Winplot -
Freeware for Pre-calculus through Calculus III
and Differential Equations.
12-3-04 CMC3 32nd Annual Conference
4:00-5:00 p.m.
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:
-
Points and Functions I
(Mainly PreCalc- Some Calc in 15 minutes!)
-
Functions II
(Mainly Calc II , Calc III and DE's in 20 minutes!)
-
3-Dimensional Functions and Vectors
(Mainly Calc III in 10 minutes!)
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.
Starting- Download and unzip:
http://math.exeter.edu/rparris/winplot.html
On-line help: Al Lehnen
has prepared a detailed
guide
to Winplot .
-
Points and Functions
I (Mainly PreCalc- Some Calc in 15 minutes!)
-
Equa Menu
- Plot an explicit
function : f(x)=...
- Plot a point : Point...
(x,y)...
- (1,3)
- (a,b), (a, a^2), (a, f(a))
- list (copied from Spreadsheet or formula)
- User
functions...
-
Anim Parameters A-W
- slider
- set L and R
- autorev & autocyc
- linked window
- library: for reference.
- The Inventory : Inventory...
Ctrl I
-
One Function Menu
- Slider
...
-
function choice
-
the "slider"
- mark
point- added to inventory!
-
secant demo: base point, slope
-
tangent line demo: slope
-
Advanced: Taylor approx- degree - added to inventory!
- Zeros...
Save as...
- Extremes...
Save as...
-
Measurement: Integration
-
Reflect...
-
Two Function Menu
- Intersections...
- Combinations
- arithmetic
- composition: (f(g(x)) f <- g f =
top g=bottom
- Integration
f-g
-
Advanced: sections: cross-section
- View Menu
- Grid
- axes
- labels (Change labels,etc. under Misc
menu)
- pi symbol (p) (Change fonts under
Misc menu)
- grid
- Connect dots
- Btns Menu
- Drag Box - Zoom recenter
- XY coordinates - recenter
- Misc Menu
- DEq Miscellany
- x(t) window, y(t) window, x(t)y(t) window
-
Build your own stuff and load file for understanding functions, examples:
-
Functions II (Mainly
Calc II , Calc III and DE's in 20 minutes!)
-
Equa Menu
- Polar:
r = f(t) Polar coordinates
r = acos(bt)
- Parametric:
x = f(t); y = g(t) parametric functions
x = acos(ct); y =
bsin(ct)
- Implicit
functions: equation with x,y variables
ax^2+by^2=1
- Recursion: Sequences defined. [See below in 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
-
One Menu
-
Integration
-
Sector (For Polar Functions)
-
Length of Arc...
-
Volume of revolution... Computes the volume: about X-Axis; about Y-Axis.
-
Surface Area of revolution.
- Recursion & Sequence...
[Omit for time!]
- IVP: set initial values.
- Set dot size!
- draw/watch/table
- Btns menu - trajectory
- Revolve
Surface: Gives result in 3 D Winplot.
-
TwoMenu [Omit for time!]
- Sections: A lot
of stuff!
-
3-Dimensional
Functions and Vectors (Mainly Calc III)
-
Equation Menu
-
z =f(x,y): cartesian coordinates
- z = rsin(ax)cos(by)
-
Misc menu
-
slicer for x and y (animation)
-
z =f(r, t): polar coordinates
- 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'= ...
- Inventory
-
View menu
-
Btns menu
-
One function menu
- 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
-
Two function menu
-
Misc menu
-
slicer for x and y (animation)
- various setings and options
The END :)