Category Archives: Derive posts

Computer lab

Math 190 Lab Home Page

The Department has a computer lab in Physical Science Building 208, equipped with Matlab, Mathematica, etc., for the benefit of students and faculty. Access is either by numerical code or by permission of the Lab Monitor.

When space is available, other students can use the lab during Math 140 exam times. However, the last Math 140 computer exam is the last day to withdraw. After that, the lab will be closed during these times.

Lab Monitor Schedule PDF

The schedule shows when the various Lab Monitors will be on duty.

Terms of Acceptable Use
Each student must agree to the Terms of Acceptable Use statement for the UH Math Dept Computer Lab. The students agree to obey all of the terms of use and conditions set forth in the UH Information Technology Resources Policy. Their policy is here:

http://www.hawaii.edu/infotech/policies/itpolicy.html

The policy for the math lab will be the same, but adds in particular that

Students agree not to:
1) Download, install software or run any outside programs or software packages.
2) Download or upload work protected by copyright or files not related to class work.
3) Attempt to gain unauthorized access to remote computer systems.

In addition you acknowledge that:
4) There is no expectation of privacy in the Math Lab and your activities may be monitored.

Accounts and passwords

Each lab account can use a portion of the network hard for storing files. You save your files to the H: drive and not the local hard disk or C: drive. In Derive you would typically save your lab by using the Save As ... option on the File tab and then saving you file with the name H:\lab1. To open a file you would use the Open option on the File tab and enter H: <cr> to see a list of your files.

In order to keep others from using your account you need to keep your password secret. For example, don't write it down next to your account number in your notebook where others can see it.

Graphing and Calculus Software

wxMaxima

Download wxMaxima (click to view info)
You can download this free software which is available for Window, MacOS, Linux and UNIX computers. This software is installed on the lab PCs and is used in the calculus classes for graphing and symbolic calculus calculations. In addition, the math department has many sample sessions available on their website.

Derive 6

Other Free Graphing Software:

Online Grapher: (click to try)
Try out this online grapher. Be sure to use the * character for multiplication and you zoom in on a point by dragging your cursor to form a rectangle around the point.
Download Winplot Software: (click for instructions)
Winplot is a small but useful plotting program that can be downloaded and used on any Windows PC. It is available on the desktop in the PC lab in addition to Derive. Give it a try!

Mac users with OS Version 7.5 or later already have a plotting program on their Apple menu. Check it out.

Other Free Software:

Just for fun ... read about an important math/computer problem:
The famous problem "P versus NP" problem is decades old and there is a million dollar prize to solve it. Now a mathematician in England has shown that the problem is equivalent to solving a larger version of the well know Minesweeper game that is included with the Windows operating system. Read the news story, Scientific American article or just play the game.

   getacro.gif (712 bytes)

Derive

Derive Basics
The Derive 6 software is installed on the lab PCs. There is an online lab manual available on the math dept website for learning to use the software. In particular, Chapter 0 of the lab manual explains the basic usage techniques. (Note: You need to have the Adobe PDF reader installed on your system. Click the icon below if you need to install this plugin.)
Online Derive Demo (click to view)
You can view and download videos from the math department website. These videos show how to get started using Derive 6. You will need a Windows PC with sound capabilities and you will need to install some video software in order to view the videos. After installing the video component software you can use the links below to listen to the videos. The videos are available on a CD in Keller 419.

Opening Derive for Windows
Entering Algebraic Expressions and Constants
Functions
Basic Graphing
Substituting
Using `Solve'
Differentiating and Integrating
Limits
More about Graphing
The Vector Function
Iterates, applied to non-overlapping generations
Matrix Operations
Inserting Text Objects, Families of Tangent Lines
Euler's Method, Foxes and Hares
Utility Functions:
We use a special collection of interesting new functions for the lab. They are contained in a Derive utility file. Click on Utilities for a discussion and examples of their use. If you use Derive at home you can download the required files ADD-UTIL.DFW and ADD-UTIL.MTH at the bottom of that page.
Purchasing Derive 6: Derive
The software is not required for our classes but it is an excellent software package. Unfortunately, it is no longer sold by Texas Instruments. It should be possible to obtain a copy online from Amazon.com or other supplier.
  Note: If you have your own version of Derive you will need to copy the utility functions on to your computer. See above.

Derive videos


Created by Karl Heinz Dovermann with the assistance of Dale Myers.
Initial installation

Before you can view the videos below, go to this: Getting Started  to install the video software.

Viewing the videos

Click a chapter video. If Windows asks if you wish to view the video in a media bar, select "No".

If you see a small video box in a left-hand media bar, click the "Media Options" / "Settings" menu and uncheck "Play web media in the bar".

If you don't see "Media Options", click the black down arrow (bottom of the media bar) by the video title.

To get a separate video window from the media bar, click the icon with a diagonal arrow in a box. Then close the media bar by clicking the "x" at the top right of the bar.
Once you have a separate video window, drag the lower right corner to give a full screen window. You can also get full screen (<Ctrl-1>) or full screen (<Alt-End> by going to the "View" menu. It might help to go to "Skin Chooser" and select "Classic".

