{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 9 "Math 2270" }}{PARA 0 "" 0 " " {TEXT -1 14 "MAPLE TUTORIAL" }}{PARA 0 "" 0 "" {TEXT -1 16 " Septemb er 2002" }}{PARA 0 "" 0 "" {TEXT -1 65 " The purpose of this tuto rial is to get you going with MAPLE," }}{PARA 0 "" 0 "" {TEXT -1 67 "p robably in our Math Lab. You can follow this tutorial to log onto" }} {PARA 0 "" 0 "" {TEXT -1 66 "the Math Lab machines, familiarize yourse lf with how they operate," }}{PARA 0 "" 0 "" {TEXT -1 69 "introduce yo urself to the software MAPLE, and use it to do some basic" }}{PARA 0 " " 0 "" {TEXT -1 69 "matrix computations. related to the linear algebra we've been talking" }}{PARA 0 "" 0 "" {TEXT -1 64 "about. Depending o n your previous eperience you may want to skip" }}{PARA 0 "" 0 "" {TEXT -1 19 "various sections. " }}{PARA 0 "" 0 "" {TEXT -1 68 " \+ Your actual Maple assignment can be found by going to the Maple" }} {PARA 0 "" 0 "" {TEXT -1 33 "page from our course homepage, at" }} {PARA 0 "" 0 "" {TEXT -1 67 "http://www.math.utah.edu/~kapovich/teachi ng11.html. (This tutorial" }}{PARA 0 "" 0 "" {TEXT -1 17 "lives there too.)" }}{PARA 0 "" 0 "" {TEXT -1 66 " Our class projects can be done in versions five and above of" }}{PARA 0 "" 0 "" {TEXT -1 59 "Ma ple, with minor changes. A student version of Maple for" }}{PARA 0 " " 0 "" {TEXT -1 70 "home computers is available from the bookstore for approximately $100." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 30 " Using the Math Computer Lab:" }}{PARA 0 "" 0 "" {TEXT -1 47 "The Math Department Computer Lab is located in:" }}{PARA 0 "" 0 "" {TEXT -1 46 "1) T.Benny Rushing Center between JW and LCB. \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 26 "2) th e South Physics 205, " }}{PARA 0 "" 0 "" {TEXT -1 63 "i.e. on the East (uphill) end of the second floor of then brick" }}{PARA 0 "" 0 "" {TEXT -1 70 "building immediately north of the Math building JWB. Roo m 205 is just" }}{PARA 0 "" 0 "" {TEXT -1 26 "inside the East entrance . " }}{PARA 0 "" 0 "" {TEXT -1 34 "Physics and Math share this lab. \+ " }}{PARA 0 "" 0 "" {TEXT -1 6 "Useful" }}{PARA 0 "" 0 "" {TEXT -1 67 "information about most aspects of the lab can be found by following" }}{PARA 0 "" 0 "" {TEXT -1 58 "links from the Math Department web page s, e.g. starting at" }}{PARA 0 "" 0 "" {TEXT -1 70 "http://www.math.ut ah.edu/ugrad/lab. You can find out about X-windows," }}{PARA 0 "" 0 " " {TEXT -1 56 "Unix commands, Maple, Netscape, file editing, mail, etc ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 15 "1a) \+ Logging on:" }}{PARA 0 "" 0 "" {TEXT -1 68 "Almost all students who ar e registered in Math 2270, or in any other" }}{PARA 0 "" 0 "" {TEXT -1 65 "math class, will already have accounts set up in our lab. Sin ce" }}{PARA 0 "" 0 "" {TEXT -1 56 "these accounts are created from Uni versity class lists, " }}{PARA 0 "" 0 "" {TEXT -1 66 "late-registering students may not be accounted for. If you fit in" }}{PARA 0 "" 0 "" {TEXT -1 63 "this case the lab assistant can help you apply for an acc ount -" }}{PARA 0 "" 0 "" {TEXT -1 66 "provided you have brought your \+ student I.D. to show that you are a" }}{PARA 0 "" 0 "" {TEXT -1 19 "Un iversity student." }}{PARA 0 "" 0 "" {TEXT -1 66 " The lab machine s are left on - move the mouse or hit a key to" }}{PARA 0 "" 0 "" {TEXT -1 69 "wake yours up. There are two possibilities for the dial og box which" }}{PARA 0 "" 0 "" {TEXT -1 10 "appears. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "(A) If you get a dia log window asking you to \"select a server to log" }}{PARA 0 "" 0 "" {TEXT -1 67 "on to\", use the mouse to select one which has \".math\" \+ in its name. " }}{PARA 0 "" 0 "" {TEXT -1 64 "Then O.K. your choice by clicking in the \"accept\" box. In a few" }}{PARA 0 "" 0 "" {TEXT -1 68 "seconds a login window should appear, asking for your login nam e and" }}{PARA 0 "" 0 "" {TEXT -1 70 "password, and have \"Mathematic s\" written in red on the top. (If the" }}{PARA 0 "" 0 "" {TEXT -1 64 "login window says \"Physics\" you have accidently chosen a physics " }}{PARA 0 "" 0 "" {TEXT -1 66 "server, and you should type \"control C\" to go back to the previous" }}{PARA 0 "" 0 "" {TEXT -1 7 "step.) \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 63 "(B) \+ If instead you get a dialog window which says \"Welcome to" }}{PARA 0 "" 0 "" {TEXT -1 65 "Orion\", highlight \"options\" with your mouse, and from its submenu" }}{PARA 0 "" 0 "" {TEXT -1 70 "choose \"remote \+ login\" and then \"choose host from list\". This will get" }}{PARA 0 "" 0 "" {TEXT -1 67 "you the window in (A), from which you proceed as \+ above. If you are" }}{PARA 0 "" 0 "" {TEXT -1 32 "confused, ask the l ab assistant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Your login name is made out of your initials. " }}{PARA 0 "" 0 "" {TEXT -1 31 "If your name is Karl Fred Gauss" }}{PARA 0 "" 0 "" {TEXT -1 55 " then your login name is c-gskf, following the recip e: " }}{PARA 0 "" 0 "" {TEXT -1 68 "c-(first letter of last name)(last letter of last name)(first letter" }}{PARA 0 "" 0 "" {TEXT -1 61 "of \+ first name)(middle initial). If there are multiple people" }}{PARA 0 "" 0 "" {TEXT -1 70 "registered this term with the same initials, then rather than c-gskf," }}{PARA 0 "" 0 "" {TEXT -1 64 "they are assigne d login names with a numerical suffix, c-gskf1," }}{PARA 0 "" 0 "" {TEXT -1 70 "c-gskf2, c-gskf3, etc. Mr. Gauss would not know beforeha nd which case" }}{PARA 0 "" 0 "" {TEXT -1 66 "he fell into, so would p robably try c-gskf first, followed by his" }}{PARA 0 "" 0 "" {TEXT -1 70 "password. In case of failure he would then try c-gskf1, then c -gskf2," }}{PARA 0 "" 0 "" {TEXT -1 64 "etc, through c-gskf4. Then he \+ would find a lab assistant. After" }}{PARA 0 "" 0 "" {TEXT -1 67 "ent ering your try at a login name, type the ``return'' key and the" }} {PARA 0 "" 0 "" {TEXT -1 38 "cursor should be in the password box. " } }{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 62 "Your in itial password is just the gskf part of your login name" }}{PARA 0 "" 0 "" {TEXT -1 70 "followed by the last four digits of your student I.D . number. If Mr." }}{PARA 0 "" 0 "" {TEXT -1 68 "Gauss has ID number 000735421 then his initial password is gskf5421," }}{PARA 0 "" 0 "" {TEXT -1 66 "regardless whether his login name was c-gskf or c-gskf3. \+ If the" }}{PARA 0 "" 0 "" {TEXT -1 70 "login fails try again and th en try the different login names suggested" }}{PARA 0 "" 0 "" {TEXT -1 67 "above. One possibility is that your account was created using \+ your" }}{PARA 0 "" 0 "" {TEXT -1 70 "social security number (which use d to be used for student ID number). " }}{PARA 0 "" 0 "" {TEXT -1 69 " If failure continues find a lab assistant and he/she will help you. \+ " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "Once \+ you are logged in successfully a ``local'' window should appear. " }} {PARA 0 "" 0 "" {TEXT -1 65 "Notice that it has various parts: borders on the top (title bar)," }}{PARA 0 "" 0 "" {TEXT -1 69 "borders on th e side (scroll bar), etc. If you move your mouse on its" }}{PARA 0 " " 0 "" {TEXT -1 69 "pad your pointer (called cursor) moves around the \+ screen. If you want" }}{PARA 0 "" 0 "" {TEXT -1 62 "to work in a windo w, the cursor should be in it. You can make" }}{PARA 0 "" 0 "" {TEXT -1 61 "multiple local windows by pressing the right mouse button and" }}{PARA 0 "" 0 "" {TEXT -1 23 "highlighting \"local\". " }}{PARA 0 " " 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 41 "1b) Changing pa ssword: After logging in" }}{PARA 0 "" 0 "" {TEXT -1 59 "you must cha nge your default password into a personal one. " }}{PARA 0 "" 0 "" {TEXT -1 70 "You do this as follows: Get your cursor into a local wind ow. Type the" }}{PARA 0 "" 0 "" {TEXT -1 13 "unix command " }}{PARA 0 "" 0 "" {TEXT -1 7 "passwd " }}{PARA 0 "" 0 "" {TEXT -1 47 "followed by return, and follow the directions. " }}{PARA 0 "" 0 "" {TEXT -1 70 "Your new password should be exactly 8 characters long. Don't choo se a" }}{PARA 0 "" 0 "" {TEXT -1 66 "word in the dictionary or a prope r name. Composites of dictionary" }}{PARA 0 "" 0 "" {TEXT -1 65 "word s, like strawdog, are good. Even better is to use one or two" }} {PARA 0 "" 0 "" {TEXT -1 69 "upper case letters, e.g. strAwdog. For s till more security, use some" }}{PARA 0 "" 0 "" {TEXT -1 69 "digits, e .g. strAw4o9. It takes about 15 minutes for a new password" }}{PARA 0 "" 0 "" {TEXT -1 70 "to take effect. If a password is not changed w ithin the first several" }}{PARA 0 "" 0 "" {TEXT -1 63 "weeks of class , then your computer account will be disabled for" }}{PARA 0 "" 0 "" {TEXT -1 68 "security reasons. Make sure to write down your password \+ in a secure" }}{PARA 0 "" 0 "" {TEXT -1 42 "place, in case your memory is not perfect." