COALITION MATH 151, FALL 1997

        Group II (S. A. Fulling, assisted by Cary Lasher)

                             Day 1.2

I LEFT THESE NOTES IN MY OFFICE -- WAS ABLE TO DO ABOUT 2/3 OF IT 
FROM MEMORY (OMITTING POINT 2).  

    1.  Expressions vs. functions in Maple

        A.  f := x -> x^2 -1;  f(2);  plot(f);

        B.  g := x^2 - 1;  g(2);  subs(x=2, g);  subs(x=2, f); plot(g,x);

        C.  h := unapply(g,x);   i := f(x);  h(2);  subs(x=2, i);
        *.  Activity:  Plot  x^2, the sine function, and the 
        natural logarithm function on the same axes.  (Try both 
        methods; even teams do expressions, odd teams functions.)

    2.  Equations in Maple

        A.  a = x^2 + 3*x;    # Contrast a := x^2 + 3*x;

        B.  eq := a = x^2 + 3*x;  solve(eq, x);

        C.  fsolve(sin(x) = 0, x, 0..10);

        D.  cuberoots := solve(x^3 + 8 = 0, x);  x := 
        cuberoots[1];

    3.  Power, exponential, and logarithmic functions (examples 
from the Web page)

        A.  plot({x^4, x^(3.9)}, x);

        B.  e;  E;  exp(1);  evalf({e, E, exp(1)});

        C.  plot({exp(x), 2^x}, x);   plot(ln);  plot(log);  
        plot(log[3]);

        D.  e := exp(1);  plot({e^x, exp(x)}, x);

        E.  plot({e^x, x^3}, x);  plot({e^x, x^8}, x);  
        #crossover?

        F.  Students continue on their own if time permits.