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Derive: The Mathematical Assistant

Derive: The Mathematical Assistant

This commercial, math program will satisfy the math-lust of almost any Palmtopper.
By David Sargeant
For most users, the HP Palmtop's Lotus 1-2-3 and HP Calc programs provide more than enough number crunching power. These applications will let you do everything from simple arithmetic to solving complicated formulas. They specialize in business math but can be coaxed into doing science and engineering computations.

However, if you need to find the definite integral of a trigonometric function or if you need to know the eigenvalue of a matrix, the Palmtop's built-in applications will be of little or no help.

 For such advanced mathematical solutions, you could try several shareware/freeware, math programs. On the other hand, if you're willing to spend some money, you can get the commercial Derive program.

 Derive may cost more than a shareware math program, but the return on your investment will pay off.

 More importantly, you won't have to worry about disappearing shareware support. The company that produces Derive has been around since the early '80's and it supports its products. There are also worldwide, user groups to provide additional support should you need it. Whereas other companies have abandoned the DOS platform, Derive continues to support this operating system.

Derive, originally called muMath, was marketed by Microsoft in the early 1980's. MuMath soon returned to the parent company, SoftWarehouse of Honolulu, Hawaii, where it was renamed Derive. The company has continually upgraded its flagship product since then. There was even a version written specifically for the HP 95LX Palmtop and sold on a PC Card.

The technology developed by SoftWarehouse has been incorporated into the latest graphing calculators from Texas Instrument: the TI 83 and TI 92 Plus. Some calculator users have claimed that the TI 92 Plus is the equivalent of the HP 48 calculator with all the add-in applications already built in.

 Recently, Texas Instruments purchased SoftWarehouse but the parent company still sells and supports Derive.

 What Does Derive Do?

 Derive is called a Computer Algebra System (CAS). This means that it is, first and foremost, a symbolic math program.

In some ways it resembles other CAS programs such as Maple V and MathCad. All these programs work with numbers but they are really designed to manipulate symbols. With Derive, you can key in a math formula just as it appears in print and the program will rearrange and solve the formula for one variable in terms of the others. This is something that people learn to do in their first algebra course. Derive has mastered basic algebra and has gone on to absorb almost all the techniques of Pre-Calculus, Calculus I, II, III, Ordinary Differential Equations and Linear Algebra. It can present solutions symbolically, graphically or numerically.

Number Crunching

 Extended precision results are one of the features that Derive users notice almost immediately.

 Granted, you could use Derive to add a column of numbers but that would be like using a baseball bat to kill a mosquito. But, if you need the solution to the problem SQRT(2)+.02, to 25 digits, Derive will respond almost instantly with the result:



 This is about as accurate as you can get. Note that the result is shown as a rational number (a numerator divided by a denominator). Derive can also give you the decimal approximation with as much precision as you could want.

Working With Matrices and Vectors

 Anyone who has taken a linear algebra course knows that finding determinants of matrices larger than 3x3 is a pain. Most graphing calculators will allow you to input a numeric matrix and find the determinant automatically. Derive handles this quite well, of course. But in addition, Derive allows you to do operations on symbolic matrices as well.

Screen 1 shows a symbolic matrix determinant. Rather than going through a complicated process of finding 2x2 determinants by hand, you can have it solved in 0.2 seconds on a double-speed Palmtop.

 For trigonometry, Derive is excellent. Screen 2 shows some of the trigonometric identities that Derive has built-in, and how it can simplify them symbolically. This particular example was solved in 0.5 seconds on a double-speed Palmtop.

 For calculus, Derive is like walking around with a differential and integral text reference. Derive can solve most of the integrals in the CRC Handbook tables. For the early calculus subjects:sums and limits and the like:Derive can be a great learning tool.

Screen 3 shows three different examples: a series sum, a product sum, and a limit. Notice that Derive can take limits from either direction or both directions. All of the above examples simplify in under two seconds.

 Screen 4 shows how Derive handles complex definite integrals. Notice that, in this example, one of the limits of integration is infinity. Derive can handle it just fine and presents the result in a very readable format. The above integral took only 0.6 seconds to solve on a double-speed Palmtop. Without a symbolic math program, this integral would probably have to be looked up in an integral table such as Gradshteyn and Ryshik.

 Screen 5 shows that Derive can also do symbolic indefinite integrals. To solve this without Derive you would have to use several rules of integration: slow and inaccurate. I typed in the integral, shown on the left of the equal sign in Screen 5, and asked Derive to solve it. My double speed Palmtop gave me the solution, shown on the right of the equal sign, 3.5 seconds later.

 Derive can also do fantastic plots in either two or three dimensions. Screen 6 shows a 2D, implicit, circle plot on the 200LX: (x^2+y^2=16).

For 3D plotting, Screen 7 shows what Derive can do on the HP 200LX.

Screen 8 shows what can be done on a VGA monitor. On the Palmtop, despite the more modest graphics capabilities, 3D plots can still be drawn. They just take more time.

 One nice feature of Derive is that it isn't limited to built-in functions. You can define custom formulas and functions somewhat like you can do in the HP Solver application. This allows expansion of the capabilities of Derive so you can do even more powerful calculations.

For example, Screen 9 shows a second-order differential equation that was solved by functions in the ODE.MTH file.

Derive will also do unit calculations and can handle your own custom-defined units. If you have a need to convert kilometers per hour to apples per oranges, you can define such a conversion in Derive without any problem.

 Derive can be run in either graphics or text mode, depending on your preference. Text mode is faster, especially when plotting, but obviously shows far less detail than graphs.

 An Aid to Programmers

 Derive can also export expressions to programming languages such as BASIC, Pascal, C, and Fortran. You can use Derive to build complicated expressions and then import them, ready-made, into your programs. I haven't tried this, but I suspect that you could even import the solutions into Solver. (Of course, you'd have to make some adjustments, but it should work.)

 The latest version of Derive, 4.13, as of this writing, runs quite well on the Palmtop. The new version offers several new functions beyond those in previous versions. However, the most important new feature is that you can run Derive on either a 16 bit Palmtop or a 32 bit Windows machine and you only need one executable file. Version 4.x will automatically take advantage of extended memory on more powerful desktops. This eliminates the need for the two separate executables that the previous versions used.

Speedwise, the new version seems about the same as the 3.x versions.

For a complete list of new features, see http://www.derive.com/dfd4feat.htm.

 In conclusion, if your math-lust is not satisfied by the Palmtop's built-in applications, try Derive. You won't be sorry.

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