3.4 Slope Fields and Euler's Method

By the end of your studying, you should know:
Onscreen applet instructions:
The applet allows the user to generate an Euler's Method approximation to the solution of the given IVP. The buttons are fairly selfexplanatory. What is the effect of changing the step size?
ExamplesAn investor has a savings account that pays 3.5% interest. The investor opens the account with $500 and makes an additional deposit of $500 at the end of each year. Assume the function S(t), which gives the amount in the savings account after t years, satisfies the differential equationUse Euler's method to estimate the amount in the account at the end of 5, 10, and 25 years, using a step size of 0.1.
Let y be a function of x that satisfies the differential equation
Assume that the point (–1, .001) is on the graph of a function that satisfies the differential equation
Match three differential equations to their slope fields. AppletsEuler's MethodVideosSee short videos of worked problems for this section.
QuizExercisesSee Exercises for 3.4 Slope Fields and Euler's Method (PDF).Work online to solve the exercises for this section, or for any other section of the textbook. 
Resources on the WebInformation on NewtonBiographical 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
Calculus Applications
Euler's Method

Interesting ApplicationNothing yet has been found. Any ideas? 
3.3 Separable Differential Equations  Table of Contents  3.5 Issues in Curve Sketching 
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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel