Neat Maple stuff for Calc [in progress for melissa]

 For context see the homework and  daily class log for each course, which has links to many worked problems and examples from Stewart Calculus ET. A selected few are highlighted here.

Maple's Explore command takes math to the next level by making it interactive for instructor demonstrations.

• 1500
• 1505
• 2500

1500  [context]

• ExploreTangentLine.mw
  Explore the tangent line along a function graph, intersection of two different tangent lines
• ExploreSecantLine.mw
  Explore the limiting secant  line along a function graph
• MeanValueThm.mw
  visualization of the mean value theorem with slider to estimate tangent line points

1505 [context]

• average value of a function.
  Maple exercise: Stewart Calculus Chapter 6. AppliedProject: Where to Sit at the Movies* (after 6.5). Assume the result of part 1 (just trigonometry), then do parts 2-4 to get a real life example of an average viewing angle. Here is a Maple worksheet to accomplish this: Maple WhereToSitAtTheMovies.mw.
• sequences: visualization and numerical values
  sequence worksheet
• geometric series in real life example
  DrugInjectionSeries
• integral test for positive series illustrated
  IntegralTest [Maple knows the  pseries]
• comparison tests with p-series, geometric series: positive series examples
  s11-4.mw
• alternating series
• irregularly signed term series
  Stewart video example
• motivating example for power series using geometric sum formula
  11.8:
• manipulating the  geometric sum formula to get new power series example
  11.9-13:
• integration via series example plus plotting family of Taylor polynomials
  11.9
• evaluating limits using power series examples
  limits with power series,  s11-10-62.mw
• tangent power series and successive Taylor approximations with Explore
  tantaylor.mw
• THESE ARE THE MOST USEFUL WAYS TO USE TAYLOR SERIES IN PRACTICE!
  examples of power series expansion lowest terms in physical applications:
  conductivity approximation 11.11-32
  electric dipole field 11.11-33
  third order optics is a bit challenging and less visual: 11.11-34
  water wave height 11.11-35
  electric field of disc 11.11-36
  curvature of Earth 11.11-37
  pendulum period correction factor 11.11-38

2500  [context]

vector stuff

• vector projection along and perpendicular to a given direction, resolving a vector
  ProjectAlongDirection.mw
• vector projection: project one side of a triangle along another side: video and slider versions
  mat2500/handouts/projectionvideo.htm
  mat2500/handouts/projectionvideo.mw
• vector projection application: pendulum oscillation
  pendulumprojectionmat2500/handouts/pendulumprojection.mw
• cross product and area of triangle formed by 3-points
  mat2500/handouts/trianglearea.mw
• vector projection: dropping a perpendicular to a plane or line
  mat2500/handouts/pendulumprojection.mw
• parametrized lines and planes
  mat2500/handouts/linesplanes.mw

vector functions and parametrized curves

• visualizing the average of a vector function
  mat2500/handouts/vectoravg.mw
• twisted cubic:
  zoom in on tangent line to a spacecurve at the point of tangency
  mat2500/handouts/tangentline.mw
  secant line video (slider)
  mat2500/handouts/secantlinevideo.mw
  zoom in on tangent line approximation
  mat2500/handouts/vectorfunctionlinearapprox.mw
• vector integration in Maple
  mat2500/handouts/vectorintegration.mw

graphs of functions of multiple variables

• tangentplanezoom.mw
  zoom in on a graph of a 2d function to see it flatten out to its tangent plane: 2d limits, continuity and differentiability
• ExploreDirectionalDerivativeGraphicalRepresentation.mw
  graphical visualization of directional derivatives and tangent plane cross-sections of 2-d function graphs
• tabular data scatterplot and data fitting for Cobbs-Douglas production function example (14.1 example 4)

scalar integration

• integration webpage
  mat2500/handouts/integration.htm
• double integration webpage
  parametrizing regions for double integration
  mat2500/handouts/intdouble.htm
  double integrals: iteration diagrams with sliders
  mat2500/handouts/intcoorditeration.mw
  mat2500/handouts/polarcoorditeration.mw
  mat2500/handouts/ellipsedoubleint.mw
  double integrals: visualize 3d region below graph
  mat2500/handouts/int2d-visual.mw
  mat2500/handouts/int2d-visual2.mw
• 2d probability integrals: normal distribution
   s15-4-probability.mw, s15-4-normal2d.mw
• triple integration webpage
  mat2500/handouts/integration.htm
  triple int iteration example (with centroid)
  mat2500/handouts/tripleintexample.mw
  parametrizing surfaces of 3d integration solids for 3d plots
  mat2500/handouts/parametrizedsurfaces.mw
  parametrizing regions for triple integration
  mat2500/handouts/parametrize123.mw
  2d partial integration in space with sliders moving the  cross-section of function graph
  mat2500/handouts/intpartial_xsection..mw
  detailed explanation and visualization of how we iterate an integral over a 3d region described by  bounding surfaces, with sliders
  TripleInt-VisualizeSuccessivePartialIntegrations.mw
  
  

vector integration

• line integrals
  mat2500/handouts/intline.htm