Winplot -
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:
-
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 a function : y = f (x)...
-
Plot a point : Point...
-
(1,3)
-
(a,b), (a, a^2), (a, f(a))
-
User
functions...
-
Anim
Menu:
A,
B, C, ...
-
slider
-
set L and R
-
autorev & autocyc
-
library: for reference.
-
The Inventory : Inventory... Ctrl
I
-
Table
-
Derive
-
family
-
reflect in ....
-
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...
-
Integration
: Integrate
-
Two Function
Menu
-
Meetings...
-
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
-
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!)
-
Equa
Menu
-
r = f(t):
Polar coordinates
r = acos(bt)
-
x = f(t);
y = g(t) : parametric functions
x = acos(ct); y = bsin(ct)
-
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
-
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'= ...
-
Lotka-Volterra 3 species.wp3
-
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 :)