User manual MAPLESOFT MAPLE 10

[. . . ] Maple User Manual Copyright © Maplesoft, a division of Waterloo Maple Inc. 2005. Maple User Manual Copyright Maplesoft, Maple, Maple Application Center, Maple Student Center, Maplet, Maple T. A. , and MapleNet are all trademarks of Waterloo Maple Inc. © Maplesoft, a division of Waterloo Maple Inc. No part of this book may be reproduced, stored in a retrieval system, or transcribed, in any form or by any means -- electronic, mechanical, photocopying, recording, or otherwise. [. . . ] For example: > Differentiating an Operator You can also specify a mathematical function as a functional operator (a mapping). For a comparison of operators and other expressions, see Distinction between Functional Operators and Other Expressions (page 293). To find the derivative of a functional operator: · Use the D operator. The D operator returns a functional operator. For example, find the derivative of an operator that represents the mathematical function . First, define the mathematical function as the operator F. 1. In the Expression palette, click the single-variable function definition item . 2. · To move to the next placeholder, press the Tab key. Note: If pressing the Tab key inserts a tab, click the Tab icon > Now, define the operator, G, that maps to the derivative of . in the toolbar. 4. 4 Calculus · 159 > F and G evaluated at > return the expected values. For more information on the D operator, refer to the ?D help page. For a comparison of the diff command and D operator, refer to the ?diffVersusD help page. Directional Derivative To compute and plot a directional derivative, use the Directional Derivative Tutor. The tutor computes a floating-point value for the directional derivative. To launch the tutor: From the Tools menu, select Tutors, Calculus - Multi-Variable, and then Directional Derivatives. Maple launches the Directional Derivative Tutor. See Figure 4. 7. 160 · 4 Mathematical Computations Figure 4. 7: Directional Derivative Tutor To compute a symbolic value for the directional derivative, use the Student[MultivariateCalculus][DirectionalDerivative] command. The first list of numbers specifies the point at which to compute the derivative. The second list of numbers specifies the direction in which to compute the derivative. For example, at the point [1, 2], the gradient of points in the direction [2, 4], which is the direction of greatest increase. The directional derivative in the orthogonal direction [-2, 1] is zero. > > 4. 4 Calculus · 161 > Series To generate the Taylor series expansion of a function about a point, use the taylor command. > Note: If a Taylor series does not exist, use the series command to find a general series expansion. For example, the cosine integral function does not have a taylor series expansion about 0. [. . . ] For example, you can link to controlled hardware via a serial port or interface with another program. The Database Integration Toolbox uses external calling to allow you to query, create, and update databases in Maple. For more information, visit http://www. maplesoft. com/products/toolboxes. 10. 5 Connectivity · 375 For more information on using external calling, refer to the ?ExternalCalling help page. Mathematica Translator The MmaTranslator package provides translation tools for converting Mathematica® expressions, command operations, and notebooks to Maple. [. . . ]