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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Easy1.mws  " }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 68 "The restart command \+
resets all previous assignments and starts over." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 " restart; w
ith(plots): # colon at end of line suppresses output " }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "Assignmen
t statements use ' := ' like in pascal . " }}{PARA 0 "" 0 "" {TEXT -1 
33 "We will assign 3 t + 4 t^2 to x. " }}{PARA 0 "" 0 "" {TEXT -1 39 "
This is not a 'formal' definition of a " }}{PARA 0 "" 0 "" {TEXT -1 
50 "function, but this informal definition works very " }}{PARA 0 "" 
0 "" {TEXT -1 36 "well in the great majority of cases." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 " Define y as a 'func
tion' of x; semicolon at end lets you see ouput" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "     x:=3*t+4*t^2; \+
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "     plot (x,t=0..4);" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "To ask for help on a t
opic or function just type '?' and the item. " }}{PARA 0 "" 0 "" 
{TEXT -1 94 "This asks for help on the plot command. At the bottom of \+
most help screens they have examples." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "     ?plot " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "     y:=16-2*t^3;
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
76 "note use of curly braces to collect things : plot both x and y as \+
fxns of t;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "     plot(\{x,y\},t=0..3); " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "When we \+
click in the plot, we find the x,y values (lower left corner in Maple \+
V release 3, " }}{PARA 0 "" 0 "" {TEXT -1 85 "upper left corner in Map
le V release 4) where y and z are equal (around x=1.33, y=11)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 75 "In the st
atement coming up, the equality statement is just a plain ' = ' ; " }}
{PARA 0 "" 0 "" {TEXT -1 76 "there is no semicolon with it. This repre
sents equality and not assignment. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 68 "Find the x value where they're equal; no
tice use of '=' without the " }}{PARA 0 "" 0 "" {TEXT -1 30 "semicolon
 in the solve command" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 "     sol:=solve(x=y , t); " }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 62 "This is not so hel
pful, so we get a floating point evaluation." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "     numsol:=evalf(sol);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 77 "Substitute \+
t back into y to get the y value using the 'subs' command (2 ways)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "     yval:=subs(t=1.34,y); " }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "  \+
   zval:=subs(t=numsol[1],x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Exercises for the user" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 82 "1) find
 the intersection of y=1-3x and y=0.5+x^2; [ answer: around (0.52, 0.1
6)] ;" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 24 "
2) policeman and speeder" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 43 "speeder travels at 60 m/s, constant speed. " }}
{PARA 0 "" 0 "" {TEXT -1 84 "cop starts from rest 1 sec after speeder \+
goes by, constant acceleration of 1.5 m/s^2" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 49 "let s = speeder's position as a
 function of time " }}{PARA 0 "" 0 "" {TEXT -1 50 "let p = policeman's
 position as a function of time" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 66 "plot both and visually find where cop ove
rtakes speeder solve for " }}{PARA 0 "" 0 "" {TEXT -1 66 "time when co
p overtakes speeder, using 'solve' command, and evalf." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "end of easy1.mws" }}
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