3.1 Modeling with Differential Equations

Summary

By the end of your studying, you should know:

• How to solve a differential equation by inspection (guess-and-check).
• What a slope field is.
• How to plot a slope field both by hand and with an applet.
• The method of separation of variables,and how and where to apply it.

On-screen applet instructions: The applet draws a slope field for an equation y' = f(x,y). It allows several choices of the function, and allows changing the resolution of the grid. Drag the mouse to draw a solution curve through the point P. Click the mouse (instead of drag) to set a new initial point P. Click here for more details.

Examples Match three equations with the differential equations they satisfy. Match four differential equations with their slope fields. Solve the following differential equation by separation of variables. Use the initial condition to solve for the unique solution. Applets Slope Field Videos See short videos of worked problems for this section. Quiz Take a quiz. Exercises See Exercises for 3.1 Modeling with Differential Equations (PDF). Work online to solve the exercises for this section, or for any other section of the textbook.

Resources on the Web Information on Newton Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Information on Leibniz Biographical data from St. Andrew's University's Web site Excerpt from W.W. Rouse Ball's "A Short Account of the History of Mathematics" Calculus Applications Project Intermath DEs and Slope Fields Tool Mathlet

Interesting Application Nothing yet has been found. Any ideas?

2.18 Case Study: Torricelli?s Law

Table of Contents

3.2 Exponential Growth and Decay

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel