3.1 Modeling with Differential Equations



This section introduces the issues to be studied in Chapter 3: Modeling with Differential Equations. Given certain differential equations, both analytical and numerical (approximate) methods will be discussed for producing solutions. Moreover, the more general notion of obtaining a function f from f' will be pursued.

By the end of your studying, you should know:

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.


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.


Slope Field


See short videos of worked problems for this section.


Take a quiz.


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.

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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