GRAPHING AND VISUALIZATION IN MATHCAD

MathCAD provides a variety of two-dimensional X-Y and polar graphs plus three-dimensional contour, scatter, and surface plots.

 

1) Match useful words with the definitions:

1.	plot	A.	a set of axes with a scale into which plots may be placed
	graph	B	a variable or expression used in a function or graph to define the region
3.	argument	C.	a small black rectangle in which you insert arguments for functions or graphs
4.	placeholder	D.	a single line, or trace, in a graph region

 

2) Look through and remember the main elements of a graph:

Main elements of a graph

vertical axis/ y axis horizontal axis/ x axis broken line dotted line   y-axis argument straight line   scale x-axis argument   curve

Graphs are easy to create and modify in MathCAD. You can create 2D graphs from functions or data sets. A 2D graph can contain up to sixteen plots, all formatted differently.

 

Examples of 2D plots

 

A. To create an X-Y Quick Plot of a single expression or function:

1. Type the expression or function of a single variable you want to plot. Click in the expression.

2. Choose Graph > X-Y Plot from the Insert menu.

3. Click outside the graph or press [Enter].

 

Example
1. Type -4x+3. 2. Without removing your cursor from this math region, select Graph > X-Y Plot from the Insert menu. In the placeholder on the x-axis, where the blue editing lines are, type: x. In the placeholder on the y-axis type -4x+3. 3. Then click outside the plot region to see the plot.
Y-axis placeholder X-axis placeholder Sizing grab-handle

 

B. To create a polar plot:

1. Choose Graph > Polar Plot from the Insert menu.

2. Fill in both the angular-axis placeholder (bottom center) and the radial-axis placeholder (left center) with a function, expression, or variable.

3. Click outside the plot or press [Enter].

 

Example

1. Type the function: sin(e). 2. Select Polar Plot from the Insert menu. In the angular-axis placeholder type e. Type sin(e)in the radial-axis placeholder 3. Then click outside the plot region to see the plot.

 

C. You can graph several traces on the same X-Y or polar plot. A graph can show several y-axis (or radial) expressions against the same x-axis (or angular) expression. Or it can match up several y-axis (or radial) expressions with the corresponding number of x-axis (or angular) expressions.

To create a Quick Plot containing more than one trace:

1. Enter the expressions or functions of a single variable you want to plot, separated by commas.

2. Click in the expressions, then choose Graph > X-Y Plot from the Insert menu.

3. Click outside the graph or press [Enter].

 

Example

1. Click the expression in the y-axis of the plot below. Then, press[Spacebar] until the entire expression is selected 2. To enter two more expressions in the plot, type:, -4x+2, -4x+1 [Enter]. y-axis scale placeholders     x-axis scale placeholders   3. To override MathCAD’s automatic limits by entering limits directly on the graph click a number in the scale placeholder, type a number to replace it and click outside the graph.

 

Three-dimensional plots enable you to visually represent a function of one or two variables and to plot data in the form of x-, y-, and z-coordinates.

 

Examples of 3D plots
Quick Plot from a function of two variables	Parametric surface plot
Bar plot	Contour plot

 

A. To create a three-dimensional plot in MathCAD:

1. Define a function of two variables or a matrix of data.

2. Choose Grap h from the Insert menu and select a 3D plot type or click one of the 3D graph buttons on the Graph toolbar.

3. Enter the name of the function or matrix in the placeholder.

4. Click outside the plot or press [Enter] to see the plot.

 

 

Example

1. Type the functions: X(u,v):=sin(v)·cos(u) Y(u,v):=sin(v)·sin(u) Z(u,v):=cos(v) 2. Choose Graph > Surface Plot from the Insert menu to display a blank 3D plot. 3. Type the name of the functions separated by commas and enclosed in parentheses in the placeholder. For this example, type: (X,Y,Z) 4. Press [Enter].   z-axis x-axis   y-axis     5. To change your plot to a different plot type: A. Double-click on the graph to bring up the 3D Plot Format dialog box. B. In the “Display As” section on the General tab, select “Bar Plot”,“Contour Plot”,or “Data Points”from the array of plot types. 6. Use the 3D Plot Format dialog box to change the appearance of a 3D graph.

 

B. The 3D Plot Wizard provides more control over the format settings of the plot as you insert it:

1. Choose Graph > Plot Wizard from the Insert menu.

2. Select a type of three-dimensional graph.

3. Make your selections for the appearance and coloring of the plot on subsequent pages of the Wizard. Click “Finish” and a graph region with a blank placeholder appears.

4. Enter appropriate arguments (a function name, data vectors, and so on) for the 3D plot into the placeholder.

5. Click outside the plot or press [Enter].

1) Look at the graph and write the appropriate letters in front of each definition:

4. the horizontal axis (or the x axis)

5. a solid line

6. the vertical axis (or the y axis)

7. a broken line

8. the scale

9. a dotted line

 

http://www.eslflow.com/describinggraphstables.html

 

2) Use MathCAD to carry out the following tasks, comment your actions:

A. Create a 3D Bar Plot of a function .

B. Give the plot a title “f(x,y)”, setting it below the graph.

C. Convert the plot into a Surface plot.

D. Draw light grey grid lines for all axes.

E. Set x-axis limits with minimum value -6 and maximum value 6.

F. Color the surface of the plot with light blue.

G. Enable lighting on a 3D Plot, make a diffuse color light green and a specular color black.

H. Set the axes at the front perimeter of the plot.

I. Delete a rectangle around the graph.

J. Draw a box around the plot. Make the border red.