active01_830.mwWed Aug 31 16:55:21 MDT 2005 This sheet just goes over the stuff we did in class on day one, 8/25/05.To run the entire sheet, top-to-bottom, and in order, click on the !!! icon at the upper right of your window. restart;

2 + 5;2*5;2/5;evalf(%);2^5;2^(1/2);evalf(%);2^0.5;(5+Pi)/(5-Pi);evalf(%);3 + 2*(12 - 7); Parentheses are the only algebra grouping symbol. The other usual grouping symbols get used for other purposes.3 + 2*[12 - 7];3 + 2*{12 - 7};

Evaluating various elementary functions listed in mid page 2:abs(-23);sqrt(4+2*14);sqrt(4.0+2*14);exp(1); exp(1.0);sqrt( exp(2) );ln(2);ln(2.0);ln(8) - 3*ln(2);sin(4)^2 + cos(4)^2;evalf(%);sin(4.0)^2 + cos(4)^2;arctan(1);sin( arctan(1) );

r := 3;R := 4; Note that Maple is case-sensitive, that is, variables R and r are different.R, r;AnnulusArea := Pi*(R^2 - r^2); evalf(%);Discriminant := b^2 - 4*a*c; "Discriminant" is a Maple expression (see page 15)Discriminant; Echo back the expression.a := 3; b := -2; c := 3; Assign some values to variables in the expression.Discriminant; Now the expression is evaluated because Maple knows the values of the variables.nerk := sqrt(Pi);evalf(nerk);

fox := x -> 3*x^2 - 7*x + 4; Defining a function named "fox".fox(-2);fox(t);fox(t + h);fox(x+h) - fox(x);

plot(fox); A default plot of function "fox"plot(fox, 0..3); Shrinking the range of x-values plotted.plot(fox, 0..3, -1..1); Chop the y-range as well.gum := x -> (x^2 - 4)/(x+1); "gum" is the function version of the expression hatched in mid page 6.gum(0);gum(-1);plot(gum); As pointed out on page 6, this plot is not too informative.plot( gum, -4..4, -8..8 ); Trimming the x- and y-ranges gives us this non-function graph. This is an artifact of Maple's default propensity to connect the points it plots with line segments.plot( gum, -4..4, -8..8, style=POINT ); We can make Maple stop connecting points with line segments by use of "style = POINT". The plot shows spurious points, however. Function "gum" is difficult for computer graphing to cope with.plot( gum, -4..4, -8..8, style=POINT, numpoints=1000 ); Plot more points. plot( gum, -4..4, -8..8, style=POINT, numpoints=1000, discont=true ); The "discont=true" option warns Maple away from plotting the near-asymptote spurious points.