By Nino Boccara

This booklet teaches how one can use Mathematica to resolve a wide selection of difficulties in arithmetic and physics. it really is in keeping with the lecture notes of a direction taught on the collage of Illinois at Chicago to complex undergrad and graduate scholars. The booklet is illustrated with many precise examples that require the scholar to build meticulous, step by step, effortless to learn Mathematica courses. the 1st half, within which the reader learns tips to use a number of Mathematica instructions, comprises examples, no longer lengthy causes; the second one half includes beautiful purposes. The CD-ROM provides the full textual content content material and interactive examples.

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Additional resources for Essentials of Mathematica: With Applications to Mathematics and Physics

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That is, r e l a t i v e e r r o r = IQ-P^^^i^^^^ and absolute e r r o r = iQ-^^^^^^^y Irrational numbers can be manipulated with any chosen precision. 14159265358979323846264338327950288\ 41971693993751058209749445923078164\ 06286208998628034825342117068 The \ indicates that the output is continuing on the next line. The function P r e c i s i o n [] gives the number of significant digits. 10356 Second, Null} Timing [expression] evaluates expression and gives the CPU time in seconds spent in the Mathematica kernel.

6 Logical Operators 13 {Greater, Equal, LessEqual, Unequal} && is equivalent to And and II to Or. {HeadEx && y ] , Head[x M y ] } {And, Or} Here are more examples combining several logical operators. , expression2, . ] gives True if an odd number of expressionk are True, and the rest are False, it gives False if an even number of express ionk are True, and the rest are False. Xor [3 == 2 + 1, 2 == 4 -- 2 False Xor [3 == 2 + 1, 2 == 0] True ((4 > 2) II (5 < D) && ((4 < 9) II (2 < D) 14 1 Panorama of Mathematica True Be careful, do not mix up = and ==.

Which is the short form of ReplaceAll, is evaluated before the replacement is made as shown in the following example. (a + 3a) / . 3 a -> A 4 a Once the expression has been evaluated, there is no 3a to be replaced by A. Compare the following outputs. x+y/. x->y/. y->a X + y / . {x -> y, y -> a} 2 a a + y 20 1 Panorama of Mathematica Entering expression / / . r u l e s repeatedly performs replacements until expression no longer changes. The same result is obtained with ReplaceRepeated. X + y //.

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