# 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