MathCS.org - Java: ZMap Features

zMap: Features

ZMap is easy to use and all parameters can be either entered interactively or be predefined via "applet tags". The "Start" button here will, this time, show how f(z) = e^z deforms circles.

Here are a few tips to use the program effectively:

You can change the function by entering the new definition in the toolbar. Most standard mathematical functions such as sin and cos are available, as are the constants e, Pi, and i. In addition, the functions Re(z) and Im(z) are available to extract the real or imaginary part of their argument, respectively. Here is a complete list of available functions:

Sine sin(z) Cosine cos(z) Tangent tan(z)
Arc Sine asin(z) Arc Cosine acos(z) Arc Tangent atan(z)
Hyp. Sine sinh(z) Hyp. Cosine cosh(z) Hyp. Tangent tanh(z)
Inv. Hyp. Sine asinh(z) Inv. Hyp. Cosine acosh(z) Inv. Hyp. Tangent atanh(z)
Natural Logarithm ln(z) Logarithm base 10 log(z) Exponential (e^z) exp(z)
Abs. Value abs(z) Square Root sqrt(z) Sum sum(x,y,z)
Real Part re(z) Imag. Part im(z) Conjugate conj(z)
Argument/Angle arg(z) If if(cond,trueval,falseval)

The toolbar contains a field to enter your function, four check boxes to determine what type of curves to draw in the domain, and a variety of buttons:

The buttons have the following meaning

start drawing/redrawing

cancel current drawing operation

to check off which curves are to be drawn and which ones not

shows dialog to define general options

shows dialog to define lines

shows dialog to define radii, arcs, and circles

zoom in/out/undo in the Domain (also available via right-click on domain)

zoom in/out/undo in the Range (also available via right-click on range)

slider to determine drawing speed to better see which curve is mapped where

show online, searchable Help

You can zoom in or out by using the various zoom buttons on the toolbar or by right-clicking on domain or range. Also, if you right-click on domain or range you can choose to pan right, left, up, or down from the popup menu. To quickly re-center domain or range, simply double-click on a point. Finally, you can also zoom in by dragging the mouse over domain or range to select an appropriate rectangle. All zoom and pan operations can be reversed by clicking on the appropriate undo buttons in the toolbar or by selecting undo from the right-click menu in domain or range.
You can check how your function maps individual points by holding down the CTRL-key while clicking once on the point in the domain you want to map. The point and its image will appear as dots. To remove points, redraw your graph by clicking the blue check icon on the toolbar.

Sine	`sin(z)`	Cosine	`cos(z)`	Tangent	`tan(z)`
Arc Sine	`asin(z)`	Arc Cosine	`acos(z)`	Arc Tangent	`atan(z)`
Hyp. Sine	`sinh(z)`	Hyp. Cosine	`cosh(z)`	Hyp. Tangent	`tanh(z)`
Inv. Hyp. Sine	`asinh(z)`	Inv. Hyp. Cosine	`acosh(z)`	Inv. Hyp. Tangent	`atanh(z)`
Natural Logarithm	`ln(z)`	Logarithm base 10	`log(z)`	Exponential (e^z)	`exp(z)`
Abs. Value	`abs(z)`	Square Root	`sqrt(z)`	Sum	`sum(x,y,z)`
Real Part	`re(z)`	Imag. Part	`im(z)`	Conjugate	`conj(z)`
Argument/Angle	`arg(z)`	If	`if(cond,trueval,falseval)`

	start drawing/redrawing
	cancel current drawing operation
	to check off which curves are to be drawn and which ones not
	shows dialog to define general options
	shows dialog to define lines
	shows dialog to define radii, arcs, and circles
	zoom in/out/undo in the Domain (also available via right-click on domain)
	zoom in/out/undo in the Range (also available via right-click on range)
	slider to determine drawing speed to better see which curve is mapped where
	show online, searchable Help