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Unformatted text preview: c function Note: When Maple cannot ﬁnd a simpler form, it leaves the expression as it is rather than convert it to an inexact form.
> ln(Pi); ln(π ) 2.3 Basic Symbolic Computations Maple can work with mathematical unknowns, and expressions which contain them. 2.3 Basic Symbolic Computations > (1 + x)^2; • 17 (1 + x)2
> (1 + x) + (3 - 2*x); 4−x Note that Maple automatically simpliﬁes the second expression. Maple has hundreds of commands for working with symbolic expressions. For a partial list, see Table 2.2.
> expand((1 + x)^2); 1 + 2 x + x2
> factor(%); (1 + x)2 As mentioned in 2.2 Numerical Computations, the ditto operator, %, is a shorthand notation for the previous result.
> Diff(sin(x), x); d sin(x) dx
> value(%); cos(x)
> Sum(n^2, n); n2
n > value(%); 13 12 1 n− n+ n 3 2 6 18 • Chapter 2: Mathematics with Maple: The Basics Divide one polynomial in x by another.
> rem(x^3+x+1, x^2+x+1, x); 2+x Create a series.
> series(sin(x), x=0, 10); x− 15 1 1 13 x+ x− x7 + x9 + O(x10 ) 6 120 5040 362880 All the mathematical functions mentioned in the previous section also accept unknowns as arguments. 2.4 Assigning Expressions to Names This section introduces the following concepts in Maple. • Naming an object • Guidelines for Maple names • Maple arrow notation (->) • Assignment operator (:=) • Predeﬁned and reserved names Syntax for Naming an Object
Using the ditto operator, or retyping a Maple expression every time you want to use it, is not always convenient, so Maple enables you to name an object. Use the following syntax for naming. name := expression ; You can assign any Maple expression to a name.
> var := x; var := x 2.4 Assigning Expressions to Names > term := x*y; • 19 term := x y You can assign equations to names.
> eqn := x = y + 2; eqn := x = y + 2 Guidelines for Maple Names
Maple names can include any alphanumeric characters and underscores, but they cannot start with a number. Do not start names with an underscore because Maple uses these names for internal classiﬁcation. • Examples of valid Maple names are polynomial, test_data, RoOt_lOcUs_pLoT, and value2. • Examples of invalid Maple names are 2ndphase (because it begins with a number) and x&y (because & is not an alphanumeric character). Maple Arrow Notation in Deﬁning Functions
Deﬁne functions by using the Maple arrow notation (->). This notation allows you to evaluate a function when it appears in Maple expressions. You can do simple graphing of the function by using the plot command.
> f := x -> 2*x^2 -3*x +4; f := x → 2 x2 − 3 x + 4
> plot (f(x), x= -5..5);
70 60 50 40 30 20 10 –4 –2 0 2 x 4 20 • Chapter 2: Mathematics with Maple: The Basics For more information on the plot command, see chapter 5 or enter ?plot at the Maple prompt. The Assignment Operator
The assignment (:=) operator associates a function name with a function deﬁnition. The name of the function is on...
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