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "1c) Logging out: Move the cursor out of all windows (int o the" }}{PARA 0 "" 0 "" {TEXT -1 65 "background), press the left mous e button and choose the last menu" }}{PARA 0 "" 0 "" {TEXT -1 70 "item : Exit X-Windows. (You probably don't want to do this now, but at" }} {PARA 0 "" 0 "" {TEXT -1 38 "least locate the menu item for later.)" } }{PARA 0 "" 0 "" {TEXT -1 62 " At this point you are ready to get \+ used to the X-windows:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 55 "2) X-windows, opening netscape, maple, mail, more: \+ " }}{PARA 0 "" 0 "" {TEXT -1 70 "Xwindows are not so different from P.C. windows or Mac windows; on the" }}{PARA 0 "" 0 "" {TEXT -1 60 "o ther hand they have their own idiosyncracies, so you should" }}{PARA 0 "" 0 "" {TEXT -1 67 "experiment to see how to open and close windows , resize them, move" }}{PARA 0 "" 0 "" {TEXT -1 56 "them about, and f ind them if they happen to get hidden. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "For your Math 2270 purposes you need to be able to open Netscape (to" }}{PARA 0 "" 0 "" {TEXT -1 63 "downl oad files) and Maple (to work on them). Open Netscape by" }}{PARA 0 "" 0 "" {TEXT -1 69 "finding it on one of your mouse buttons, under th e choice \"browsers\"," }}{PARA 0 "" 0 "" {TEXT -1 69 "or by moving yo ur cursor into a local window and then typing netscape" }}{PARA 0 "" 0 "" {TEXT -1 67 "&, followed by . The & tells X-windows to cr eate a separate" }}{PARA 0 "" 0 "" {TEXT -1 66 "process for netscape, \+ keeping your local window free for more UNIX" }}{PARA 0 "" 0 "" {TEXT -1 69 "commands. Once netscape opens, go to the Math undergraduate pa ges at" }}{PARA 0 "" 0 "" {TEXT -1 64 "http://www.math.utah.edu/ugrad, and follow the links to explore " }}{PARA 0 "" 0 "" {TEXT -1 27 "comp uter lab information. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "Finally, open a Maple window one of two ways: from \+ the middle mouse" }}{PARA 0 "" 0 "" {TEXT -1 69 "button you may choose xmapleV7, or you can type the command xmaple &," }}{PARA 0 "" 0 "" {TEXT -1 69 "followed by , into a local window. The Math Depar tment's site" }}{PARA 0 "" 0 "" {TEXT -1 69 "license for version 7 of \+ Maple only allows a certain number of people" }}{PARA 0 "" 0 "" {TEXT -1 67 "to use it at once. If this number is exceeded you won't be abl e to" }}{PARA 0 "" 0 "" {TEXT -1 70 "run version 7, but you can use th e Mouse to open xmapleV5.1, for which" }}{PARA 0 "" 0 "" {TEXT -1 40 " our site license allows unlimited use. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "3) Maple: " }}{PARA 0 "" 0 "" {TEXT -1 69 " If you are starting the tu torial at this point (because you're doing" }}{PARA 0 "" 0 "" {TEXT -1 63 "it on your own at another location or already knew the Math Lab " }}{PARA 0 "" 0 "" {TEXT -1 68 "system), you should have opened a map leV6 or mapleV7 (worst case V5)" }}{PARA 0 "" 0 "" {TEXT -1 32 "window as well as a web browser." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "Maple is partly just a very fancy calculator; it \+ can do practically" }}{PARA 0 "" 0 "" {TEXT -1 68 "any undergraduate m athematics computation or symbolic manipulation. " }}{PARA 0 "" 0 "" {TEXT -1 70 "You can write programs in Maple and draw pictures as well . If you are" }}{PARA 0 "" 0 "" {TEXT -1 70 "doing a homework assignm ent you can intersperse text with computations" }}{PARA 0 "" 0 "" {TEXT -1 67 "using the toolbar: to get a computation prompt click on \+ the ``[>''" }}{PARA 0 "" 0 "" {TEXT -1 69 "box near the top. To inser t text click on the ``T'' box. Or you can" }}{PARA 0 "" 0 "" {TEXT -1 70 "change command fields (starting with \"[>\") into text fields b y putting" }}{PARA 0 "" 0 "" {TEXT -1 69 "the cursor into them and the n choosing \"T\". You can use the mouse to" }}{PARA 0 "" 0 "" {TEXT -1 68 "cut, paste, and edit a document. You can change fonts, formats , and" }}{PARA 0 "" 0 "" {TEXT -1 66 "use other standard text editing \+ tools by choosing appropriate menu" }}{PARA 0 "" 0 "" {TEXT -1 69 "ite ms. This document you are reading is a Maple document even though" }} {PARA 0 "" 0 "" {TEXT -1 65 "it is largely text. You will learn by do ing - and by asking your" }}{PARA 0 "" 0 "" {TEXT -1 30 "neighbor or t he lab assistant." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 18 "New User's Tour: " }}{PARA 0 "" 0 "" {TEXT -1 68 "Under \+ the Help button at the top right of your Maple window you will" }} {PARA 0 "" 0 "" {TEXT -1 63 "find the choice \"New User's Tour\". Thi s is a good way to learn" }}{PARA 0 "" 0 "" {TEXT -1 65 "generally abo ut what Maple can do. After making this menu choice" }}{PARA 0 "" 0 " " {TEXT -1 70 "Maple may hide the beginning of the tour behind other a ctive windows; " }}{PARA 0 "" 0 "" {TEXT -1 68 " use the \"Window\" me nu item to bring the tour window to the front. " }}{PARA 0 "" 0 "" {TEXT -1 66 "If you wish you can explore now, or you can continue with the Math" }}{PARA 0 "" 0 "" {TEXT -1 67 "2270 notes below and come ba ck to the tour later. To close the new" }}{PARA 0 "" 0 "" {TEXT -1 67 "tour (or any other top window), use the ``close'' option inside th e" }}{PARA 0 "" 0 "" {TEXT -1 70 "``file'' menu item. To keep the tou r open but bring another window to" }}{PARA 0 "" 0 "" {TEXT -1 36 "the front, use ``window'' menu item." