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

Martin Flashman
Professor of Mathematics
Humboldt State University
flashman.neocities.org

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

Outline
• Introduction- "Gaul is Divided into Three Parts..." J. Caesar
• This talk is divided into three parts:
1. Points and Functions I (Mainly PreCalc- Some Calc in 15 minutes!)
2. Functions II (Mainly Calc II , Calc III and DE's in 20 minutes!)
3. 3-Dimensional Functions and Vectors (Mainly Calc III in 10 minutes!)

4. Disclaimer: Any errors in this presentation are those of the presenter and not the responsibility of Richard Parris- the author and creator of Winplot.
Winplot is a tool primarily to assist in the learning of mathematics and is freeware.
On-line help: Al Lehnen has prepared a detailed guide to Winplot .

• Points and Functions I (Mainly PreCalc- Some Calc in 15 minutes!)
• Plot a function : y = f (x)...
• y = x sin(x)
• Plot a point : Point...
• (1,3)
• (a,b), (a, a^2), (a, f(a))
• User  functions...
• f(x) = sin(x)
• Anim Menu: A, B, C, ...
• slider
• set L and R
• autorev & autocyc
• library: for reference.
• The Inventory : Inventory... Ctrl  I
• Table
• Params
• Derive
• family
• reflect in ....
• Slider...
• function choice
• 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
• Meetings...
• Combinations
• arithmetic
• composition: (f(g(x))    f <- g   f = top g=bottom
• Integration  f-g
• Grid
• axes
• labels (Change labels,etc. under Misc menu)
• pi  symbol (p) (Change fonts under Misc menu)
• grid
• Connect dots
• Drag Box  - Zoom recenter
• XY coordinates - recenter
• DEq Miscellany
• x(t) window, y(t)  window, x(t)y(t) window
• strobe
• Build your own stuff and load file for understanding functions, examples:
• Mapping figures   tfigwvel.wp2
• Circles and Trigonometry. circles_sines.wp2
• Dot Racing. dot_races.wp2

• Functions II (Mainly Calc II , Calc III and DE's  in  20 minutes!)

•
• r = f(t): Polar coordinates

• r = acos(bt)
• Tangent vector demo
• x = f(t); y = g(t) : parametric functions

• x = acos(ct); y = bsin(ct)
• Tangent vector demo
• 0 = f(x,y) : implicit functions

• ax^2+by^2=1
• Recursion: Sequences defined. [See One menu for visualization.]
• DEq: Differential Equations
• dy/dx...pred_prey_de.wp2
• dy/dx = F(x,y)

• dy/dx = kx
dy/dx = ky
dy/dx = ax-by
• field
• Euler
• dy/dt...Lotka-Volterra.wp2
• x' = box for dx/dt= P(x,y)

• x' = ax-bxy
• y' = box for dy/dt= Q(x.y)

• y' = -cy+dxy
• field - slope or scaled vector

• Integration
• Sector (For Polar Functions)
• r = rcos(bt)
• Length of Arc...
• r = rcos(bt)
• Surface Area of revolution.
• Recursion & Sequence... [Omit for time!]
• IVP: set initial values.
• (x,y)==>(1+abs(x)-y,x)
• Set dot size!
• draw/watch/table
• Revolve Surface: Gives result in 3 D Winplot.
• Sections:  A lot of stuff!

•   3-Dimensional Functions and Vectors (Mainly Calc III)
• z =f(x,y): cartesian coordinates
• z = rsin(ax)cos(by)
• slicer for x and y (animation)
• z =f(r, t): polar coordinates
• z = rsin(at)cos(bt)
• x= x(t,u), y=y(t,u), z=z(t,u): parametric surface
• x = asin(u)cos(t);
• y = bsin(u)sin(t);
• z = rcos(u)
• F(x,y,z)= 0  : Implicit surface [omit]
• x=x(t), y=y(t), z=z(t) :Parametric curve
• x = rcos(at); y = rsin(bt); z = t
• tube... around a curve. (E.g. The torus )
• Segment...
• Point...
• Recursion... x,y,and z
• Diff eqn...: Differential equation:

• x' =... y'= ..., z'= ...
• Lotka-Volterra 3 species.wp3
• 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