Use the Calculus > Table command, press Ctrl+Shift+A, or use the TABLE function to generate a table (i.e. a matrix) of data values.  The table shows the values of an expression evaluated at a sequence of points.  The command allows you to select a variable and to enter the starting value, the ending value, and the step size.


Alternatively, an expression of the form TABLE(u, k, n) simplifies to a table of n rows and 2 columns generated by simplifying the expression u(k) with the variable k stepping from 1 through n in steps of size 1.  For example,

TABLE(x^2, x, 5)

simplifies to

⎡ 1   1 ⎤
⎢       ⎥
⎢ 2   4 ⎥
⎢       ⎥
⎢ 3   9 ⎥
⎢       ⎥
⎢ 4  16 ⎥
⎢       ⎥
⎣ 5  25 ⎦


If u is a vector of m elements, an expression of the form TABLE(u, k, n) simplifies to a table of n rows and m+1 columns generated by simplifying each of the elements of u with the variable k stepping from 1 through n in steps of size 1.  For example,

TABLE([x^2, x^3, x^4], x, 5)

simplifies to

⎡ 1   1   1    1  ⎤
⎢                 ⎥
⎢ 2   4   8   16  ⎥
⎢                 ⎥
⎢ 3   9  27   81  ⎥
⎢                 ⎥
⎢ 4  16  64   256 ⎥
⎢                 ⎥
⎣ 5  25  125  625 ⎦


TABLE(u, k, m, n) simplifies to a table of n-m+1 rows generated by simplifying the expression u(k) with the variable k stepping from m through n in steps of size 1.  For example,

TABLE(j!, j, 0, 4)

simplifies to

⎡ 0   1 ⎤
⎢       ⎥
⎢ 1   1 ⎥
⎢       ⎥
⎢ 2   2 ⎥
⎢       ⎥
⎢ 3   6 ⎥
⎢       ⎥
⎣ 4  24 ⎦


TABLE(u, k, m, n, s) simplifies to a table of (n-m)/s+1 rows, rounded down, generated by simplifying the expression u(k) with the variable k stepping from m through n in steps of size s.  For example,

TABLE([SIN(z), COS(z)], z, 0, π/4, 0.2)

approximates to

⎡  0         0             1      ⎤
⎢                                 ⎥
⎢ 0.2  0.1986693307  0.9800665778 ⎥
⎢                                 ⎥
⎢ 0.4  0.3894183423   0.921060994 ⎥
⎢                                 ⎥
⎣ 0.6  0.5646424733  0.8253356149 ⎦


If the third argument of TABLE is a vector or a set, the variable ranges over the elements of the vector or set.  For example,

TABLE(k^2, k, [2, 3, 5, 7, 11])

simplifies to a table of the squares of the first five prime numbers

⎡  2   4  ⎤
⎢         ⎥
⎢  3   9  ⎥
⎢         ⎥
⎢  5  25  ⎥
⎢         ⎥
⎢  7  49  ⎥
⎢         ⎥
⎣ 11  121 ⎦


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