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 25 "Entering Maple commands: " }}{PARA 0 "" 0 "" {TEXT -1 70 "To give you a flavor of what Maple can do, we will t ry a few commands." }}{PARA 0 "" 0 "" {TEXT -1 66 " Move your cursor i nto the \"Untitled\" (new) Maple window which you" }}{PARA 0 "" 0 "" {TEXT -1 64 "created in step (2). Commands begin on lines having a \+ command" }}{PARA 0 "" 0 "" {TEXT -1 70 "prompt ``>'', and should be en ded with either a semicolon ; or a colon" }}{PARA 0 "" 0 "" {TEXT -1 70 ": If you end with a semicolon you will see visible output, if you end" }}{PARA 0 "" 0 "" {TEXT -1 69 "with a colon the output will be s uppressed even though the command is" }}{PARA 0 "" 0 "" {TEXT -1 62 "e xecuted. Maple will not execute a command until you type the" }} {PARA 0 "" 0 "" {TEXT -1 65 "``return'' or ``enter'' key. If you have a multiline command use" }}{PARA 0 "" 0 "" {TEXT -1 52 "``shift-retur n'' to change lines without executing. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "If you incorrectly align parentheses or brackets, or do something else" }}{PARA 0 "" 0 "" {TEXT -1 69 "whi ch makes your command unexecutable you will get a ``syntax error''" }} {PARA 0 "" 0 "" {TEXT -1 68 "message and Maple will try to point out y our mistake with the cursor" }}{PARA 0 "" 0 "" {TEXT -1 70 "and crypti c diagnostic phrases. After a while you will become good at" }}{PARA 0 "" 0 "" {TEXT -1 68 "fixing these mistakes but they can be annoying \+ at first. Spaces are" }}{PARA 0 "" 0 "" {TEXT -1 68 "ignored in Maple , so you may use them to make input easier to read. " }}{PARA 0 "" 0 " " {TEXT -1 67 "You can enter explanatory comments in a command line by inserting a" }}{PARA 0 "" 0 "" {TEXT -1 70 "``#'' to the left of the \+ comments; Maple ignores any text after the #." }}{PARA 0 "" 0 "" {TEXT -1 68 " Sometimes this is more informative then entering nearby \+ explanatory" }}{PARA 0 "" 0 "" {TEXT -1 69 "text, especially if you ar e explaining various steps in a subroutine." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 " Now, let's try some comman ds. (You try just the math commands," }}{PARA 0 "" 0 "" {TEXT -1 69 "t he editorial comments were only added to explain what the particular" }}{PARA 0 "" 0 "" {TEXT -1 66 "commands are illustrating ! ) Check th at you understand what each" }}{PARA 0 "" 0 "" {TEXT -1 17 "command is doing." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "3+4; 4+5: 6 * 7; #one of these computations will not be sh own " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " #even tho ugh all three will be done." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "(3 +4)7; #if you want to multiply you must use *, so after " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " #trying the comman d as given insert a * to fix the " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " #resulting syntax error. You can execute a line or" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 " #exec ution group (bracketed on the left) if " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 " #your cursor is anywhere in it. You can mov e the " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 " #cursor with the mouse or the arrow keys. Maple will " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 64 " #try to put it in a good place if it detects an error." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "(3+4) ^2/7; 3+4^2/7; evalf(3+4^2/7); #the evalf command gives a" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "decimal " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 62 " #approximation instead of an algebraic ex pression. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 " #Notice th at if given a choice, Maple computes powers " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 58 " #first, then multiplies and divides, and fi nally" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 " #adds or subtrac ts." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "diff(x^2,x); #``differentia te x^2 with respect to x''" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "diff(exp(sin(x))*x^3,x); #a harder differentiation problem" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " #you should get ou tput:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "f:= x-> exp(sin(x) )*x^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "diff(f(x),x); \+ #the same problem done in two steps. