A Quick Introduction to Maple 14 Maple is a computer algebra system that can do many computations for you. It also has good graphics capability. Among the tools available are student LinearAlgebra, MultivariateCalculus and VectorCalculus packages. (The bluish sections are links to help topics. Try one to see a help topic.) There are also standard LinearAlgebra and VectorCalculus packages. The student routines are meant specifically for learning. The regular packages are usually more flexible and contain more commands. Maple worksheets have two modes, document mode and worksheet mode. Document mode is good for documenting work. The worksheet mode is nice for computing. This is a document block in a worksheet mode document. This is a very short introduction. To get a more complete interoduction to the worksheet interface, see Chapter 2 of the User's Manual. Between these you will have seen all of the basics of Maple 11.

Most users eventually use the Maple mathematics format for input. Change to this mode by going into the tools>options>display menu. Set the input display to "Maple Notation." Here is how one does addition. Enter "3+4;" and hit the enter key. Note that the semicolon is required in multiline computations. Using a colon will suppress output. 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 To store a quantity in a named location use ":=". Here 10! is stored in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. a := 10!; There is no implicit multiplication in Maple 11, when using Maple Notation for input. (Some implicit multiplication is allowed in the document mode and in 2-D input mode.) a := 3; b := 4; 5*a; a*b; Most of the standard functions are accessed in the same manner as on a calculator. Here are sin and cos of 1.1. (In this case a <shift><enter> was used to put the expressions on different lines.) 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 A couple problem spots for people new to Maple are the exponential function and pi. You cannot use "e^x" for the exponential function or "pi" for the value of pi. The exponential function is exp(x) and the constant pi is in Pi. sin(pi); sin(Pi); e^2.; exp(2.); One can use the evalf command to evaluation an expression numerically. Here are a couple examples. Maple usually uses 10 decimal digits for numerical computations. a := cos(2); evalf(a); evalf(a,5); b := exp(2); evalf(b);

Maple can do many calculus operations. It can take derivatives or do integrals using the diff and int commands. diff(exp(x)-x/(x^2+1),x); int(exp(x)-x/(x^2+1),x); To do a definite integral one simply adds a range for the variable of integration. int(exp(x)-x/(x^2+1),x=0..5); To get a numerical answer, one uses the evalf command. evalf(int(exp(x)-x/(x^2+1),x=0..5));

There are two formats for vectors in Maple 10. They are incompatable with each other. The newer version is the one used in this worksheet. It is the Vector format. One can enter a vector in two basic ways. Here they are. a := Vector([1,2,3]); b := <1,2,3>; The operations of addition, subtration, and scalar multiplication are the same as for numbers. u := <2,-5,6>; v := <-3,4,-1>; u+v; v-u; 5*u; To compute vector products one needs a vector package. Here the LinearAlgebra package is loaded using the with command. with(LinearAlgebra): DotProduct(u,v); CrossProduct(u,v);

Ploting a function is fairly simple in Maple. One normally uses the plot command. Here is a plot of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiQtSSNtbkdGJDYkUSIyRidGOUY5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y5 from -4 to 4. plot(x^2,x=-4..4); There are many options that one can use for the plot command. They are list in plot,options. Here is the same plot with a different color, axes labels, and a title. plot(x^2,x=-4..4,title="y=x^2",labels=[x,y],color="DarkGreen"); Sometimes is is useful to limit the vertical range or to constrain the scaling by making the axes use the same scale. plot(x^2,x=-4..4,title="y=x^2",labels=[x,y],color="DarkGreen",view=[-4..4,-1..10],scaling=constrained);

To do these exercises, open a new worksheet using File>New>Worksheet Mode. Put your name at the top of the worksheet using a text block (CTRL-T). Insert a section, Insert>Section, for each problem. To insert a new prompt, [>, use CTRL-J. To insert a new line without executing, use CTRL-ENTER.

Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkmbWZyYWNHRiQ2KC1GLDYlUScmIzk2MDtGJ0YvRjItRiM2JC1JI21uR0YkNiRRIjRGJ0YyRjIvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRksvJSliZXZlbGxlZEdGMUYyRjItRiw2I1EhRidGMg== and 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.

Find the sum of the vectors (1,2,3,4) and (-3,4,-5,1) using Maple.

Find the square root of 141 to 5 decimal places. (If you do not know how to get the square root, go the Help>Maple Help and search for sqrt.)

Find the derivative and antiderivative of 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

Find the integral of 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 from 0 to 10.

Plot 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 from -5 to 5.

Plot 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 from -2 to 2 without vertical lines as vertical asymptotes and a vertical range of -20 to 20. (Hint: Look at plot,options.)