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where j = 1, , n and i = 2, , n - 1 These two boundary conditions are satis ed by:

22:

Format Currency (that is, a monetary value) Same as C Whole number numeric data (Use with integers only) Same as D Scientific notation (uses uppercase E) Scientific notation (uses lowercase e) Fixed-point notation Same as F Use either E or F format, whichever is shorter Use either e or f format, whichever is shorter Fixed-point notation, with comma separators Same as N Percentage Same as P Numeric value that can be parsed, using Parse( ), back into its equivalent internal form (This is called the roundtrip format) Hexadecimal (uses uppercase letters A through F ) Hexadecimal (uses lowercase letters a through f )

(527)

Specifies the number of decimal places The default is six Specifies the number of decimal places The default is six Specifies the number of decimal places

Simplify the expression log3 81 5 log2 8 3 ln(e4 )

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Minimum number of digits Leading zeros will be used to pad the result, if necessary Minimum number of digits Leading zeros will be used to pad the result if necessary

5 Collect the values of initial or boundary conditions Fj, ( j = l, , n) and the differential equation at collocation points, and form the linear systems of equations, in terms of the unknowns, Aj as follows (and as done earlier): A1 E1,1 M + A1 E1,2 M A2 En ,2 + + M + + An E1,n M An En ,n = F1 (55, repeated) = Fn

It is important to understand that the argument associated with a format specifier is determined by the argument number, not the argument s position in the argument list This means the same argument can be output more than once within the same call to WriteLine( ) It also

Part II:

SOLUTION The expression equals log3 (34 ) 5 log2 (23 ) 3 ln e4 = 4 log3 3 5 [3 log2 2] 3 [4 ln e] = 4 1 5 3 1 3 4 1 = 23 You Try It: What does log3 5 mean in terms of natural logarithms EXAMPLE 622

Combine the equations above for the coef cients EI,k (i, j = 1, n) The rst subscript identi es the initial or boundary condition or the collocation point, and the second identi es the spline Written, in matrix notation, the system of equations above becomes

means that arguments can be displayed in a sequence different than they are specified in the argument list For example, consider the following program:

using System; class FormatDemo2 { static void Main() { // Format the same argument three different ways: ConsoleWriteLine("{0:F2} {0:F3} {0:e}", 1012345); // Display arguments in non-sequential order ConsoleWriteLine("{2:d} {0:d} {1:d}", 1, 2, 3); } }

[ E ][ A] = [ F ]

The output is shown here:

Applying the rules for logarithms we obtain ln(5x ) + ln(23x ) = ln 4 ln(7x ) or x ln 5 + 3x ln 2 = ln 4 x ln 7 Gathering together all the terms involving x yields x [ln 5 + 3 ln 2 + ln 7] = ln 4 or x [ln(5 23 7)] = ln 4 Solving for x gives x= EXAMPLE 623

In the first WriteLine( ) statement, the same argument, 1012345, is formatted three different ways This is possible because each format specifier refers to the first (and only) argument In the second WriteLine( ) statement, the three arguments are displayed in nonsequential order Remember, there is no rule that format specifiers must use the arguments in sequence Any format specifier can refer to any argument

(56, repeated)

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