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 " #The first line shows the format for def ining" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 " #functio ns in Maple. (Did you use ``shift-ret''?) " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "int(t^2*exp(t),t); #``integrate (t^2)*exp(t) wit h respect " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 " #to t'' (Maple doesn't put in the integration constant.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "int(t^3*exp(sin(t)),t); #this show s that Maple is not God:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 " #If it can't find an elementary-function" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 " #antiderivative it just echos w hat you put in." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " \+ #you should get: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "eva lf(int(t^3*exp(sin(t)),t=0..1)); #But you could do " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 " #a definite integral numericall y even if Maple " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 " \+ #can't compute an elementary antiderivative" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 45 "Pi;exp(1);evalf(Pi);evalf(exp(1));infinity; \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 " #some importa nt numbers" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 14 "Entering Text:" }}{PARA 0 "" 0 "" {TEXT -1 70 "Scroll to somewhere in your worksheet and add s ome text with the ``T''" }}{PARA 0 "" 0 "" {TEXT -1 69 "menu item. (I f you move your cursor to a command field and the press" }}{PARA 0 "" 0 "" {TEXT -1 62 "the [> button with your mouse, Maple makes a new com mand field" }}{PARA 0 "" 0 "" {TEXT -1 70 "directly below it. If you \+ move to the new command field and press the" }}{PARA 0 "" 0 "" {TEXT -1 67 "T button you will have a text field into which you may write, u sing" }}{PARA 0 "" 0 "" {TEXT -1 60 "the rudimentary word processing t ools on the Maple menu bar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 66 "Now scroll to the top of your file and insert t he title ``My first" }}{PARA 0 "" 0 "" {TEXT -1 70 "Maple worksheet'' \+ (center it with the menu option on the right side of" }}{PARA 0 "" 0 " " {TEXT -1 65 "the toolbar), as well as your name and today's date. Wh en you are" }}{PARA 0 "" 0 "" {TEXT -1 69 "doing your Maple projects y ou will be expected to hand in more than a" }}{PARA 0 "" 0 "" {TEXT -1 70 "page of computations: You will be expected to add text explanat ions of" }}{PARA 0 "" 0 "" {TEXT -1 24 "what you've been doing. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Saving Fi les:" }}{PARA 0 "" 0 "" {TEXT -1 66 "It is always a good idea to save \+ your maple file periodically. Do" }}{PARA 0 "" 0 "" {TEXT -1 69 "this now using the tool bar, using the \"save\" option under the \"File\" " }}{PARA 0 "" 0 "" {TEXT -1 67 "menu item. The first time you save a \+ new file, and any time you use" }}{PARA 0 "" 0 "" {TEXT -1 65 "the \"s ave as\" option, you will be asked to name your file and say" }}{PARA 0 "" 0 "" {TEXT -1 68 "where you want to keep it. You name it in the \+ left part of the box," }}{PARA 0 "" 0 "" {TEXT -1 69 "being careful to keep the suffix \".mws\" so that Maple knows this file" }}{PARA 0 "" 0 "" {TEXT -1 69 "is a Maple Work Sheet. If your directory is new you probably haven't" }}{PARA 0 "" 0 "" {TEXT -1 68 "made any subdirector ies yet (unix command mkdir, in a local window)," }}{PARA 0 "" 0 "" {TEXT -1 68 "but as you create more files you may wish to organize whe re you save" }}{PARA 0 "" 0 "" {TEXT -1 65 "them using the tree struct ure of Unix directories, which you can" }}{PARA 0 "" 0 "" {TEXT -1 68 "follow in the right side of your saving box. Unfortunately our UN IX" }}{PARA 0 "" 0 "" {TEXT -1 67 "is not set up so that you can visua lly see your directory/file tree" }}{PARA 0 "" 0 "" {TEXT -1 66 "like \+ in PC windows or Macs. You use various UNIX commands in your" }} {PARA 0 "" 0 "" {TEXT -1 70 "local window to organize your directories . For more information about" }}{PARA 0 "" 0 "" {TEXT -1 65 "this, g o to http://www.math.utah.edu/ugrad/helpforunix.html. