By Martha L. Abell, James P. Braselton
Thoroughly up-to-date to be suitable with Mathematica model 2.2, this e-book specializes in the main frequently used beneficial properties of Mathematica and gears its procedure towards the start Mathematica consumer. The presentation is aimed toward renowned functions of arithmetic in the a variety of topical parts and contains step by step directions
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Extra resources for Mathematica® by Example
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Plot[Abs[x],{x,-5,5}] -4 -2 L o g [ x ] computes the natural logarithm of x, which is usually denoted by lnx or loge x. Thus, entering Log[E] 1 returns 1; entering Log[E"3] 3 returns 3; and entering Exp[Log[Pi]] Pi returns π. The Log function is also used to calculate logarithms with base other than e. Log [ a , b ] computes loga b = . 1 Numerical Calculations and Built-in Functions 31 ΜΚ&ΦΛΡ* mmtmxAmm^mmmm'mmmtmmm returns . An approximation to 10 digits of accuracy is obtained below with N. 001,5].
Wk EXAMPLE: Define g to be the vector-valued function g(x) = (x2,l-x2). g(l) and g(sinb). Calculate SOLUTION: We remark that Mathematica uses braces " { . . } " to denote vectors, lists, and sets. These topics are discussed in more detail in Chapters 4 and 5. Since 50 2 Mathematical Operations on Numbers, Expressions, and Functions g is a function of a single variable, we define g in the same manner as defining functions of a single variable, discussed above. As before, be sure to place an underline (or blank) "_" after the argument on the left-hand side of the definition of the function (but not on the right-hand side).
Where n l , n2,... are numbers. Graphs of functions, like expressions, can be named. This is particularly useful when one needs to refer to the graph of particular functions repeatedly or to display several graphs on the same axes. The command used to display several graphs on the same axes is Show. To show two graphs named g r a p h 1 and g r a p h 2 , the command entered is Show [ g r a p h 1, g r a p h 2 ]. EXAMPLE: Show the graphs of f, g, and h, defined in the previous example, on the same axes.