1. Slope Fields: Motivation, Activity, APcalcAB04#6, DE matching, TI89
Matching slope fields handout with accompanying TI-89 script will make graphing and teaching about differential equations for the AP Calculus exam so much easier.
StudyCards™ for AP Physics and Calculus will also be shared.
194 ■ Slope fields the Easy Way on the
TI-89 and StudyCard™ Sharing
60-Minute Hands-On ■ IntermediateTI-89 ■ Calculus, Physics
Slope Fields: Motivation, Activity, APcalcAB04#6, DE matching, TI89
Sean Bird
Beginning with the 2004AB Calc Exam
“Geometric interpretation of differential equations via slope fields and the relationship between slope fields and solutions curves for differential equations.”
This topic has been part of the topic outline for Calc BC since the 1998 exam
AP Physics & Calculus
Covenant Christian High School
7525 West 21st Street
Indianapolis, IN 46214
Phone: 317/ x104
Website:
Psalm 111:2

2. Three/Four Pronged approach
We now know how to algebraically solve separable differential equations.
Today we will graphically find the particular solution for any DE using SLOPE FIELDS.
In calcBC we will then numerically solve DEs using Euler’s Method
Verbally
(Recall new sign chart policy)

3. Slope Fields
If you enjoyed connecting the dots, you’ll love slope fields
It is a graphical method to find a particular solution to any differential equation.
a DE is nothing but a slope equation -

4. Given:
Sketch the slope field …

5. But how?
Substitute the x and y into the differential equation for each of the points.
Plot this slope on the graph.

7. 1st the slopes will be positive when the differential equation is positive, i.e.
And x2 is always positive (except when x=0)
y – 1 > 0 when y > 1
ANSWER: y > 1, but x ≠ 1

8. Separate the variables
Exponentiate both sides
Let K

9. Form B 2004#5 was the same question but

10. The thought process… E C A G
Isoclines along horizon. lines → DE depends only on y
Same slope along vert. line → DE depends only on x
Sinusoidal
Consider a specific point – what is the slope there.
What makes the slope zero? What values of x and y make the slope 1?
Note y'(x) = x+y has same slopes along the diagonal.
Solve the separable DE B D I H F K J

11. Running the DEmatch script
Select TEXT EDITOR under APPS
Open…
Folder: calculus, Variable: dematch
Green (chartreuse for Titanium) diamond, Up arrow will quickly jump cursor to the top. 2nd, up arrow scrolls up a page.
Press F4 all the way down
Note what each step accomplishes and READ important rules at the end.

12. StudyCard Stacks Trig/PreCalc: study of functions Calculus:
identity **
limits83 **
limits89 **
derivative **
integral **
Algebra:
slope,
slope/intercept for 89
for 83/84 new!
Physics:
AP Physics for the TI89 ** 83*
Prefix for the 83/84 **
History of Physics for the 89 ** or 83/84 **new!