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "It will probably h appen some time that you will crash Maple long after" }}{PARA 0 "" 0 " " {TEXT -1 69 "your last save. This will not make you feel happy but \+ will teach you" }}{PARA 0 "" 0 "" {TEXT -1 22 "an important lesson. \+ " }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}{PARA 0 "" 0 "" {TEXT -1 9 "Pr inting:" }}{PARA 0 "" 0 "" {TEXT -1 66 "Go to the file menu option and choose the print option. You get a" }}{PARA 0 "" 0 "" {TEXT -1 65 "l ittle printer setup box. If you then click on the print command" }} {PARA 0 "" 0 "" {TEXT -1 68 "diamond, followed by ``enter'' or by a cl ick on the print box at the" }}{PARA 0 "" 0 "" {TEXT -1 62 "bottom of \+ the window, a paper copy will come out of one of the" }}{PARA 0 "" 0 " " {TEXT -1 67 "printers at the side of the lab. Do this now. Alterna tely, if you" }}{PARA 0 "" 0 "" {TEXT -1 63 "want to use a different p rinter, you can use the output to file" }}{PARA 0 "" 0 "" {TEXT -1 70 "diamond to create a postscript file which you can then print anywhere ," }}{PARA 0 "" 0 "" {TEXT -1 61 "using the appropriate unix commands. For example, to print a" }}{PARA 0 "" 0 "" {TEXT -1 68 "postscript f ile to the lab printers from a local window, the command" }}{PARA 0 " " 0 "" {TEXT -1 66 "would be \"lpr -P b129lab1\", or \"lpr -P b129lab 2\", followed by the" }}{PARA 0 "" 0 "" {TEXT -1 70 "return key. You \+ do not put in the quote marks, but you are careful to" }}{PARA 0 "" 0 "" {TEXT -1 68 "leave spaces exactly as indicated. The lpr stands for line printer," }}{PARA 0 "" 0 "" {TEXT -1 70 "the -P stands for print , and the b129lab1 or b129lab2 are the names of" }}{PARA 0 "" 0 "" {TEXT -1 67 "the two printers. If you have trouble printing ask a lab assistant" }}{PARA 0 "" 0 "" {TEXT -1 9 "for help." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Downloading Maple docum ents:" }}{PARA 0 "" 0 "" {TEXT -1 68 " This document is available onli ne in several formats, if you follow" }}{PARA 0 "" 0 "" {TEXT -1 34 "t he links from the 2270-2 homepage" }}{PARA 0 "" 0 "" {TEXT -1 66 "at h ttp://www.math.utah.edu/~kapovich/teaching11.html. Files with" }} {PARA 0 "" 0 "" {TEXT -1 68 "suffix \".mws\" or \".txt\" can be downlo aded from your browser and then" }}{PARA 0 "" 0 "" {TEXT -1 63 "opened from Maple. The \".mws\" suffix means the file is a Maple" }}{PARA 0 "" 0 "" {TEXT -1 67 "Worksheet, and should open from Maple to look j ust like this file. " }}{PARA 0 "" 0 "" {TEXT -1 66 "The \".txt\" suff ix is Maple text, and you should only try it if the" }}{PARA 0 "" 0 " " {TEXT -1 63 "\".mws\" file doesn't open. It's a cruder form of this file, but" }}{PARA 0 "" 0 "" {TEXT -1 68 "potentially more universal. The \".pdf\" versions of the file are for" }}{PARA 0 "" 0 "" {TEXT -1 70 "reading from your browser (with Acrobat reader), but you can't \+ execute" }}{PARA 0 "" 0 "" {TEXT -1 17 "these from Maple." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Go to the course h omepage address using your browser, follow the link" }}{PARA 0 "" 0 " " {TEXT -1 67 "to the Maple page, and find and save the 2270proj1.mws \+ file to your" }}{PARA 0 "" 0 "" {TEXT -1 15 "home directory." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "Now return to y our Maple window and use the ``file'' menu item to open" }}{PARA 0 "" 0 "" {TEXT -1 64 "proj1.mws. It should appear in the central box afte r you choose" }}{PARA 0 "" 0 "" {TEXT -1 66 "\"open\". Click on it wi th the mouse to highlight it and then click" }}{PARA 0 "" 0 "" {TEXT -1 70 "``OK'' or type ``return''. A copy of this tutorial should then appear" }}{PARA 0 "" 0 "" {TEXT -1 64 "in your Maple window, as a Map le document that you can work in. " }}{PARA 0 "" 0 "" {TEXT -1 66 "Not ice you can use the \"Window\" menu item at the top of your Maple" }} {PARA 0 "" 0 "" {TEXT -1 70 "window to change between various open fil es. (Sometimes when you open" }}{PARA 0 "" 0 "" {TEXT -1 65 "a new fi le it goes to the back of your pile. Then use the Window" }}{PARA 0 " " 0 "" {TEXT -1 38 "option to bring it back to the front.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "If you know the e xact URL of a Maple file, and you are in version 6 or" }}{PARA 0 "" 0 "" {TEXT -1 66 "7 of Maple, you can use the \"open URL\" option under \+ \"File\" to have" }}{PARA 0 "" 0 "" {TEXT -1 69 "Maple do the download ing and opening for you. This saves steps if it" }}{PARA 0 "" 0 "" {TEXT -1 16 "works correctly." