DERIVE's utilization in physics

Sergey V. Biryukov, Moscow State Pedagogical University (MPSU)

The DERIVE (http://www.derive.com) [1] is compact (~1 Mb) and easy to use computer algebra system. It assists a physicist in calculations and analytical transformations. Two-dimensional and three-dimensional graphs assigned in Cartesian and polar coordinates as well as in parametric form are plotted. Equations and equation sets including differential ones are solved by this system. Russian localized version and documentation [2,3] provide with fast familiarization to the DERIVE. The MPSU's physical department courses on computer physics [4] and physical problems based on ecology utilize the DERIVE. The first year students get acquainted with the DERIVE system at the lessons of computer science. The DERIVE is used at physics lessons as a calculator and then it is used for problems solving and data processing. As a result, calculation and graph plotting speed up, and two-dimension surfaces can be plotted. Thus, students develop their intellectual facilities. The Derive provides with dimension and precision analysis. A function created operates with expression and dimension of result, dimension and precision of source data. It results in dimension testing, evaluating the expression and evaluating the mistake. Another function determines admitted analytical expressions due to dimension of source data and result. The experiment on soliton modeling [5] demonstrates quite evidently how the wave changes its form in dispersion medium. It is also demonstrated how the wave transforms into blast one, in nonlinear medium, and the soliton is formed in couple with the dispersion and nonlinearity being compensated. 2D and 3D plots including animation illustrate the results. The animation is supported by macrocommand integration of the DERIVE and 3D animation surfaces the ACROSPIN, CYCLON99 and DPGraph (http://www.davidparker.com), software. The integration is implemented with Hotkeys key simulator and simple file converter written in Pascal. The macrocommand integration of software is reviewed below. There is no multi-purpose software. Thus, there is need in utilizing several program applications to exchange converted data. Over ten primitive operations are performed when the data is processed. That distracts from the main operations performing. A program's macrocommand may unify all the programs utilized, as realized in [6] or in keyboard simulator which presses pre-defined keys. We have selected a freeware SCANCODE simulator for DOS (http://members.aol.com/bretjohn) and a very cheap shareware Hotkeys for Windows 95 (http://members.xoom.com/PostcardWare).

After SCANCODE was utilized to combine educational computing L-micro (http://www.l-micro.ru) laboratory with the DERIVE, the experimental data can be processed by the DERIVE at one key instead of about ten keys pressing. Graphical calculators such as TI-92 and TI-89

(http://www.ti.com/calc) are controlled by software quite similar to the DERIVE's one. Several DERIVE solutions are already ported to TI-92Plus (MHz, 180Kb ROM, 390 Kb Flash Hard Disk) [5].

References

1. Дьяконов В.П. DERIVE - жемчужина символьной математики// Монитор - Аспект (Москва), 1993, N2
2. Дьяконов В.П. Справочник по системе символьной математики DERIVE. М., "СК Пресс", 1998, 256с.
3. Лобанова О.В. Практикум по решению задач в математической системе DERIVE . М., Финансы и Статистика, 1999, 539с.
4. Sergey V. Biryukov. Teaching Physics with DERIVE // The International DERIVE Journal, 1997, vol.2, N2, p. 56-71.
5. Sergey V. Biryukov, J. Fydorova. Tsunami in DERIVE and TI-92. In: Austrian Center for Didactics of Computer Algebra Summer Academy: Recent Reset on DERIVE/TI-92 - Supported Mathematics Education, August 25-28, 1999, Goesing, Lower Austria. (to be published )
6. Andrei I. Kirillov. DERIVE interfaces with Word and Multi Edit. In: Austrian Center for Didactics of Computer Algebra Summer Academy: Recent Reset on DERIVE/TI-92 - Supported Mathematics Education, August 25-28, 1999, Goesing, Lower Austria. (to be published )