By C.A. Reiter, W.R. Jones

ISBN-10: 0534128645

ISBN-13: 9780534128647

This e-book will be of curiosity to arithmetic scientists operating within the components of linear algebra, summary algebra, quantity concept, numerical research, operations learn and mathematical modelling

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Because deﬁnitions of functions and names of objects are frequently modiﬁed, we introduce the command Clear. Clear[expression] clears all deﬁnitions of expression, if any. symbol. In Mathematica, an elementary function of a single variable, y f x expression in x, is typically deﬁned using the form f[x_]=expression in x or f[x_]:=expression in x. ]) and place an underline (or blank) “_” after the argument on the left-hand side of the equals sign in the deﬁnition of the function. 6: Entering In[80]:= f x x Out[80]= 1 x2 x/ xˆ2 1 39 40 Chapter 2 Basic Operations on Numbers, Expressions, and Functions x/ x2 deﬁnes and computes f x 1 .

1 In[65]:= Apart Out[65]= 2 1, an assumption made x 1 3 x In[66]:= Cancel 2 x 1 x Out[66]= 1 x 3 2 x x 1 1 1 x 2 1 2x 1 In addition, Mathematica has several built-in functions for manipulating parts of fractions. 1. 2. 3. 4. Numerator[fraction] yields the numerator of fraction. ExpandNumerator[fraction] expands the numerator of fraction. Denominator[fraction] yields the denominator of fraction. ExpandDenominator[fraction] expands the denominator of fraction. 2x2 x 2 , (a) factor both the numerator x2 4x 4 3 2 x 2x x 2 and denominator; (b) reduce 3 to lowest terms; and (c) x x2 4x 4 3 x 2x2 x 2 ﬁnd the partial fraction decomposition of 3 .

19615 (b) Mathematica automatically simpliﬁes 82/ 3 . In[20]:= 8ˆ 2/3 Out[20]= 4 When computing odd roots of negative numbers, Mathematica’s results are surprising to the novice. Namely, Mathematica returns a complex number. We will see that this has important consequences when graphing certain functions. 3: Calculate (a) 1 3 27 64 2 and (b) 27 64 2/ 3 . SOLUTION: (a) Because Mathematica follows the order of operations, (-27/64)ˆ2/3 ﬁrst computes 27/ 64 2 and then divides the result by 3. In[21]:= 27/64 ˆ2/3 243 Out[21]= 4096 (b) On the other hand, (-27/64)ˆ(2/3) raises 27/ 64 to the 2/ 3 power.