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 70 "If you couldn't open the Maple worksheet \+ file, go back to your browser" }}{PARA 0 "" 0 "" {TEXT -1 68 "and save the \".txt\" version of the tutorial. Then go back to Maple," }} {PARA 0 "" 0 "" {TEXT -1 63 "and follow these directions: In order to open a ``Maple text''" }}{PARA 0 "" 0 "" {TEXT -1 64 "document, which this is, you must chose open from the file menu" }}{PARA 0 "" 0 "" {TEXT -1 70 "option. In the resulting open file dialog box go to the \+ filetype box" }}{PARA 0 "" 0 "" {TEXT -1 68 "at the bottom, click on \+ the triangle to see the list of choices, and" }}{PARA 0 "" 0 "" {TEXT -1 55 "use your mouse to choose ``Maple text.'' At this point" }} {PARA 0 "" 0 "" {TEXT -1 56 "``tut.txt should appear as a choice in th e central box. " }}{PARA 0 "" 0 "" {TEXT -1 67 "Click on it with the m ouse to highlight it and then click ``OK'' or" }}{PARA 0 "" 0 "" {TEXT -1 68 "type ``return''. A copy of this tutorial should then app ear in your" }}{PARA 0 "" 0 "" {TEXT -1 68 "Maple window, as a Maple d ocument that you can work in. The copy is" }}{PARA 0 "" 0 "" {TEXT -1 64 "not as pretty as your xerox (the execution groups are all singl e" }}{PARA 0 "" 0 "" {TEXT -1 69 "lines, and the text formatting is no t as neat, and some output may be" }}{PARA 0 "" 0 "" {TEXT -1 58 "lost ), but it is O.K. It has text and it has Maple input." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 17 "Execution Groups:" }}{PARA 0 "" 0 "" {TEXT -1 70 "You can modify the text and input using the toolbar and menu options. " }}{PARA 0 "" 0 "" {TEXT -1 69 "You wi ll notice many brackets on the left of the document. These are" }} {PARA 0 "" 0 "" {TEXT -1 65 "execution groups. Maple will execute eve rything in one execution" }}{PARA 0 "" 0 "" {TEXT -1 69 "group at once , and then move the cursor to the next execution group. " }}{PARA 0 " " 0 "" {TEXT -1 67 "You can create large execution groups by highlight ing sections of a" }}{PARA 0 "" 0 "" {TEXT -1 70 "document, going to t he Edit option and picking join execution groups. " }}{PARA 0 "" 0 "" {TEXT -1 63 "You can remove brackets by highlighting them with the mou se and" }}{PARA 0 "" 0 "" {TEXT -1 70 "deleting them with the delete k ey or the menu option. And you already" }}{PARA 0 "" 0 "" {TEXT -1 70 "learned how to insert new prompts or new text wherever your cursor is," }}{PARA 0 "" 0 "" {TEXT -1 46 "by using the [> and T buttons on \+ your toolbar." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 " Linear Algebra, and us ing Maple's help windows: So, it looks" }}{PARA 0 "" 0 "" {TEXT -1 70 "like Maple might be interesting to use in Calculus, but how do we \+ find" }}{PARA 0 "" 0 "" {TEXT -1 69 "out what it can do for us in that subject, or in another subject, say" }}{PARA 0 "" 0 "" {TEXT -1 69 "l inear algebra? It is instructive to use the Help directory located" }}{PARA 0 "" 0 "" {TEXT -1 64 "at the upper right-hand corner of the m aple window. That's what" }}{PARA 0 "" 0 "" {TEXT -1 23 "you're going to do now." }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}{PARA 0 "" 0 "" {TEXT -1 69 " Can Maple do matrix operations, or even define matr ices???? Of" }}{PARA 0 "" 0 "" {TEXT -1 69 "course!!! Here's how you would try to find the right commands if you" }}{PARA 0 "" 0 "" {TEXT -1 65 "didn't know them already, or if I wasn't going to tell you belo w:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 " \+ Click on the Help option at the upper right corner of your Maple" }} {PARA 0 "" 0 "" {TEXT -1 64 "window. A little window opens with furth er choices. Pick Topic" }}{PARA 0 "" 0 "" {TEXT -1 68 "Search, by hig hlighting it, and a help window should appear. (If it" }}{PARA 0 "" 0 "" {TEXT -1 69 "doesn't, it's hidden behind your worksheet; use the \+ ``window'' option" }}{PARA 0 "" 0 "" {TEXT -1 66 "in your menu to brin g it to the front.) Try searching for linear" }}{PARA 0 "" 0 "" {TEXT -1 69 "algebra. At this point you should get a help window abou t the linear" }}{PARA 0 "" 0 "" {TEXT -1 67 "algebra library. There s eem to be a lot of commands. You could try" }}{PARA 0 "" 0 "" {TEXT -1 65 "finding the one you wanted from this page, or you could do a mo re" }}{PARA 0 "" 0 "" {TEXT -1 68 "specific search. For example, eith er look up matrix, or click on it" }}{PARA 0 "" 0 "" {TEXT -1 66 "from the linear algebra page. Notice if you go to the bottom of a" }} {PARA 0 "" 0 "" {TEXT -1 67 "help window, you can often figure out how the command works without" }}{PARA 0 "" 0 "" {TEXT -1 35 "reading all the fine print above. " }}{PARA 0 "" 0 "" {TEXT -1 65 " We can u se matrices if we load the linear algebra library of" }}{PARA 0 "" 0 " " {TEXT -1 11 "procedures:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "with(linalg); #to hide the list of comman ds in this" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " #package use a colon instead of a semicolon" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "And now we copy the commands fr om the matrix help window: (For long" }}{PARA 0 "" 0 "" {TEXT -1 29 " ones we would use our mouse!)