Special Focus: Differential Equations by the College Board (pdf - 61 pages)

AB Calculus Ch 11 FRQ Review Differential Equations & Slope Fields Complete these FRQ on your own paper, except for graphing the slope fields. Consider the differential equation 2 1 dy y dx x. (a) On the axes provided, sketch a slope field for the given differential equation at the six points indicated. Slope fields are little lines on a coordinate system graph that represent the slope for that (x,y) combination for a particular differential equation (remember that a differential equation represents a slope).

Slope fields are visual representations of differential equations of the form dy / dx = f (x, y). At each sample point of a slope field, there is a segment having slope equal to the value of dy / dx. Any curve that follows the flow suggested by the directions of the segments is a solution to the differential equation.

The Domain of Solutions to Differential Equations by the College Board (pdf - 8 pages)

Differential Equations (DE)

Sports head football european editionobey games today. 1) Introduction and Characteristics of Differential Equations

• 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

Our friends bike across the united states for a great cause. 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:
  • Create a Slope Field given DE WS | Answers

3) Reading and analyzing slope fields

• Explanation:
  • Notes | Annotated
• Practice Problems:
  • Reading Slope Fields WS | Answers

Particular Solutions to Differential Equations (DE)

4) Graphing a particular solution given a slope field and a point

• Explanation:
  • Notes | Annotated
• Practice Problems:
• Sketch a solution curve on a Slope Field WS | Answers
• Match Slope Field with Possible Solution WS | Answers

5) Verifying particular solutions to DE through substitution:

• Explanation:
  • Notes | Annotated
• Practice:
  • Match the DE with a possible solution WS | Answers
  • 2007 Q4 - part b

6) Finding a particular solution through Separable Differential Equations:

• Explanation:
  • Notes | Annotated
  • Kahn Videos:
• Practice Problems
  • Separable Differential Equations WS #1 | Answers
  • Separable Differential Equations WS #2 | Answers

7) Domain of solutions to DE

• Explanation:
  • Notes | Annotated

8) DE Word problems

• Explanation:
  • Notes | Annotated
  • Websites:
    • Models Exponential Growth (includes a java app)
    • Models Logistic Growth (includes a java app)
• Practice Problems:
  • Worksheet | Answers

9) Local Linearization

• 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).
• Practice Problems:
• Linear Approximation WS | Answers

10) Review WS | Answers

11) 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.

10 1 Slope Field Sap Calculus Equation

• 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