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### 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 EquationsExplanation:Notes | AnnotatedKhan Video: What is a differential equation? (don't worry about the classifications - after 8:00)Rabbit versus Wolves interactive Simulator (Shodor - Java)Practice ProblemsCharacteristics of Differential Equations WS | AnswersSlope Fields2) Create a slope field given a differential equationExplanation:IntroCreate a slope field in Grapher (on a Mac)Websites:Slope Field GeneratorSlope 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 | Answers3) Reading and analyzing slope fieldsExplanation:NotesPractice Problems:Reading Slope Fields WS  | AnswersParticular Solutions to Differential Equations (DE)4)  Graphing a particular solution given a slope field and a pointExplanation:Notes | AnnotatedPractice Problems:5)  Verifying particular solutions to DE through substitution:Explanation:Notes | AnnotatedPractice:6)  Finding a particular solution through Separable Differential Equations:Explanation:Practice Problems7)  Domain of solutions to DE Explanation:Notes | Annotated8) DE Word problemsExplanation:Websites:Models Exponential Growth (includes a java app)Models Logistic Growth (includes a java app)Practice Problems:9) Local Linearization Explanation:Notes | AnnotatedInteractive 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 RiderPractice Problems:Linear Approximation WS | Answers10) Review WS | AnswersAP 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 equation2011 Q5 - separable equations & linear approximation2010 (Form B) Q5 - slope field and separable2010 Q6 - separable equation & linear approximation2008 Q5 - slope field and separable equation2007 (Form B) Q5 - slope field, second derivative, max/min 2007 Q4 - solve for a constant by substitution of a DE2006 (Form B) Q5 - slope field and separable equation2006 Q5 - slope field and separable equation- slope field and separable equation2005 Q6 - slope field, linear approximation and separable equation2004 (Form B) Q5 - slope field and separable equation2004 Q6 - slope field and separable equation2003 (Form B) Q6 - separable equationpart b and c - separable equation2002 (Form B) Q5 - max/min and separable equation 2001 Q6 - separable equation2000 Q6 - separable equation1998 Q4 - linear approximation and separable equation