Introducing Differential Equations Through Slope Fields
Lesson 1 of 8
Objective: SWBAT sketch slope fields and estimate solutions graphically to basic differential equations.
Warm-up and Homework Review
Setting the Stage
Distribute the Volumes of Solids Quiz, which is 25 minutes timed. The directions tell students to use the fnInt command on their calculators to evaluate each integral, but read these directions aloud to students as an added reminder.
In prior years some students have wasted a lot of time working the integrals by hand, which causes them to run out of time and also weakens our ability to assess students’ ability to setup the integrals correctly. 25 minutes is enough time if students are reasonably proficient with sketching the regions, because writing the integrals from the sketched regions and evaluating the integrals with fnInt does not take a lot of time.
Closure + Homework
Slope fields applets
Stewart Calculus - Tools for Enriching Calculus, http://www.stewartcalculus.com/tec
University of Michigan, http://www.math.lsa.umich.edu/courses/116/slopefields.html