Easy1.mws

This document contains information along the following lines

text and input lines (can switch from one to the other)

executing an input line (click anywhere in the line)

creating an extra input line

a few finicky features of Maple

What Went Wrong - some suggestions when maple gets huffy.

Problems between release 3 and release 4.

xxx.**ms** is a Maple V **Release 3** file. *It can
be read by Maple V Release 4
*xxx.

**A summary of some points which come up in Easy 1.**

the** restart** command resets all previous values

**with(plots)**: brings up the plot package

: at the end of a line suppresses output from that line

; is used to complete the line when output is required

**#** is used to put comments on a line. Maple ignores characters
after the #

**:=** is used for *assignment* to the
left-hand side of what's on the left-hand side (as in **x := 3 + 4*y**
)

**=** is used to express equality between expressions
inside an equation as in **eqn1 := 3*x^2 = t ;
** (here
eqn1 is assigned the equation 3*x^2 = t)

plotting a 'function' (**plot** command)

cursor moved around on graph will give coordinates in lower left (version
3)

cursor moved around on graph will give coordinates in upper right(version
4)

two or more functions may be plotted when grouped as a set, e. g. **{x,y}**

solving an equation (**solve** command)

solution via **solve** is 'exact' (rational fractions)

solution often has parts, which can be identified and used later on

floating point evaluation (**evalf**) is available

substituting a value in an expression (**subs** command; very handy
later on)

**Start of Easy1 ( **for Maple V release 4. Things
are slightly different in Release 3.**)**

The restart command resets all previous assignments and starts over.

A # on a line of Maple code lets you put comments on that line. The danger is that text from the comment may 'wrap around' and wind up on a separate line if the program is re-opened. The line coming up has a comment on it.

**restart; with(plots):** # begin and bring up plot package. Try
changing to a semicolon at the end to see all the plot types.

Assignment statements use ' := ' like in pascal . We will assign 3 t + 4 t^2 to x. This is not a 'formal' definition of a function, but the informal definition works well in almost every situation.

**x:=3*t+4*t^2;** # define y as a 'function' of t; semicolon at end
lets you see ouput

Plotting a function. Execute the command **plot(x,t=0..4);
**. (click anywhere on the line). After a moment, a plot should appear.

**plot (x,t=0..4);**

Move the cursor around over the plot to a spot where you want the coordinates, then click the mouse. This gives the coordinates at the lower left (release 3) or upper left (release 4). It is very handy for identifying specific features of graphs. For practice, locate the value of t when x=5.0. (It's a little tricky, since X,Y are generic on the graph and in this case Y is playing the role of x, and X is playing the role of t. It should come out near t=0.8)

To ask for help on a topic or function just type '?' and the item. The
next command asks for help on the **plot** command. Most help screens
have examples at the bottom. You can cut and paste right into your program
from help if you wish.

**?plot **

**y:=16-2*t^3;**

**plot({x,y},t=0..3);** # note use of curly braces to collect things
: plot both x and y as functions of t;

When we click in the plot, we find the x,y values (upper left corner in release 4, lower left corner in release 3) where xand y are equal (around x=1.33, y=11)

In the statement coming up, the equality statement is just a plain ' = ' ; there is no semicolon with it. This represents equality and not assignment.

Find the t value where x and y arequal; notice use of '=' without the semicolon in the solve command

**sol:=solve(x=y , t); **

This is not so helpful, so we get a floating point evaluation.

**numsol:=evalf(sol);**

Substitute t back into y to get the y value using the 'subs' command (2 ways)

**yval:=subs(t=1.34,y);**

**xval:=subs(t=numsol[1],x);**

xval and yval should be nearly the same.

Exercises for the user

1) Find the intersection(s) of y=1-3x and y=0.5+x^2; [ answer: around (0.16,0.53) and around (-3.16,10.5) ] ;

2) policeman and speeder

speeder travels at 60 m/s, constant speed.

cop starts from rest 1 sec after speeder goes by, constant acceleration
of 1.5 m/s^2

let s = speeder's position as a function of time

let p = policeman's position as a function of time

plot both and visually find where cop overtakes speeder solve for time when cop overtakes speeder, using 'solve' command, and evalf.

End of easy1.mws