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Take[matrix, n] returns the first n rows of matrix. Take[matrix, n] returns the last n rows of matrix. Take[matrix, {m, n}] returns rows m through n of matrix. Take[matrix, m, n] returns a submatrix containing rows 1 through m and columns 1 through n of matrix. Take[matrix, {m, n}, {p, q}] returns rows m through n and colums p through q of matrix. Drop[matrix, n] returns matrix with its first n rows deleted. Drop[matrix, n] returns matrix with its last n rows deleted. Drop[matrix, {n}] returns matrix with its nth row deleted. Drop[matrix, { n}] returns matrix with the nth row from the end deleted. Drop[matrix, {m, n}] returns matrix with rows m through n deleted. Drop[matrix, m, n] returns matrix with rows 1 through m and columns 1 through n deleted. Drop[matrix, {m},{n}] returns matrix with row m and column n deleted. Drop[matrix, {m, n}, {p, q}] returns matrix with rows m through n and columns p through q deleted. Delete[matrix, n] deletes the nth row of matrix. Delete[matrix, n] deletes the nth from the last row of matrix. Delete[matrix, {{p1},{p2}, ...}] deletes rows p1, p2 ...

Beta functions, 375, 378, 379, 382, 384 relation, to gamma functions, 379 Bilinear transformation, 422 (See also Fractional linear transformation) Binary scale, 16, 21 system, 2 Binomial coe cients, 21 series, 275 theorem, 21 Bolzano-Weierstrass theorem, 6, 12, 19, 117 Boundary conditions, 339 Boundary point, 117 Boundary-value problems: and Fourier integrals, 371 and Fourier series, 339, 356, 357 in heat conduction, 356, 357 in vibration of strings, 361 separation of variables method for solving, 356 Bounded functions, 40, 41 sequences, 24, 30 32, 36 sets, 6 Bounds, lower and upper, 6, 12, 13 Box product, 155 Branches of a function, 41 Branch line, 417 Branch point, 396, 417 Calculus, fundamental theorem of integral, 94, 95, 104 Cardinal number of the continuum, 5 Cardioid, 114 Catenary, 113 Cauchy principal value, 310, 321 Cauchy-Riemann equations, 393, 400 403 derivation of, 401

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m = Partition[Range[20],5]; m //MatrixForm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Take[m, 3] //MatrixForm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

In 6, we looked at some of the access controls that can be applied to Samba shares. We'll review them here, focusing on how they affect access to file shares specifically. Table 11.1 lists the set of access control parameters we'll cover in the next few sections of the text. Table 11.1 Useful Access Control Parameters

Take[m, {1, 4}, {3, 5}] //MatrixForm 3 4 5 8 9 10 13 14 15 18 19 20 Take[m, {2, 3}] // MatrixForm 6 7 8 9 10 11 12 13 14 15 Take[m, 3, {2, 3}] //MatrixForm 2 3 7 8 12 13 Take[m, {2, 3}, {2, 4}] //MatrixForm 7 8 9 12 13 14

12.20 Construct a 10 10 upper triangular matrix whose nonzero entries are random digits. Show that its determinant is equal to the product of the entries on its main diagonal.

Necessity. Suppose the sequence fun g converges to l. Then given any > 0, we can nd N such that jup lj < =2 for all p > N Then for both p > N and q > N, we have jup uq j j up l l uq j @ jup lj jl uq j < =2 =2 Su ciency. Suppose jup uq j < for all p; q > N and any > 0. Then all the numbers uN ; uN 1 ; . . . lie in a nite interval, i.e., the set is bounded and in nite. Hence, by the Bolzano Weierstrass theorem there is at least one limit point, say a. If a is the only limit point, we have the desired proof and lim un a. Suppose there are two distinct limit points, say a and b, and suppose b > a (see Fig. 2-1). By de nition of limit points, we have jup aj < b a =3 for infinnitely many values of p juq bj < b a =3 for infinitely many values of q Then since b a b uq uq up up a , we have jb aj b a @ jb uq j jup uq j jup aj 3 1 2

f[i_ , j_ ] Random[Integer,{0,9}] /; i < j f[i_ , j_ ] 0/; i j m = Array[f, {10, 10}]; m //MatrixForm 3 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 6 7 5 0 0 0 0 0 0 0 7 5 6 1 0 0 0 0 0 0

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