DE & Slope Fields
Special Focus: Differential Equations by the College Board (pdf - 61 pages)
The Domain of Solutions to Differential Equations by the College Board (pdf - 8 pages)
1) Introduction and Characteristics of Differential Equations
Explanation:
Khan Video: What is a differential equation? (don't worry about the classifications - after 8:00)
Rabbit versus Wolves interactive Simulator (Shodor - Java)
Practice Problems
Slope Fields
2) Create a slope field given a differential equation
Explanation:
Create a slope field in Grapher (on a Mac)
Websites:
Slope Field Calculator (java) by Marek Rychlik; (click on a point to show a particular solution [or type it in]& adjust many parameters)
Softwares: WINPLOT (Windows software to download)
Practice Problems:
3) Reading and analyzing slope fields
Explanation:
Practice Problems:
Particular Solutions to Differential Equations (DE)
4) Graphing a particular solution given a slope field and a point
Explanation:
Practice Problems:
6) Finding a particular solution through Separable Differential Equations:
Explanation:
Practice Problems
8) DE Word problems
Explanation:
Websites:
Models Exponential Growth (includes a java app)
Models Logistic Growth (includes a java app)
Practice Problems:
9) Local Linearization
Explanation:
Interactive website: This Java website shows how a function looks like a line when you zoom in on the graph. It also visually shows how the value of the function is similar to the value of the tangent line (drag the red point).
Practice Problems:
Review
Differential Equations Connection Project
AP Questions: Slope fields have been a topic on the AP Calculus BC Exam since 1998 and on the AP Calculus AB Exam since 2004.
2012 Q5 - second derivative of a DE and separable equation
2011 Q5 - separable equations & linear approximation
2010 (Form B) Q5 - slope field and separable
2010 Q6 - separable equation & linear approximation
2008 Q5 - slope field and separable equation
2007 (Form B) Q5 - slope field, second derivative, max/min
2007 Q4 - solve for a constant by substitution of a DE
2006 (Form B) Q5 - slope field and separable equation
2006 Q5 - slope field and separable equation
2005 (Form B) Q6 - - slope field and separable equation
2005 Q6 - slope field, linear approximation and separable equation
2004 (Form B) Q5 - slope field and separable equation
2004 Q6 - slope field and separable equation
2003 (Form B) Q6 - separable equation
2003 Q5 - part b and c - separable equation
2002 (Form B) Q5 - max/min and separable equation
2001 Q6 - separable equation
2000 Q6 - separable equation
1998 Q4 - linear approximation and separable equation