Bruce W. Char's First Leaves: A Tutorial Introduction to Maple V PDF

By Bruce W. Char

ISBN-10: 0387941258

ISBN-13: 9780387941257

ISBN-10: 1461569966

ISBN-13: 9781461569961

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Extra info for First Leaves: A Tutorial Introduction to Maple V

Example text

T2 := series(ln(x). x=l. 4); The order information in series results is used when doing arithmetic on series themselves. In this example, the result is only O(x7 ) since tl is only O(x6 ). >S 356 tl := x - 1/6 x + 1/120 x + O(x ) t2 := x - 1 - 1/2 (x - 1) := series(tl*tl. x-OJ 10); 2 2 4 + 1/3 (x - 1) 6 3 4 + O«x - 1) ) 7 S := x - 1/3 x + 2/45 x + O(x ) 1 46 Interactive Use of Maple To evaluate a series at a value, compute it, then convert it to a polynomial to remove the order term using the built-in convert function.

Maple is designed to handle mathematical operations involving symbols (variables with no assigned values) as well as numbers. Example 11 Maple calculations with mathematical unknowns Maple expressions can involve symbolic unknowns as well as numbers. Such expressions can be labeled, just as with numerical results. Maple automatically performs a limited amount of simplification as it evaluates the expression. 19, which starts on page 38. > expr1 := (x + y + x + x*x*x + x) / 2; Symbolic expressions can include any function.

X) = y(x). y(O) = o. z(O) .. 2 }; sys :- {z(O) = 2. y(O) = d o. ---dx z(x) = r(x). d ---- y(x) = z(x)} dx > fens :- {y(x). z(x)}; fens :- {y(x). z(x)} > dsolve(sys. fens); {z(x) - exp(x) + exp(- x). y(x) .. 4 Power series series ( expression. variable .. expansion point. order of truncation ) Maple can construct any finite number of terms of the Taylor series (and more generally, Laurent series) for an expression. (XA n) is tacked on to the end of the series if the terms up to x n - 1 are not the complete expression.

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First Leaves: A Tutorial Introduction to Maple V by Bruce W. Char


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