DE & Slope Fields

• Explanation:

  • Notes | Annotated

  • 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

  • Characteristics of Differential Equations WS | Answers

• Explanation:

  • Intro

  • Create a slope field in Grapher (on a Mac)

  • Websites:

    • Slope Field Generator

    • 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:

  • Create a Slope Field given DE WS | Answers

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Reading Slope Fields WS | Answers

• Explanation:

  • Notes | Annotated

• Practice Problems:

  • Sketch a solution curve on a Slope Field WS | Answers

  • Match Slope Field with Possible Solution WS | Answers

  • Card match Activity

• Explanation:

  • Notes | Annotated

• Practice:

  • Match the DE with a possible solution WS | Answers

  • 2007 Q4 - part b

• Explanation:

  • Notes | Annotated

  • Kahn Videos:

    • Simple Differential Equations

    • Separable Differential Equations

    • Separable differential equations 2

• Practice Problems

  • Separable Differential Equations WS #1 | Answers

  • Separable Differential Equations WS #2 | Answers

• Explanation:

  • Notes | Annotated

• Explanation:

  • Notes | Annotated

  • Websites:

    • Models Exponential Growth (includes a java app)

    • Models Logistic Growth (includes a java app)

• Practice Problems:

  • Worksheet | Answers

• Explanation:

  • Notes | Annotated

  • 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).

  • Line Rider

• Practice Problems:

  • Linear Approximation WS | Answers

Review WS | Answers

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