Derive utilities

Download Utility Files

In the manual several functions are defined such TL(a) which computes the tangent line of a predefined function f(x) at the point x = a. In Chapter 5 and later there will be many more such functions which will approximates roots, integrals and solutions to differential equations.  To make it easier to compute with these function we have added a utility file add-util.mth with all the functions defined.  The way this utility file works is that you simply use the  File/Load/Utility menu and select the file add-util.mth.   DfW then loads the file "quietly" meaning that just the definitions are entered and nothing is displayed.  The file just takes a second or two to load in quiet mode.  To make this process easier we suggest having every lab file start out with the add-head.mth at the top and then add your name and lab number in double quotes.  See the sample session below where the first four lines are obtained by loading the add-head.mth file, then the file is renamed using the File/Save As menu as LAB3.MTH.

f-lab1.gif (9355 bytes)

We have changed the names and the way these function work by eliminating the need to predefine a function f(x).  For example, if you want to compute a tangent line for say f(x)=x3/3 at x=1 you would Author and Simplify:

TANGENT(x^3/3, x, 1)

The result will be y = x - 2/3.  . We describe the variables for this and the other functions typically as

TANGENT( u, x, a)

where the u refers to any expression in the variable x and a is a parameter in the function.

Example 1.  Suppose that you want to find the tangent line to the function sin x at the point (0,0) on its graph.  Assuming that you have loaded the utility file add-util.mth as above then just  Author i-author.bmp (1340 bytes) the expression tangent( sin x, x, 0).  Simplify i-simp.bmp (1300 bytes) and then plot i-plot.bmp (1372 bytes) the resulting expression along with the plot of the function to make sure the computation is graphically correct.

Example 2.  Suppose that you want to find the quadratic polynomial ax2 + bx + c that passes through the three points: (0,0), (1,2) and (2,8).  You load the utility file add-util.mth and then Author CURVEFIT( x, [[0,1], [1,2], [2,8]]).  After simplifying the result will be 2x2.  Probably the best way to do this is to start by defining the 3x2 matrix of points using the matrix button i-matrix.bmp (1468 bytes) and then plotting i-plot.bmp (1372 bytes) the 3 points on a graph.   Next you Author i-author.bmp (1340 bytes) the CURVEFIT( x, part and then right click and insert the matrix of data points.  Simplify i-simp.bmp (1300 bytes) and plot to make sure the answer function does indeed pass through the 3 data points.  The CURVEFIT function will find the appropriate degree polynomial through the data regardless of the number of points.

Example 3.  Suppose that you want to find the quadratic polynomial ax2 + bx + c that passes through the two points: (0,0) and (1,2).  In addition, you want the derivative to be 1 when x=0.  You load the utility file add-util.mth and then Author CURVEFIT( x, [[0,1], [1,2]], [[0,1]]).  In other words, you enter one matrix for the points satisfied by the function and another matrix for the points satisfied by the derivative.  The degree of the answer polynomial is always one less than the total number of equations for both the function and its derivative.


Partial List of Utility Functions:

SUBST(u,x,a) Substitutes x=a in the expression u.
SECANT(u,x,a,h) Secant line of u(x) through x = a and x = a + h.
TANGENT(u,x,a) Tangent line of u(x) at x = a.
CURVEFIT(x,data,ddata) Fits a polynomial in the variable x, though the points data:=[[x0,y0],[x1,y1],...] provided ddata is either omitted or []. Otherwise, the graph of the derivative must pass through the ddata points.
NEWT(u,x,x0) Newton algorithm for root of u(x)=0 with initial guess x0. If the optional k argument is used then a vector of k iterates is returned.
DRAW_COMPLEX(v) Converts the vector of complex numbers [x0+iy0, x1+iy1,...] into a matrix of points [[x0,y0], [x1,y1],...] which can then be plotted in a 2D-plot window.
LEFT(u,x,n,a,b) Numerical approximation to the integral of u(x) over [a,b] using the left-endpoint method with n rectangles.
MID(u,x,n,a,b) Numerical approximation to the integral of u(x) over [a,b] using the midpoint method with n rectangles.
RIGHT(u,x,n,a,b) Numerical approximation to the integral of u(x) over [a,b] using the right-endpoint method with n rectangles.
TRAP(u,x,n,a,b) Numerical approximation to the integral of u(x) over [a,b] using the trapezoid method with n trapezoids.
SIMP(u,x,n,a,b) Numerical approximation to the integral of u(x) over [a,b] using Simpson's method with n subdivisions.
DRAW_LEFT(u,x,n,a,b) Draws graphic demonstration of the left-endpoint method for numerically integrating u(x) over the interval [a,b] using n rectangles.
DRAW_RIGHT(u,x,n,a,b) Same as above except for the right-endpoint method.
DRAW_TRAP(u,x,n,a,b) Draws graphic demonstration of the trapezoid method for numerically integrating u(x) over the interval [a,b] using n trapezoids.

 

Need to Download add-util.mth?

Version 6

The files add-head.dfw (note the new file extension) and add-util.mth are in the folder G:\DfW5\M242L and is a small text file that can be copied onto a floppy disk.  Otherwise just click below:

add-head.dfw (1KB)
add-util.mth (6KB)

Note: In the lab we set the start in directory on the Derive 6 desktop icon to be H:\ so that whenever you start Derive this is where it looks for the file DFW.INI which contains your default settings such as the number of precision digits. We place the add-head and add-util files in the subfolder M242L in the DFW install folder. If you do things differently at home then you will need to modify the LOAD command in your add-head file so that both the lab and home locations will work. We suggest having two load commands as follows:

#2:  LOAD("G:\Dfw5\M242L\add-util.mth")
#3:  LOAD("C:\Dfw5\M242L\add-util.mth")

Here, in line 3 above just use the path on your system where the file add-head.mth is  is located.