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Ans. (a) z 1, pole of order 4 2 (b) z 1, simple pole; z 2, double pole (c) simple poles z 1 i

{{1,

The matrix is input using Insert Table/Matrix New. Mathematica outputs the matrix as a nested list of numbers.

2, 3},{4, 5, 6},{7, 8, 9}}

NetBIOS name service uses two methods for registering, resolving, and releasing NetBIOS names, groups, and addresses. The first method administers the namespace using network broadcasts. The client machine queries or announces a name on the network as a broadcast and then waits for a response to the request. Because delivery is not guaranteed, the client may have to retransmit its request a number of times before it is resolved. This method works in small networks but quickly breaks down on large networks due to heavy broadcast traffic. The second method for managing the namespace uses point-to-point communication. Name registration and IP address resolution requests are directed to a NetBIOS Name Server (NBNS) in a manner similar to Internet dynamic DNS. NetBIOS point-to-point name service is defined in RFC 1001 and RFC 1002 and implemented as Microsoft's Windows Internet Name Service (WINS) (Figure 3.5).

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16.62. Find Laurent series about the indicated singularity for each of the following functions, naming the singularity in each case. Indicate the region of convergence of each series. a cos z ;z z a b z2 e 1=z ; z 0 c z2 ;z 1 z 1 2 z 3

2 1 5 B = 4 7 2 1 3 2

{{2,

1, 5},{4, 7, 2},{1, 3, 2}}

Ans:

A + B //MatrixForm 3 3 8 8 12 8 8 11 11 A B //MatrixForm 1 1 2 0 2 4 6 5 7 3 A //MatrixForm 3 6 9 12 15 18 21 24 27 A.B //MatrixForm 13 24 15 34 57 42 55 90 69

- 41 -

It is useful to remember that if list is a simple list of numbers, list.list yields the sum of their squares. The result is printed as a single number without braces.

1 z z 3 z 5 ; simple pole, all z 6 4! 6! z 2! 1 1 1 1 ; essential singularity, all z 6 0 2! 3! z 4! z2 5! z3

Tables are also stored as nested lists, but are represented as tables with TableForm. Although this command allows representation of tables of any dimension, we will discuss only one- and two-dimensional tables in this book.

list = {{12, 7, 10}, {105, 205, 7}, {3, 30, 300}};

12 105 3

NetBIOS name-to-IP address mappings can also be hard coded in LMHOSTS tables and stored on each machine. The LMHOSTS table is a flat ASCII file of IP address and name pairs. If both WINS and LMHOSTS information are available for resolving names, clients will first consult their local NetBIOS cache and then WINS before using LMHOSTS information. It is also possible to prime the client NetBIOS cache at system startup with LMHOSTS entries that have been flagged as #PRE (Example 3.2). Example 3.2 LMHOSTS Stanza 149.110.5.12 Wizard #PRE

CHAP. 16]

7 205 30

10 7 300

TableForm[list, options] allows the use of various formatting options in determining the appearance of a table.

RESIDUES AND THE RESIDUE THEOREM 16.63. Determine the residues of each function at its poles: a Ans. 2z 3 ; z2 4 b z3 z 3 ; 5z2 c ezt ; z 2 3 d z : z2 1 2

The broadcast and point-to-point capabilities of various LAN clients for name-to-address resolution are based on their node type as defined in Table 3.2. Table 3.2 Name Resolution Methods

From Example 47 we can observe that the numbers in a table are, by default, left justified. This can sometimes make the table confusing to read. Justification can be controlled with the TableAlignments option. TableAlignments Left justifies the columns to the left (default). TableAlignments Right justifies the columns to the right. TableAlignments Center centers the columns.

list = {{12,7,10},{105,205,7},{3,30,300}}; TableForm[list, TableAlignments Right] 12 7 10 105 205 7 3 30 300

TableForm[list, TableAlignments Center]

(a) z 2; 7=4; z 2; 1=4 (b) z 0; 8=25; z 5; 8=25

12 105 3 7 205 30 10 7 300

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