# Freeware for Pre-calculus through Calculus III and Differential Equations.

Martin Flashman
Professor of Mathematics
Humboldt StateUniversity
flashman.neocities.org

Abstact:Winplot is freeware developed by Richard Parris. This workshop will give a hands on introduction to using Winplot to illustrate concepts from precalculus through Calculus III and Differential Equations.

Participants will learn how to graph using parameters to illustrate various pre-calculus and calculus concepts with plane and three dimensional figures.

Outline

• Points and Functions I (Mainly PreCalc- Some Calc)
• Plot a function : y = f (x)...
• Plot a point : Point...
• (1,3)
• (A,B), (A, A^2), (A, f(A))
• Anim Menu:  A, B, C, ...
• slider
• set L and R
• autorev & autocyc
• ax +by = c: lines
• segment
• polynomial: Lagrange interpolation.
• library: for reference.
• User  functions...
• The Inventory : Inventory... Ctrl  I
• Table
• Params
• Derive
• Edit
• Dependency
• Pen width
• color
•  Hide/ Show
• graph
• equation
• dupl
• family
• reflect in ....
• Slider...
• function choice
• x box [use enter]
• the "slider"
• mark point- added to inventory!
• secant demo: base point, slope
• tangent line demo: slope
• Zeros...   Save as...
• Extremes... Save as...
• Integration : Integrate
• definite
• indefinite
• View: corners or center
• fit window
• Restore
• Axes
• Grid
• axes
• labels (Change labels,etc. under Misc menu)
• pi  symbol (p) (Change fonts under Misc menu)
• grid
• Connect dots
• Drag Box  - Zoom recenter
• text
• Font
• position
• XY coordinates - recenter
• Meetings...
• Combinations
• arithmetic
• composition: (f(g(x))    f<-g   f = top g=bottom
• Integration  f-g
• Various settings
• DEq Miscellany
• x(t),window, y(t)  window, x(t)y(t) window
• strobe

• Functions II (Mainly Calc II , Calc III and DE's)

•
• Reminder: Derivatives, Integrals for most of calc I done previously.
• r= f(t): Polar coordinates
•  Secant demo
• Tangent vector demo
• x=f(t) y = g(t) : parametric functions
•  Secant demo
• Tangent vector demo
• 0 = f(x,y) : implicit functions [NO SLIDER!]
• Recursion: Sequences defined. [See One menu for visualization.]
• DEq: Differential Equations
• dy/dx...
• dy/dx = F(x,y)
• field
• dy/dt...
• x' = box for dx/dt= P(x,y)
• y' = box for dy/dt= Q(x.y)
• field - slope or scaled vector
• Integration
• Sector (For Polar Functions)
• Length of Arc...
• Volume of revolution... Computes the volume.
• Surface Area of revolution.
• Sequence...
• IVP: set initial values.
• Set dot size!
• draw/watch
• table
• Revolve Surface: Gives result in 3 D Winplot.
• Sections:  A lot of stuff!

•   3D Winplot (Mainly Calc III)
• z =f(x,y): cartesian coordiantes
• z =f(r, t): polar coordinates
• x= x(t,u), y=y(t,u), z=z(t,u): parametric surface
• F(x,y,z)= 0  : Implicit surface
• x=x(t), y=y(t), z=z(t) :Parametric curve
• tube... around a curve. (E.g. The torus )
• Segment...
• Point...
• Recursion... x,y,and z
• Diff eqn...: Differential equation: x' =... y'= ..., z'= ...
• Inventory
• table
• levels
• box
• family
• Integrate...:      value=
• Length of arc..
• Slider...
• tangent line
• mark point
• average velocity demo: base point
• Instantaneous velocity demo
• Sequences :   like 2 dimension sequences
• DE trajectory