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0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 205 "" 0 "" {TEXT 217 121 "Author: Prof. Jim Calv ert, University of Idaho; calvert@uidaho.edu Modified by J. Johns on, Spring 1998, Spring 2007" }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 65 " \+ " }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 69 " \+ INTRODUCTION TO MAPLE" }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 119 "This worksheet has been mo dified from a worksheet designed for the \"Classic Maple.\" It works \+ best in the Classic mode." }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 206 "" 0 "" {TEXT 217 203 "1. MAPLE uses a worksheet in which you enter commands and view output from MAPLE. The workshee t is divided into regions which you can select from the INSERT menu a t the top of the MAPLE screen or the " }{TEXT 219 3 "[T]" }{TEXT 220 5 " and " }{TEXT 221 2 " [" }{TEXT 221 1 "]" }{TEXT 217 336 " icon. T he text you are now reading is written in a \"text region\". In a tex t region, MAPLE acts like a word processor. You enter commands for MA PLE to process in an \"input region\". An input region has the symbol \+ > in the left column; you can see many occurrences of > below. The ou tput from MAPLE is written in an \"output region\". " }{TEXT 203 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 206 "" 0 "" {TEXT 217 129 "If you find the type used for commands to be too small to read, you c an enlarge it by choosing the font size or the icons [x] " }{TEXT 222 3 "[X]" }{TEXT 217 3 " or" }{TEXT 223 4 " [X]" }{TEXT 217 1 "." } {TEXT 203 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 195 " Here are some examples of entering expressions and commands. The operation * must be used for multiplication. Each com mand ends with a semicolon. A quote refers to the previous expression. " }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 491 "The next line contains a command that I typed in. T here is no output from the command because it has not yet been execute d. This is true of all commands in this worksheet and in all of the ot hers. You must execute the commands yourself so you can see the outpu t develop. To execute the next command line, move the cursor to it wi th the mouse or by using down-arrow. When the cursor is on a command \+ line, you execute the command by pressing ENTER. The cursor may be an ywhere on the line." }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 " " }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 18 "(x+1)^4 * (x+2)^3;" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 196 "Now exe cute each of the next two commands and continue to execute commands as you encounter them while reading the text. Note that the % is used t o mean the \"answer\" in the last executed command." }{TEXT 217 0 "" } }{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 10 "expand(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 10 "factor(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 599 "2. You can assign any expression to a varia ble for use in later commands. You do this with the assignment operat ion \":=\" (colon followed by an equality sign). The next example sho ws that rational arithmetic is usually done exactly. You use \"evalf \" to see a decimal approximation. The default for decimals is 10 pla ces; however, you can see more places by specifying the number of digi ts with evalf. MAPLE has many built-in constants; the one we will most ly use is Pi. Note the capital P; MAPLE is case sensitive! If you typ e pi you will only get the Greek letter pi, not the numerical constant ." }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 38 "p:= 1153 * (3^58 + 5^40)/(29! - 7^36);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 9 "ev alf(p);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 12 "evalf(p,40);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 16 "h:= tan(3*Pi/7);" }{MPLTEXT 1 211 0 "" }}} {EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 12 "evalf(h,15);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 514 "3. There are two commands for differentiation, diff and D. They behave somewhat diffe rently as we will see through examples. The diff operator is used on \+ expressions and the D operator is used on functions. The diff operator is partial differentiation, and so you must specify the variable you \+ are differentiating with respect to; for higher derivatives you repeat the variable. (Notice the use of (\") below. You can use \" to refe r to the output of a previous line without having assigned it an name \+ with := .)" }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }} {PARA 207 "> " 0 "" {MPLTEXT 1 211 24 "diff(sin(x) * cos(x),x);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 10 "d iff(%,x);" }{MPLTEXT 1 211 0 "" }}{PARA 208 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 24 "diff(sin(x)*cos(x), x,x);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 12 "D(sin* cos);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 14 "D(sin*cos)(x);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 357 "4. The functions sin and cos (and many others) are built-in to Maple. Y ou can define your own functions with an arrow \"->\" which is forme d by typing minus (-) and greater than (>). Note that the D operator t akes a function as its argument and produces a function; whereas, the \+ diff operator takes an expression as its argument and produces an expr ession." }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 19 "f:= x -> sin(x)/x; " }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 5 "f(2);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 7 "f(2.0);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 5 "D( f);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 13 "diff(f(x),x);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 33 "g:= (x,y) -> (x^2-y^2)/(x^2+y^2);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 7 "g(3,4);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 8 "D[ 1](g);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 8 "D[2](g);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 601 "5. We now look at the Help that Maple provides. You wil l see that it is quite extensive. In fact, you do not need to remembe r the syntax of complicated commands because it is so easy to look it \+ up in Help. There are two ways to get help. If you know the name of \+ the command, you can get help with it directly by entering a ? followe d by the command name. Let us try it with diff and D. Move to the nex t command and execute it. Another option is to type the demand, place the cursor on the command, click and then move the \"arrow\" cursor t o the \"Help\" tab at the top of the page and click on Help." }{TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 5 "?diff" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 2 "?D" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 345 " If \+ you cannot remember the command, then you can get Help by working thro ugh an index. That method has the advantage that you need not know th e name of the command or feature that you need help with. Move the cu rsor to the Help menu at the top of the screen and choose Browser. Af ter you browse a while exit Help and return to this point." }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 723 "6. You can plot a function of one variable with plot and a fu nction of two variables with plot3d. You specify the range of the vari ables(s) with two dots. The plot is drawn in another window. You can g et full information on plotting by typing ?plot. You can shrink the \+ size of the plot by first clicking on the plot. Then move the cursor to the lower right corner of the frame and hold the left button of th e mouse down. With the cursor on this corner \"square,\" drag the cor ner of the frame until the plot is a desirable size. You may copy the \+ plot by moving the cursor to Edit and selecting Copy. Move the curso r to the location you want the plot to appear in worksheet, and choose Paste from the Edit menu. Try it!" }{TEXT 217 0 "" }}{PARA 205 "" 0 " " {TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 14 "plot(f,-5..5 );" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 0 "" }} {PARA 205 "" 0 "" {TEXT 217 246 "7. We will often use sets and lists. \+ A set is a group of objects without any implied order; the elements o f the set are enclosed in braces. A list is an ordered vector. Many \+ operations can be performed on sets and lists. Here are some samples." }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 17 "z:=\{sin,tan,exp\};" }{MPLTEXT 1 211 0 "" }}} {EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 5 "D(z);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 18 "zz:=[sin,tan,exp]; " }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 6 "D(zz);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 23 "plot(\{f,D(f)\},-20..20);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 188 "8. Maple can also integrate very well. Here are some examples. If you w ant a full discussion of the syntax, look at ?int. (Note: The # below \+ makes the rest of the command line a comment.)" }{TEXT 217 0 "" }} {PARA 207 "> " 0 "" {MPLTEXT 1 211 43 "int(sin(x),x=0..2); # A defin ite integral" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 62 "int(tan (x),x); \+ # An indefinite integral or antiderivative" }{MPLTEXT 1 211 0 "" }}} {EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 39 "int(1/(x^2 + 3*x + 1),x= 1..3); " }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 44 "9. Here are some misc ellaneous calculations." }{TEXT 217 0 "" }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 5 "100!;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 11 "ifactor(%);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 28 "e1:=(3*x^2-2*x-1)/(x^2+x-2);" } {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 13 "s implify(e1);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 28 "(x^2+2*x+3)*(x^3-2*x+3*x+5);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 10 "expand(%);" } {MPLTEXT 1 211 0 "" }}{PARA 208 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 17 "e2:= x-> e^(3*x);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 13 "evalf(e2(2)) ;" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 16 "e3:=x->exp(3*x);" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 13 "evalf(e3(2));" }{MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 207 "Look hard at the functions e2 and e3; there is an important lesson here. You enter the exponential function as exp(x) and not as e to the x power. The symbol e is just a letter that has no built-in value. " }}}{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 211 0 "" }}}{EXCHG {PARA 205 "" 0 "" {TEXT 217 166 "You can continue to experiment with Maple. When you are finished choose Exit from the file menu. You should respond to the query about saving the \+ worksheet with N. " }{TEXT 217 0 "" }}{PARA 205 "" 0 "" {TEXT 217 0 " " }}{PARA 207 "> " 0 "" {MPLTEXT 1 211 0 "" }}}{PARA 209 "" 0 "" {TEXT 224 0 "" }}{PARA 210 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0 0" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }