” Who is right? How can we tell?

6
Separable Diffy-Q’s Example: Suppose the chocolate started out at 150 o and was 100 o 15 minutes later. How would you solve this initial value problem?

Similar presentations

Presentation is loading. Please wait....

OK

LOGISTIC GROWTH.

LOGISTIC GROWTH.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on market friendly statements Ppt on viruses and bacteria structure Ppt on 2nd world war records Ppt on rural education and sustainable development Ppt on industrial revolution in india Ppt on traction rolling stock maintenance Ppt on input output device management Ppt on nuclear family and joint family history Ppt on structure in c language Ppt on asian continent landmark