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "ma trix(2,2,[5,4,6,3]); #a 2 by 2 matrix with" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " #successive entries as indicated" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "matrix([[5,4],[6,3]]); #same matri x" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 " So that's how to make a mat rix. By the way, to close the help files" }}{PARA 0 "" 0 "" {TEXT -1 62 "after you've used them use the ``file/close '' sequence in the " }}{PARA 0 "" 0 "" {TEXT -1 64 "toolbar, or the equivalent key stroke given next to it, which is" }}{PARA 0 "" 0 "" {TEXT -1 69 "simultaneo us ``control-F4'' on my work station. Or you can keep them" }}{PARA 0 "" 0 "" {TEXT -1 68 "around and return to your worksheet with the `` window'' menu option." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 " Some Linear Algebra computations: Can you figure o ut the syntax" }}{PARA 0 "" 0 "" {TEXT -1 67 "of the commands and thei r meanings? Some of these commands will be" }}{PARA 0 "" 0 "" {TEXT -1 70 "useful later, use the help windows for more details about them . This" }}{PARA 0 "" 0 "" {TEXT -1 67 "simple example could easily be done by hand; larger ones could not." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "A:=matrix([[1,1,1],[2,3,2],[3,8,2]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " #coefficient matrix for a linear system," }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 " #``:='' is used to de fine the object on" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 " \+ #its left by the construction on its right" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A[2,3]; #one of the entries of A" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "b:=vector([1,1,-3]); #the right-ha nd side for" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 " #a li near system Ax=b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "augAb:= augment(A,b); #the augmented matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "C:=rref(augAb); #compute the reduced row echelon form " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 " #of the augmented matrix" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "x:=col(C,4); #r ead off the solution vector to Ax=b " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "evalm(A&*x)=evalm(b); #check your answer" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 " #NOTE A good way to do matrix operations use the evalm" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 " #command. Addition is +, but matrix multiplication" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 " #is &*. (Scalar times matrix is *.)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "x:=linsol ve(A,b); #another way to solve linear systems." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 53 "Ainv:=inverse(A); #the inverse matrix (if it e xists)!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "x:=evalm(Ainv &* b); #yet another way, for nonsingular matrices," }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 20 " #to solve Ax=b" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 48 "evalm(A&*Ainv); evalm(Ainv&*A); #just checkin g!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "evalm(A^3); evalm(A&* A&*A); evalm(A+3*A); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 " \+ transpose(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 " \+ #matrix powers, multiplications, addition," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " #transpose (what's that?) " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "with(plots): #this command loads pa ckages for plotting graphs" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 26 "To \+ plot graph of the line " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 5 "x+y=1" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "use the command " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "implicitplot(x+y=1, x=-1..3, y=-2.. 2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Or you can firs solve this equation using the command " }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "solve(x+y=1, y);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "and now you can plot the solution:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(\", x=- 1..3);" }}{PARA 0 "" 0 "" {TEXT -1 39 "Alternatively, you can plot as \+ follows:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "line:=implicitplot(x+y= 1, x=-1..3, y=-2..2):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "display(\{ line\});" }}{PARA 0 "" 0 "" {TEXT -1 73 "Using this command you can di splay two or more lines on the same picture:" }}{PARA 0 "" 0 "" {TEXT -1 24 "display(\{line1, line2\});" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }