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Thrd = new Thread(thisRun); ThrdName = name; currentName = name; } // Begin execution of new thread void Run() { ConsoleWriteLine(ThrdName + " starting"); do { Count++; if(currentName != ThrdName) { currentName = ThrdName; ConsoleWriteLine("In " + currentName); } } while(stop == false && Count < 1000000000); stop = true; ConsoleWriteLine(ThrdName + " terminating"); } } class PriorityDemo { static void Main() { MyThread mt1 = new MyThread("High Priority"); MyThread mt2 = new MyThread("Low Priority"); // Set the priorities mt1ThrdPriority = ThreadPriorityAboveNormal; mt2ThrdPriority = ThreadPriorityBelowNormal; // Start the threads mt1ThrdStart(); mt2ThrdStart(); mt1ThrdJoin(); mt2ThrdJoin(); ConsoleWriteLine(); ConsoleWriteLine(mt1ThrdName + " thread counted to " + mt1Count); ConsoleWriteLine(mt2ThrdName + " thread counted to " + mt2Count); } }

dvar = 1000; // assign dvar the value 1000 ConsoleWriteLine("Original value of ivar: " + ivar); ConsoleWriteLine("Original value of dvar: " + dvar); ConsoleWriteLine(); // print a blank line // Now, divide both by 3 ivar = ivar / 3; dvar = dvar / 30; ConsoleWriteLine("ivar after division: " + ivar); ConsoleWriteLine("dvar after division: " + dvar); } }

Using formula ( ) , we conclude that 2 cos x F ( x) = + + ln 5 F ( x) x sin x hence F ( x) = cos x 2 + + ln 5 [x 2 ( sin x) 5x ] x sin x

The output from this program is shown here:

Original value of ivar: 100 Original value of dvar: 100 ivar after division: 33 dvar after division: 333333333333333

As you can see, when ivar (an int variable) is divided by 3, a whole-number division is performed, and the outcome is 33 the fractional component is lost However, when dvar (a double variable) is divided by 3, the fractional component is preserved As the program shows, when you want to specify a floating-point value in a program, you must include a decimal point If you don t, it will be interpreted as an integer For example, in C#, the value 100 is an integer, but the value 1000 is a floating-point value There is one other new thing to notice in the program To print a blank line, simply call WriteLine( ) without any arguments The floating-point data types are often used when working with real-world quantities where fractional components are commonly needed For example, this program computes the area of a circle It uses the value 31416 for pi

// Compute the area of a circle using System; class Circle { static void Main() { double radius; double area;

Many processes of nature and many mathematical applications involve logarithmic and exponential functions For example, if we examine a population of bacteria, we notice that the rate at which the population grows is proportional to the number of bacteria present To see that this makes good sense, suppose that a bacterium reproduces itself every 4 hours If we begin with 5 thousand bacteria then after 4 hours after 8 hours there are there are 10 thousand bacteria 20 thousand bacteria

updated equipment, for instance), but to employees or guests it s probably irrelevant It may also be confusing What has the fact that it s computerized got to do with the fact that it will be tested on Tuesday It s more concise to eliminate it Sometimes the adjective is redundant, as in this example:

Part I:

radius = 100; area = radius * radius * 31416; ConsoleWriteLine("Area is " + area); } }

The output from the program is shown here:

after 12 hours there are after 16 hours there are etc The point is that each new generation of bacteria also reproduces, and the older generations reproduce as well A sketch (Figure 612) of the bacteria population against time shows that the growth is certainly not linear---indeed the shape of the curve appears to be of exponential form Notice that, when the number of bacteria is large, then different generations of bacteria will be reproducing at different times So, averaging out, it makes sense to hypothesize that the growth of the bacteria population varies continuously as in Figure 613 Here we are using a standard device of mathematical analysis: even though the number of bacteria is always an integer, we represent the graph of the population of bacteria by a smooth curve This enables us to apply the tools of calculus to the problem 40 thousand bacteria 80 thousand bacteria