{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 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 } {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 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {TEXT -1 18 "Maple Command list" }}{PARA 257 "" 0 "" {TEXT -1 9 "Fall 2008" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 87 "Helpful commands for Math 2250, 2280. Su ggest more and I will add them to this list! " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 285 "If you see a command \"f oo\" that you like, try it! If you want more information or extra opt ions for foo, type ?foo in a math field and hit enter...the \"foo\" he lp window should open. (You can also find out about \"foo\" from the \+ help directory, at the upper right of your Maple window.)" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 256 9 "Constants" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 511 "c:=3; #defines c to be 3, then shift-enter \n #for another line\n #before executi ng an entire command field\nd:=4; #to define d to be 4 (could leave \+ both on \n #one line too)\nc;d; c+d; #should list 3, then 4, then 7.\nunassign('c','d'); #turn c, d back into letters \n \+ #(forward quotes!)\nc; d; c+d; #should be symbo ls c,d, c+d. \n #Maple ignores spaces\nc: d: c+d: #with a colon, Maple does the math, \n #but doesn't show you!" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 11 "Text fields" }}{PARA 0 "" 0 "" {TEXT -1 341 "I Made a text field h ere by first hitting the math prompt [> button in the menu bar, and th en turning that field into a text field by putting my cursor into it a nd hitting the T button. I erased the bracket (which originally looke d like the ones surrounding math fields) by highlighting the bracket w ith my mouse and hitting the delete key." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 9 "Functions" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1054 "restart: #clears ALL memory. You \+ can then reload\n #any commands you want by puttin g your\n #cursor anywhere into the command field a nd \n #hitting enter.\nf:=t->t^2*exp(t); #defin e the function f(t)=t^2*exp(t)\nf(z); #should return f( z)\nf(2); #should return f(2)\nevalf(f(2)); #sh ould be decimal value (i.e. floating point)\ng:=(z,w)->z^2+w^2; #a f unction of two variables\nggg:=(a,b,c)->a^2+b*exp(c); #or of three va riables\ng(2,1); #should be 5\nggg(1,2,0); #shou ld be 3\nggg(1,2,c); #should be 1+2*exp(c)\nz:=3; \+ #set z equal to 3\nz; #should be 3\ng(z,w); \+ #should be g(3,w), i.e. 9+w^2\nunassign('z'); #undefine z, and set it back to a letter\nz; #should be z aga in\nunassign('f'); #turn f back into a variable!\nf(t); \+ #maple echos f(t) because f no longer \n #h as meaning as a function\n " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT 259 25 "Integrals and Derivatives" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 724 "f:=t->t^2; #define f(t) to be t^2\nint(f(z ),z); #should be z^3/3 (Maple doesn't \n \+ #include the +C)\nint(f(x),x=0..1); #definite integral, should be 1 /3\ndiff(f(y),y); #should be 2*y\ndiff(f(t)^4,t); #should \+ equal 4*(f(t)^3)*2*t, by the \n #chain rule\nint(t ^3*exp(5*t)*sin(3*t),t); #maple is good!\nint(exp(sin(t)),t); #but n ot every integral has an \n #answer in terms\n \+ #of elelmentary functions - \n #i f maple can't do a computation, \n #it just echos \+ what you typed.\nint(exp(sin(t)),t=0..1); #no symbolic answer\nevalf( int(exp(sin(t)),t=0..1)); #decimal (approximate) answer" }}}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 5 "Plots" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 162 "with(plots): #loads the plotting library ( to see all the\n #commands in this library replace colon with\n #semicolon" }}}{PARA 0 "" 0 "" {TEXT 261 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 444 "f:=theta-> sin(theta); #f(x)=sin(x)\nplot(f(t),t=0..2*Pi,color=green,title=`sin usoidal!`);\n #plain vanilla plot of a graph in th e plane\n #click on the plot, then on a point in\n #the plot, and a window at upper left says\n \+ #where you are!\n #resize plots as if you were in MSWord -\n #grab a corner with you r mouse, and move it." }}}{PARA 0 "" 0 "" {TEXT 262 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 290 "plot1:=plot(f(t),t=-2*Pi..2*Pi,col or=green): #use colon or maple\n #will list all t he points in the plot!\nplot2:=plot(.2*t^2,t=-5..5,color=black):\nplot 3:=plot([cos(s),s,s=0..2*Pi],color=blue): #parametric curve\ndisplay( \{plot1,plot2,plot3\},title=`three curves at once!