JSFHMAT 156 Sp '08Lab 1 Maple ReviewThis Lab is a quick review of things you learned in Mat 155. Note that there is a built-in tutorial for Maple and a Help Menu. Since there is no manual you should become adept at using both. Operations: To use Maple as a calculator, you just type the formula you are interested in and hit enter. Use +, -,*,/ and ^ fAddition +Subtraction - Multiplication * may appear as a dotDivision /Exponent ^ may appear as a superscriptMaple obeys the order of operations so it will do exponents first, then multimplication and division, thenaddition and subtraction. If you want it to do addition first, you must put it in parentheses. Click on the following lines and hit "Enter" to see examples:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJyZwbHVzO0YnRi8vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGRy1GLDYkUSIyRidGLy1GMzYtUScmc2RvdDtGJ0YvRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGUS1GLDYkUSIzRidGLy8lK2V4ZWN1dGFibGVHRjhGLw==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 Expansions If Maple starts with integers then it gives the answer in terms of integers whenever it can. If you want decimals either start with decimals or use the evalf command.5/3; 5.0/3; evalf(5/3);JSFH Making a Worksheet 1.) Start a new worksheet by clicking the new file icon (the leftmost icon on the menu bar) or selecting File/New from the Main menu. 2) Write your name on the top of the file.3) Save the file with the name Assn1 4) To see both files at once select Window/Vertical from the main menuAssignments Each week there will be an assignment to complement the lab notes. Assignments count 30% of your grade and must be completed by the end of the next lab. To do the assignment, open a new file as above and answer all the "Assignment" Sections of the lab. Assignment Part 2: Compute the following using Maple. You may either use "New" Maple or Classic Maple. In Classic Maple, you must type your command on a line beginning with a [> (red) symbol which is called a prompt. Don't forget the ; or Maple will write : "Warning, premature end of input". In New Maple there is no prompt. The input line comes out in italics. You don't need the semi-colon at the end of an input. If you type a fraction, say 3/2, the slash becomes a horizontal line. To move on from the fraction type a right arrow key. The same is true for an exponent. There are other differences and we will mention them as we go along. a) 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b) 1+15 7+1 Use parentheses to make sure you get the right answer (2) c) 5(3+2) Built in functions Maple has many built in functions. Some common ones are sqrt(x) ( for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYsNiZRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKzJEfkNvbW1lbnRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGKy9GPFEnbm9ybWFsRic= ) sin(x) cos(x) tan(x) exp(x) (for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSSNtb0dGJDYuUSJlRicvJTBmb250X3N0eWxlX25hbWVHUSsyRH5Db21tZW50RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk0tRiw2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnRjYvRjpRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjk=) 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNidGKy1JJm1mcmFjR0YkNigtRjM2JFEiMUYnRjZGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRi8lKWJldmVsbGVkR1EmZmFsc2VGJ0YrLyUrZXhlY3V0YWJsZUdGS0Y2LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRkxGNg==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Remember that there is no real square root of (-1). There is an imaginary square root for (-1) which is called i or I. In Calculus I we do not use imaginary or complex numbers. So be careful if you get an I in an answer.When using the trig functions keep in mind that angles are measured in radians not degrees. Maple also has a built in value for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1ErMkR+Q29tbWVudEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y1When you want to use LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEnJiM5NjA7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lMGZvbnRfc3R5bGVfbmFtZUdRMkNoYXJhY3RlclN0eWxlMjY3RicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjovRjlRJ25vcm1hbEYn type in Pi. Maple is case sensitive so be sure to type Pi and not pi or PI.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For a quick conversion from radians to degrees just remember that a full circle has 360 degrees and 2*Pi radians. The conversion is proportional: since 45 degrees is 1/8 of 360, it corresponds to 1/8 of 2*Pi radians. In other words 45 degrees corresponds to Pi/4.Assignment Part 3:a) Find the cos of 60 degrees.b) Compute the cosine of 30 degrees.User defined functionsAlthough there are many built in functions almost every application of Maple requires you to define your own functions. There is special syntax for this that must be followed exactly. Here is the general formnameOfFunction := x-> definitionOfFunctionIt is a common mistake to use = instead of :=Example. To define f(x) = LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JkYrLUklbXN1cEdGJDYlLUYsNiZRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lMGZvbnRfc3R5bGVfbmFtZUdRKzJEfkNvbW1lbnRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtbkdGJDYlUSIyRidGOi9GPlEnbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRitGREYrRkQ= in Maple you write the commandf:= x->x^2;Once you have defined the function you can use the usual notation to evaluate the function at points in the domainf(5);f(-3);Restart It often causes trouble to use the same letter to define a function or expression without clearing the memory. To clear the memory we use the restart; command. This has the effect of removing all definitions from the computers memory. If there are definitions that you still want to use you must go back, put the cursor on the line with the definition and hit enter. The plot command The feature of Maple that we will use the most is the ability to draw detailed graphs. The basic command is named plot. A typical statement has the form plot (expression in x , x=a..b);restart;Example: Draw the graph of the function f:(x) = 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 showing x values between -2 and 4.The first step is to name the function. f:= x-> x^3-2*x + 1;
Now that the function is named we use the plot command as follows.plot(f(x),x=-2..4);
To use the plot command effectively you must choose the domain that best suits your problem.Topic 2: Finding zeroes of a function with plotExample: Use the plot command to find, to an accuracy of three decimal places, a positive value of x such that f(x)=0 It appears that there is a crossing around 0.8 so we use this as the center of plot interval.plot(f(x),x=0.4..1.2);
Now we have a pretty good idea about the crossing. Let's refine our graph for the pont near 0.6plot(f(x),x=0.6..0.64);
Since we want three decimal place accuracy we keep refining the plot.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We can now be sure that the crossing is 0.618 to an accuracy of three places.LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JlEiP0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRKlsyNTUsMCwwXUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==Assignment Part 4) Use the plot command to determine how many times the graph of y = x^5 -2*x^3 + x^2 -7 crosses the x-axis. Find one of the crossings to an accuracy of 3 decimal places.Interactive graph plotting You can also plot the graph without remembering the exact commandLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSJmRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEwJkFwcGx5RnVuY3Rpb247RicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlEtSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSJ4RidGNEY3Rj5GKw==JSFHRight click on the blue f(x) above and choose plot and then plot builder from the menu that appears. Then choose plot. The graph appears and also the explicit command that we could have typed.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JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlExJkludmlzaWJsZVRpbWVzO0YnLyUwZm9udF9zdHlsZV9uYW1lR1ErMkR+Q29tbWVudEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZGRisvJStleGVjdXRhYmxlR0Y3RjI=You can change the range and domain interactively by right clicking on the graph above and select Axes and then Range from the menu. Then choose the domain and range that you want. Assignment Part 5 Experiment with this feature to recreate what we did above with explicit formulas.Topic 3: Plotting several graphs at onceIt is often useful to plot several graphs on the same set of axes. This is done by putting them inside { }. In Maple language this creates a list of functions and all of the functions in the list are plotted together.restart;f:= x-> -x;
g:= x-> 2*x+4;
h:= x-> 3;
plot({f(x),g(x),h(x)},x =-5..5);
Assignment Part 6: On the same set of axes draw the graphs of 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, 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 and 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. Which color graph goes with which equation? Describe in detail how adding a constant to a function changes the graph. Does it matter if you add a positive or a negative number? How?Assignment Part 7: On the same set of axes draw the graphs of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYmUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJTBmb250X3N0eWxlX25hbWVHUSsyRH5Db21tZW50RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjcvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtRiM2Jy1GLDYmUSRzaW5GJy9GNUZFRjdGQS1GPjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0ZBRkNGRkZIRkpGTEZORlAvRlNRJjAuMGVtRicvRlZGW28tRiM2Ji1GPjYuUSIoRidGN0ZBL0ZERjZGRi9GSUY2RkpGTEZORlAvRlNRLDAuMTY2NjY2N2VtRicvRlZGZW8tRiM2JC1GLDYmUSJ4RidGNEY3RjpGQS1GPjYuUSIpRidGN0ZBRmJvRkZGY29GSkZMRk5GUEZkby9GVlEsMC4xMTExMTExZW1GJ0ZBRitGQUYrRkFGK0ZB, 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 and 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 with domain x= 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. In Maple LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUwZm9udF9zdHlsZV9uYW1lR1ErMkR+Q29tbWVudEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y1 is written Pi (not pi and not PI). Which color graph goes with which equation? Describe in detail how multiplying a function by a positive constant changes the graph. Does it matter if you multiply by a number bigger than one or smaller than one? How?Assignment Part 8: Let f(x) = 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. (The Maple name of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictSSVtc3VwR0YkNiUtSSNtb0dGJDYuUSJlRicvJTBmb250X3N0eWxlX25hbWVHUSsyRH5Db21tZW50RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRk0tRiw2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnRjYvRjpRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0YrRjk= is exp(x). Never write e^x or exp^x. ) On the same set of axes draw the graphs of y=f(x) and y = -f(x). Describe in detail how multiplying a function by -1 changes the graph.