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In this example, if a match is found for 20, it will fall through to the next case clause. This is legal as long as it runs into a break statement before it reaches the end brace of the switch statement. When it falls to case 21:, it is still considered a match because case 20: was empty. You can use this to specify a range of values much like Select-Case in VB .NET. If none of the cases match, you can use a default to process a default command.

(651)

The function F (s) is the Laplace transform of f (t) and is a function of the complex frequency, s = + j , considered earlier in this section Note that the function f (t) is de ned only for t 0 This de nition of the Laplace transform applies to what is known as the one-sided or unilateral Laplace transform, since f (t) is evaluated only for positive t In order to conveniently express arbitrary functions only for positive time, we introduce a special function called the unit step function, u(t), de ned by the expression u(t) = 0 1 t <0 t >0 (652)

6

Find the Laplace transform of f (t) = e at u(t)

53 91

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Of course, like other languages, both VB .NET and C# support loops and jumps. Loops allow you to repeat one or more statements based on a condition. Jumps allow you to force your program to jump over one or more lines of code to another line.

Known Quantities: Function to be Laplace-transformed Find: F (s) = L{f (t)} Schematics, Diagrams, Circuits, and Given Data: f (t) = e at u(t) Assumptions: None Analysis: From equation 651:

F (s) =

Find the Laplace transform of f (t) = cos( t)u(t)

Known Quantities: Function to be Laplace-transformed Find: F (s) = L{f (t)} Schematics, Diagrams, Circuits, and Given Data: f (t) = cos( t)u(t) Assumptions: None Analysis: Using equation 651 and applying Euler s identity to cos( t) gives:

F (s) =

You looked at the For-Each/foreach loop already in the Arrays section. This loop was designed specifically to work with arrays and collections. VB .NET Dim numbers As Integer() = {5, 10, 15} For Each i As Integer In numbers Console.WriteLine(i) Next C# int[] numbers = {5, 10, 15}; foreach (int i in numbers) { Console.WriteLine(i); } Some advanced topics you should know about loops are the following: Although other loops allow you to change data while the loop is running, in C#, the foreach loop is read only. In other words, you cannot change the values of your variable from within the loop. VB .NET does not have this restriction. With loops that allow you to change the data, reference types and value types react differently when you make changes within a loop. VB .NET Class Customers Public Name As String End Class

619 Find the Laplace transform of the following functions:

444 313

a u(t) b sin( t)u(t) c tu(t)

Table 61 Laplace transform pairs f(t) (t) (unit impulse) u(t) (unit step) e at u(t) sin t u(t) 1 1 s 1 s+a s 2 + 2 s s 2 + 2 (s + a)2 + 2 s+a (s + a)2 + 2 1 s2 F(s)

620 Find the Laplace transform of the following functions:

a e sin t u(t) b e at cos t u(t)

Sub Main(ByVal args As String()) 'Integers are value types, so you get a copy of the value Dim numbers As Integer() = {5, 10, 15} For Each i As Integer In numbers Console.WriteLine(i) i = 20 ' i is only a copy of the original integer's data Next Console.WriteLine(numbers(0)) 'Still shows 5 'Even though Strings are Reference types, you still get a copy of the value Dim Names As String() = {"Bob", "Sue", "Tim"} For Each s As String In Names Console.WriteLine(s) s = "Joe" 's is only a copy of the original string's data Next Console.WriteLine(Names(0)) 'Still shows Bob 'Normal Reference Types, like the Customers Class we made earlier, ' act as a true reference. Dim c1 As New Customers c1.Name = "Bob" Dim c2 As New Customers c2.Name = "Sue" Dim arrCust() As Customers = {c1, c2} For Each c As Customers In arrCust Console.WriteLine(c.Name) c.Name = "Joe" 'c points to the same memory as each array element Next Console.WriteLine(c1.Name) 'Now shows Joe Console.WriteLine(c2.Name) 'Now shows Joe End Sub C# (foreach is Read Only) int[] numbers = {5, 10, 15}; foreach (int i in numbers) { Console.WriteLine(i); i = 20; // This is NOT allowed! } Console.WriteLine(numbers(0));

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