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Introduction to Maple V. Student version. (Einführung in Maple V. Studentenversion. Mit Unterst. von J. S. Devitt. Teilw. auf d. Grundl. d. Arbeiten von B. W. Char. Incl. 1 CD-ROM.) (English) Zbl 0858.68047

Berlin: Springer. ix, 280 p. (1996).
Maple V is both an expert system and a development system (thus a programming one) to work, learn, teach and, most important, to exploit high level mathematics, at the highest level of user friendliness and efficiency. The student version of Maple V, release 4, provides a library of over 2500 functions, covering various various fields of mathematics, computing (including computer programming aspects), and editing.
It is important to list just some of the fields where Maple V system offers a beautiful expertise: (1) Symbolic and numerical calculi; (1.1) Analysis: derivation, symbolic and numerical integration, integral transformations (Laplace, Henkel, Fourier), discrete transformations (Z, FFT); (1.2) Equation Solving: linear and nonlinear systems, (partial) differential equations, calculus of sequence limits, recurrence relations, transcendental equations, inequations; (1.3) Elementary and special functions: trigonometric, exponential, logarithmic, Bessel, Zeta, Gamma, hypergeometric etc. functions; (1.4) Linear algebra: matrix operations, eigenvalues and eigenvectors, special matrices, matrix normal forms etc. (1.5) Other mathematical fields: algebraic numerical corps, combinatorics, complex numbers, finance and statistics analysis, formal logic, Galois groups, geometry, graph theory, Gröbner theory, linear optimization etc. (2) Graphics: (2.1) 2D-design: half-, double- and logarithmic-design, parametric, phase, and circle diagrams, implicit curves, multiple coordinate systems etc. (2.2) 3D-graphics: multiple variable functions, surface smoothing, user-defined colour functions etc.; (2.3) Animation: 2D and 3D animation, interactive control of animation etc.; (3) (Computer) Programming; (3.1) Maple V procedural programming language; (3.2) Similar syntax to standard languages; (3.3) Mathematical data types; (3.4) User-defined data types etc.; (4) Maple V input and output: Data and output similar to (language) C, Transformation of Fortran or C code, Export into LaTeX; (5) User services: various text processing, mathematical text (or expression) input and output, hyperlinks, design into text etc.
Many other possibilities in computer science and computing applications are present. The list of all these items is important but three things really impress the mathematician when Maple V is put to work: its calculus power, its simplicity in use, and the beauty of graphical (including coloured) representations of mathematical objects.
The “Introduction into Maple V” of K. M. Heal, M. L. Hansen, K. M. Rickard is a wonderful guide, applying the learning-by-example method to Maple V teaching and training. The proposed examples and topics give to the reader the first but real flavour of Maple. After I installed Maple V and began to work with, a strong and stable feeling came into my soul: the joy of (re)discovering a beloved and faithful friend.
Reviewer: N.Curteanu (Iaşi)

MSC:

68W30 Symbolic computation and algebraic computation
68-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

Software:

Maple
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