By James A. Carlson (Author), Jennifer M. Johnson (Author)
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Extra info for Multivariable Mathematics with Maple: Linear Algebra, Vector Calculus and Differential Equations
Example text
0/x^2; Then S( f, 4 ) gives the sum. 0/x^2, 4 ); To sum up a different series, we just change the arguments to S. For example, > S( i -> 1/i, 10 ); sums the first ten terms of the harmonic series: 1+ 1 1 1 + + ... + + ... 2 3 n Lists Another way to think about the behavior of an infinite sum is to plot the partial sums Sn versus n. This gives a picture of how the sum grows as n increases. We can modify our procedure S to produce a list of points (n, Sn ) and then use plot to graph them. To define our list we use Maple’s sequence-building command.
Exercise 2. 2). Exercise 3. (a) Use the procedures S and Spts to investigate the limit of the partial sums 1 1 Sn = 1 + + . . + 2 4 n as n → ∞. Does the limit exist? That is, do the partial sums approach some well-defined number or do they grow without bound? (b) Repeat for the harmonic series 1+ 1 1 + ... + + ... 2 n (c) Plot the partial sums for both series together: > plot( {Spts(x ->1/x, 100), Spts(x->1/x^2, 100)}); Exercise 4. Study the alternating harmonic series 1− 1 1 1 1 + − + ... ± + ...
In loops, do must be balanced by a subsequent od. In conditionals, if must be balanced by a subsequent fi. A procedure definition that begins with proc( ... ) must be be terminated by a subsequent end. ). If you use a function in a package, load the package first. Thus, to use matrix, load linalg; to use display, load plots. You load linalg by the command with( linalg ). Do not confuse unassign with unapply. Remember to use ? plot for information about plot or just ? for general information.