# 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)

**Differential Equations (DE)**

**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

__Slope Fields__

**2) Create a slope field given a differential equation**

- 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:

**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:
- Sketch a solution curve on a Slope Field WS | Answers
- Match Slope Field with Possible Solution WS | Answers
- Card match Activity

**5) Verifying particular solutions to DE through substitution:**

- Explanation:
- Practice:

**6) Finding a particular solution through Separable Differential Equations:**

- Explanation:
- Practice Problems

**7) Domain of solutions to DE **

**8) DE Word problems**

- Explanation:
- Notes | Annotated
- Websites:
- Models Exponential Growth (includes a java app)
- Models Logistic Growth (includes a java app)

- Practice Problems:

**9) Local Linearization **

- Explanation:
- Line Rider
- Practice Problems:
- Linear Approximation 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.

- 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