AP Calculus Favorite Web Sites

Geogebra applets for Calculus, use Internet Explorer
http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html

Video Lectures by chapter/lesson for AP Calculus
http://www.centerofmath.org/video_ap.html

Khan Academy: videos on zillions of math topics
http://www.khanacademy.org/

In particular, construct a derivative graph by estimating slopes of tangent lines
http://www.khanacademy.org/exercises?exid=derivative_intuition

Lots of interactive math
http://interactivemaths.net

Awesome site, huge, need to pick out specific applets
www.merlot.org

Student written wiki on AP Calculus topics
http://hkiscalc.wetpaint.com/

Motion Simulations

The Moving Man, download, needs Java

Limits

Flash movies explaining limit, continuity, IVT and derivative rules
http://www.calculus-help.com/funstuff/phobe.html

Nice applets on limits, derivatives and integration. Good for volumes of revolution. I like the graphical product rule, but students may find it complex
http://www.ies.co.jp/math/products/calc/menu.html

Continuity

Nice lesson on IVT (go on to next lesson, too) with self-checking concept questions
http://oregonstate.edu/instruct/mth251/cq/Stage4/Lesson/IVT.html

Flash movies explaining limit, continuity, IVT and derivative rules
http://www.calculus-help.com/funstuff/phobe.html

Continuity of piece-wise defined functions,
http://www.mathdemos.org/mathdemos/piecewise/piecewise_continuity.html QuickTime movie
http://www.mathdemos.org/mathdemos/piecewise/Examples/Java_continuity.html Java applets
10 examples, print out equations, Launch MultiGraph applet, choose example at top of window, slide parameters to make the graph continuous

Intro to Derivatives

ID-1
Definition of Derivative, graphically
http://mathdemos.gcsu.edu/mathdemos/defofderiv/

ID-2/3
Choose Mathlets >> Derivative Plotter; open in a new window; sketches derivative of given graph, several examples or user defined functions
http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=409

Choose Mathlets >> Differentiation; open in a new window; f, f’, f” matching graphs
http://www.joma.org/mathDL/47/?pa=content&sa=viewDocument&nodeId=2651

Graphing Antiderivatives
http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=410

ID-4
Scroll down to secants and tangents. I like the secant line behavior for non-differentiable functions. Also look at zooming in on a tangent line. Further down the page, check out a differentiable nowhere function.
www.math.psu.edu/dna/graphics.html

ID-6/7/8
Flash movies explaining derivative rules
http://www.calculus-help.com/funstuff/phobe.html , chapter two, lessons 1 - 4

Scroll down to Derivatives, select product rule. This is a graphical explanation of the product rule. It’s a great connection between area and change, but students may find it complex.
http://www.ies.co.jp/math/products/calc/menu.html

ID-9
Motion along a line. Illustrations, explorations and problems about distance and velocity. Particularly recommended for students who are not taking physics.
http://webphysics.davidson.edu/physlet_resources/physlet_physics/contents/mechanics/one_d_kinematics/default.html

More Derivatives

MD-2
http://www.calculus-help.com/funstuff/phobe.html , chapter two, lesson 5, chain rule

MD-6
Graphical visualization of derivative of inverse sin function
http://www.mph.net/coelsner/JSP_applets/InvFunThm.htm

Slopes of inverse functions are reciprocals.This software is a combination of a graphing calculator and Geometer’s Sketchpad. Requires the latest version of Java, link provided
http://www.geogebra.at/

MD-8
Differentiability of piece-wise defined functions
http://www.mathdemos.org/mathdemos/piecewise/Examples/Java_differentiability.html

Definite Integrals

Riemann sums applet, includes L, R, M, Trap and Simpson’s Rule
http://www.slu.edu/classes/maymk/Riemann/Riemann.html

Visualizing the Mean Value Theorem for Integrals
http://math.dartmouth.edu/~klbooksite/appfolder/403unit/MVTIntegrals.html

Graphing Antiderivatives: accumulation functions
http://mathdl.maa.org/mathDL/23/?pa=content&sa=viewDocument&nodeId=410

Differential Equations and Modeling

Slope fields
http://alamos.math.arizona.edu/ODEApplet/JOdeApplet.html
Select JODE applet, then slope fields for f(x,y)

Awesome applet for slope fields, you can draw a solution curve atop the slope field, it will compute the actual curve, it will show the family of curves, can choose preset diff. eqns or input your own
http://math.dartmouth.edu/~klbooksite/appfolder/301unit/SlopeField.html

Integral Applications

Volumes of Known Cross Sections
http://mathdemos.gcsu.edu/sectionmethod/sectiongallery.html

Student Models of Volumes of Known Cross Sections
http://www.dade.k12.fl.us/msprings/skoski/calc/

Volumes of Revolution – disk method
http://mathdemos.gcsu.edu/diskmethod/diskmethod.html

Gallery of Shapes for volumes of revolution
http://mathdemos.gcsu.edu/diskmethod/diskmethodgallery.html

Washers
http://mathdemos.gcsu.edu/washermethod/

Short movies of graphical concepts, not interactive, not a lot of options , use for areas and volumes of revolutions, also has polar graphs
http://clem.mscd.edu/~talmanl/MathAnim.html

I like Volume of solid of revolution 2, slides showing volume of rotation with washers around a vertical line (not the y-axis), not interactive
http://www.convergesoftware.com/ choose slide shows, manual,

Download Winplot, an awesome, free, graphing program, graphs in 2D or 3D, graphs explicit and implicit functions and differential equations (slope fields)
http://math.exeter.edu/rparris/winplot.html
General Winplot tutorial
http://www2.spsu.edu/math/Dillon/Peanutdocs/GaWinPlotTutorial.pdf

Winplot: graph a solid with known cross sections
After graphing the 2 curves that form the base (use y = 0 for the x-axis if necessary) go to the pull down list called "TWO" and click on "Sections" and fill in the things there. Then click on "See Solid" and you'll get a 3D picture that can be rotated with the arrow keys on your keyboard.
Winplot: graph solids of revolution
Under the "ONE" list you can choose "Revolve Surface" to see solids of revolution and you'll get a 3D picture that can be rotated with the arrow keys on your keyboard.

L'Hopital's Rule

Mean Girls video clip (http://www.youtube.com/watch?v=oDAKKQuBtDo ) pause at 1:07 to see the function, limit as x --> 0 (ln (1-x) - sin x)/ (1 - (cos x)^ 2)

Review

Operation Mother Hen (http://motherhen.eng.buffalo.edu) features streaming video clips of an instructor as she solves problems that illustrate basic calculus concepts, with close-ups of the problem so that students can see what she's doing as she explains. Math 141 is Calc AB with area/volume in Math 142. Math 142 continues with Calc BC topics. RealPlayer (free download) required.

Calculus on the Web (COW). You can register your class, they work on certain problems you've assigned, and you get a report of problems completed. Its EXCELLENT practice with immediate feedback for students - and easy for you to grade! Good practice for skill problems, step by step breakdowns
http://cow.math.temple.edu/

Stuff You Need to Know Cold
http://fc.woodberry.org/~david_mcrae/BC_Cal/apindex.html
Same sheet in color
http://cs3.covenantchristian.org/bird/Smart/Calc1/StuffMUSTknowColdNew.htm

Flash cram sheet, includes some non-AP Calc AB stuff
http://www.calculus-help.com/funstuff/cheatsheet.html

Problem of the week archive
http://www.calculus-help.com/oldproblems.html

Review questions and solutions by topic, both multiple choice and free response, great model cards
http://www.livebinders.com/shelf/search_author?terms=ryanjgrady