MapleTech Volume 3 Number 2, 1996

WWW

Maple and the World Wide Web
R.M. Pinchback

This is the first of a series of articles devoted to Maple's connection with the World Wide Web. To inaugurate this new column in MapleTech, this article begins with a discussion of the methods that can be used for effectively turning Maple plots into graphic images suited for use in Web pages, a topic which will be continued in the next issue. The column concludes with a short list of some particularly interesting Maple Web sites.

Maple Functionality

The Maple V Release 4 Graphical User Interface
C. Howlett, T. Tyhurst

The Maple V Release 4 graphical user interface introduces several new features, including collapsible sections, character-level font control, styles, standard math notation in input and text areas as well as output, in-line plots, and a hypertext help system with full text search. The authors describe the broad goals of the Release 4 interface, and the specific design objectives. The authors review the implementation in some detail, illustrating how the design goals were met.

Summation in Maple
W. Koepf

This article describes the functionality of the new sumtools package in Release 4. It includes facilities for definite and indefinite summation. The article is suitable for a reader who wants to know how Maple computes sums. The article describes Gosper's algorithm and Zeilberger's algorithm, and extensions of the two algorithms available in the sumtools package. Examples are given and discussed which illustrate the new capabilities.

The Differential Algebra Package: diffgrob2
E. Mansfield

The diffgrob2 package is a set of tools for studying partial differential systems PDEs, in particular overdetermined systems. The tools are based on an extension of Groebner bases for algebraic systems to differential systems, including linear and non-linear systems. The tool has been useful for rendering tractable overdetermined non-linear systems of PDEs.

Maple Applications

Solving Stochastic Differential Equations with MAPLE
S. Cyganowski

The Maple package Stochastic contains algorithms which solve Stochastic Differential Equations (SDEs) explicitly as well as algorithms which construct numerical schemes for SDEs. This article demonstrates those algorithms which provide explicit solutions to SDEs.

Solving the Aberration and Power Equations for the Cooke Triplet Lens
R. Ditteon

The Cooke triplet is a lens system consisting of three separate lenses with air spaces between the lenses. The two outer lenses of this arrangement are positive lenses and the middle lens which serves as the aperture stop is a negative lens. The six curvatures (two for each lens) and two air spaces give a total of eight free parameters. With these eight parameters, it is theoretically possible to design a lens with a target optical power which does not suffer from either lateral or axial chromatic aberration or from spherical aberration, coma, astigmatism, Petzval curvature, or distortion. A Maple worksheet has been developed which solves the eight equations describing the optical power and aberrations in the eight unknown parameters. The system of equations is too complex for the normal Maple solve command, so Ross Taylor's newton's method is used instead.

Solving Stiff Differential Equations and Differential Algebraic Systems with Maple V
D. Schwalbe, H. Kooijman, R. Taylor

Many systems of ordinary differential equations (ODEs) encountered in practice defy analytical solution and call for numerical methods. A stiff system of equations may be difficult to solve with an explicit Euler or Runge-Kutta method. Schwalbe, Kooijman and Taylor discuss an implementation, in a Maple code they call BESIRK, of a third order Semi-Implicit Runge-Kutta (SIRK) method of Michelsen combined with an extrapolation technique modeled after that of Bulirsch and Stoer. The resulting method, is capable of solving stiff ODEs quickly and efficiently. They also show that BESIRK can be used to solve mixed systems of differential and algebraic equations (DAEs).

Maple in Education

Tips for Maple Instructors
R. Lopez

This is the first of a series of articles devoted to Maple's use within education. This is a new column in MapleTech devoted specifically to issues instructors face when using Maple in courses. Robert Lopez has taught many classes using Maple. He has learned what works and what doesn't work, and how to get around problems that Maple creates. The editors of MapleTech are very glad that he has agreed to share with us his experiences in this column. His first article provides some do's and don'ts for students who are solving problems in worksheets. And not just students! It also addresses the difficult issue of whether we introduce both formulae (Maple expressions) and functions (Maple procedures) to the students.

Thermodynamics with Maple: IV, The Properties of Steam
R. Taylor

Engineers frequently need to evaluate the properties of water and steam and thermodynamic textbooks almost always include an appendix devoted to so-called steam tables. Tables are, however, less useful for computer-based calculations since it may not be practical to create the necessarily huge look-up table of the thermodynamic properties of water and steam. In the fourth part of a series on Thermodynamics with Maple, Ross Taylor implements the very complicated equation of state for water and uses it in the analysis of thermodynamic systems. He also shows how to create various thermodynamic property tables and phase diagrams with Maple.

Previous articles in this series:

I

Equations of State

II

Phase Equilibria in Binary Systems

III

Thermodynamic Property Relations and the Maxwell Equations

Teaching Maple to Engineering Students
M. Rybowicz, J.-P. Massias

For instructors teaching Maple courses, finding interesting problems to test the student's level of achievement is often a headache. In order to cover the entire range of Maple functionalities, the problem must include symbolic, graphics and numerical parts. Moreover, it must be solvable in a limited amount of time by beginners, following a natural sequence of Maple commands. The authors present two of the problems that we have used in the past as examination for Maple courses taught to Engineering students.