Programming with Mathematica-: An Introduction
Language: English
Pages: 728
ISBN: B00ADP76YU
Format: PDF / Kindle (mobi) / ePub
Starting from first principles, this book covers all of the foundational material needed to develop a clear understanding of the Mathematica language, with a practical emphasis on solving problems. Concrete examples strewn throughout the text demonstrate how the language can be used to solve problems in science, engineering, economics/finance, computational linguistics, geoscience, bioinformatics and a range of other fields. The book will appeal to students, researchers and programmers wishing to further their understanding of Mathematica. Designed to suit users of any ability, it assumes no formal knowledge of programming so it is ideal for self-study. Over 275 exercises are provided to challenge the reader's understanding of the material covered and these provide ample opportunity to practise using the language. Mathematica notebooks containing examples, programs and solutions to exercises are available from www.cambridge.org/9781107009462.
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have no effect. For example, Plus@Plus@a, bDD is equivalent to Plus@a, bD, hence only one addition is performed. In[3]:= FullForm@Plus@Plus@a + bDDD Out[3]//FullForm= Plus@a, bD The Orderless attribute indicates that the function is commutative, that is, a + b = b + a. This allows Mathematica to write such an expression in an order that is useful for computation. It does this by sorting the elements into a canonical order. For expressions consisting of letters and words, this ordering is
0.52071< model = LinearModelFit@times, 8x, Log@xD<, xD; model@"BestFit"D 0.112765 + 0.0408967 x - 0.0191854 Log@xD Show@8Plot@model@tD, 8t, 1, 10 , Select, Pick , and many others. Scoping constructs are explicitly called out in a separate section. A section on pure functions includes numerous examples to help understand this important construct in the context of concrete problems. Adding options, error trapping and messaging, so important for well-designed functions and programs, are discussed in this chapter so that they can be used in all that follows. Numerous applied examples are included such as protein Preface xv interaction Log@8a, E, 1 we wished to square each number and then add 1 to it. The pure function that does this is Ò2 + 1 &. So that is what we need to map across this list. In[12]:= Out[12]= MapAÒ 2 + 1 &, lisE 85, 26, 38.21< In the next example we will create a set of data and then use the Select function to filter out outliers. In[13]:= data = 824.39001, 29.669, 9.321, 20.8856, 23.4736, 22.1488, 14.7434, 22.1619, 21.1039, 24.8177, 27.1331, 25.8705, 39.7676, 24.7762<; A plot of the data shows there are two
