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// Demonstrate the HashSet<T> class using System; using SystemCollectionsGeneric; class HashSetDemo { static void Show(string msg, HashSet<char> set) { ConsoleWrite(msg); foreach(char ch in set) ConsoleWrite(ch + " "); ConsoleWriteLine(); } static void Main() { HashSet<char> setA = new HashSet<char>(); HashSet<char> setB = new HashSet<char>(); setAAdd('A');

24:

(773a) (773b) (773c)

SOLUTION When sines and cosines occur together, we always focus on the odd power (when one occurs) We write sin3 x cos2 x = sin x sin2 x cos2 x = sin x 1 cos2 x cos2 x = cos2 x cos4 x sin x Then sin3 x cos2 dx = cos2 x cos4 x sin x dx A u-substitution is suggested: We let u = cos x, du = sin x dx Then the integral becomes u3 u5 + + C 3 5 Resubstituting for the u variable, we obtain the nal solution of u2 u4 du = sin3 x cos2 dx = You Try It: Calculate the integral sin2 3x cos5 3x dx cos5 x cos3 x + + C 3 5

setAAdd('B'); setAAdd('C'); setBAdd('C'); setBAdd('D'); setBAdd('E'); Show("Initial content of setA: ", setA); Show("Initial content of setB: ", setB); setASymmetricExceptWith(setB); Show("setA after Symmetric difference with SetB: ", setA);

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setAUnionWith(setB); Show("setA after union with setB: ", setA); setAExceptWith(setB); Show("setA after subtracting setB: ", setA); ConsoleWriteLine(); } }

where P is a third-rank tensor that is cubic and homogeneous in p It is omitted here, the interested reader being referred to Al-Daccak and Angeles (1993) for further details Moreover, Gi denotes the polygonal boundary of Si contained in the plane Pi Note that, just as the GDT is used in 3-D to reduce volume integrals, it is used in 2-D to reduce surface integrals to line integrals Now let Gi,k denote the kth side of the m-sided polygon Si that joins the kth and the (k + 1)st vertices, numbered counterclockwise when the face of interest is viewed from outside the polyhedron Moreover, a sum over subscript k is to be understood, henceforth, as being modulo m Furthermore, the position vector p, shown in Fig 712, of any point of Gi,k is de ned in the plane Pi as p = m i ,k + h i ,kSi ,k , p Gi ,k , 0 si ,k 1 (774)

The output is shown here:

Initial content of setA: A B C Initial content of setB: C D E setA after Symmetric difference with SetB: A B D E setA after union with setB: A B D E C setA after subtracting setB: A B

/2 0

where mi,k and hi,k are the vectors ri,k - ri and ri,k+1 - ri,k, respectively, ri,k being the position vector of the kth vertex of the polygon Si Similar to vector p, vectors mi,k and hi,k lie solely in the plane Pi Consequently, their representation as 2-D vectors in that plane is used to apply the GDT to reduce the surface integrals de ned over Si to line integrals de ned over Gi,k Let ni,k be the unit normal vector to Gi,k pointing outward of Si and si,k be the length of the kth side of Gi Thus, quantities Ai, ai, and bi can be evaluated as indicated below, keeping in mind that si,k = ||hi,k|| and p ni,k = mi,k ni,k, since hi,k ni,k = 0 Then

For the sake of simplicity, the foregoing examples have stored built-in types, such as int, string, or char, in a collection Of course, collections are not limited to the storage of built-in objects Quite the contrary The power of collections is that they can store any type of object, including objects of classes that you create Let s begin with an example that uses the non-generic class ArrayList to store inventory information that is encapsulated by the Inventory class:

// A simple inventory example using System; using SystemCollections; class Inventory { string name; double cost; int onhand; public Inventory(string n, double c, int h) { name = n; cost = c; onhand = h;

(775a)

Part II:

/2 0

} public override string ToString() { return StringFormat("{0,-10}Cost: {1,6:C} name, cost, onhand); } } class InventoryList { static void Main() { ArrayList inv = new ArrayList(); // Add elements to the list invAdd(new Inventory("Pliers", 595, 3)); invAdd(new Inventory("Wrenches", 829, 2)); invAdd(new Inventory("Hammers", 350, 4)); invAdd(new Inventory("Drills", 1988, 8)); ConsoleWriteLine("Inventory list:"); foreach(Inventory i in inv) { ConsoleWriteLine(" " + i); } } }

On hand: {2}",

(775b)

The output from the program is shown here:

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