`);" }}}{PARA 0 "" 0 "" {TEXT 263 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 619 "f:=(x ,y)->x^2-y^2; #function of two variables \nplot1:=plot3d(f( x,y),x=-1..1,y=-1..1,color=blue):\n #graph of z=x^ 2-y^2\nplot2:=plot3d([.5*cos(theta),.5*sin(theta),z],\n theta =0..2*Pi,z=0..1,color=pink): #vertical cylinder,\n \+ #defined parametrically!\nplot3:=plot3d(.5,x=-1..1,y=-1..1,color=bro wn): \n #horizontal plane z=0.5\ndisplay(\{plot1,p lot2,plot3\},axes=boxed); #if you click\n #on the plot you can \+ move it around in space!\n #and a box in upper left of window wi ll give you\n #the spherical coordinates you're looking from!" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 383 "implicitplot(f(x,y)=.5,x= -1..1,y=-1..1,color=black); #this is the\n #level curve w here x^2-y^2=.5\ng:=(x,y)->3*x^2-2*x*y+5*y^2: \n #a quad ratic function of two variables\nimplicitplot(g(x,y)=1,x=-2..2,y=-2..2 ); \n #rotated ellipse,kind of badly drawn!\nimplicitplot (g(x,y)=1,x=-2..2,y=-2..2,color=blue,grid=[80,80]);\n #be tter resolution" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 22 "Differential equations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "with(DEtools): #differential equation package" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 424 "deqtn:=diff(y(x),x)=y(x); \+ #the DE dy/dx = y ....note you \+ \+ \+ #must write y(x), and not just y\ndsolve (deqtn,y(x)); #general solution\ndsolve(\{deqtn,y(0)=2\},y(x)); #IVP\ndsolve(\{deqtn,y(0)=y[0]\},y(x)); #general IVP" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "DEplot(deqtn,y(x),x=-1..1,y=-2..2, [[y(0)=0],[y(0)=1],\n [y(.3)=-2]],arrows=line,color=blue,linecolor =green);\n #slope field with solution graphs" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 265 21 "Algebra \+ and equations" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "g:=t->exp( -k*t)*(cos(omega*t)*exp(2*k*t));\nsimplify(g(z)); #simplify will try to simplify\n #you can ask it to try special tricks, \n #see help windows.\nh:=x->sin(x)^2+cos(x)^2;\nsimp lify(h(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "F:=x->((3*x^ 2+5*x+7)/(x^4-x));\nconvert(F(x),parfrac,x); #partial fractions!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "g:=t->exp(t);\nsolve(g(t)=2 ); #solve an equation, maple tries \n # symbolic solution\nsolve(g(t)=2.); #unless you enter a decimal" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 189 "Digits:=5; #use a different number of sig nificant\n #digits, rather than the default of 1 0.\nsolve(g(t)=2.); #cleaner looking, but less accurate answer. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PAGEBK }{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 14 "Linear Algebra" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 255 "with(linalg): #thi s package contains the linear algebra\n #commands ...there's another package called\n #LinearAlgeb ra, and it has different \n #commands to do the s ame sort of operations" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 " A:=matrix(3,3,[1,2,3,4,5,6,7,8,9]);\n #matrix, 3 \+ rows, 3 columns, entries in order\n #going across rows, then down columns" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "rref(A); #reduced row echelon form\n \+ #notice this matrix does not\n #reduce to i dentity, so has no inverse" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 409 "b:=vector([0,-3,-6]);\nC:=augment(A,b); #augmented matrix\nrr ef(C); #read off the solutions to Ax=b\nlinsolve(A,b); \+ #solve the same linear system\ninverse(A); #DOES NOT EXIST !\ndet(A); #so the determinant should be zero\nA^(-1); \+ #just echoes 1/A\nevalm(A^(-1)); #evalm stands for ev aluate matrix -\n #the inverse matrix does not exi st" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 545 "B:=matrix(3,3,[1,2,3 ,4,5,6,7,8,10]);\nId:=diag(1,1,1); #3 by 3 diagonal matrix, in thi s case\n #the identity matrix\nC2:=augment(B,Id); \nrref(C2); #can you see the inverse of B?\ninverse(B); \+ #check answer above\ndet(B); #non-zero determinant \nevalm(B^(-1)); #one more way to write the inverse\nevalm(B&*in verse(B)); #matrix multiplication symbol -\n #s hould get identity\nmultiply(B,inverse(B)); #also the identity, anoth er way to \n #multiply\n\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 433 "x:=linsolve(B,b); #the solution to Bx =b\nevalm(inverse(B)&*b); #x is the inverse of B times b!\nevalm(B&*x ); #Bx should equal b\nevalm((3*A+2*B)^2); #compute this \+ expression\nevalm(9*A^2 + 6*A&*B + 6*B&*A +4*B^2);\n \+ #using matrix algebra to expand \n #previou s expression, remembering\n #that matrix multipl ication does not\n #commute" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "52" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }