An example of text. Use this for comments.

1+2-(3/5); #Can be used like a normal calculator.

2^5; #Exponentiation is done by either a caret or **

2**5;

exp(x); #The exponential function- must use the exp function.

evalf(exp(1));

ifactor(60);

evalf(pi);

evalf(Pi);

Assignment and Equality

Bob:=(x+5)^2; #We can assign an expression to a variable name

x:=5; #We could assign the value 5 to x, but this is not good programming.

Bob;

x^2;

x:='x'; #Clears this variable.

Bob;

subs(x=5,Bob); # Use the substitution command to evaluate expressions!

expand(Bob); #Expand the expression out.

int(Bob,x); #Integrate the expression with respect to x.

diff(Bob,x); #Differentiate the expression with respect to x

Eqn1:=3*x+5*P=-3; # We can store an equation into an expression.

solve(Eqn1,P);

solve(Eqn1,x);

Summary: Assignment is ":=", and A:=B means to store B in A. Equality is used in other contexts (like substitution, and in equations).

Functions versus Expressions

F:=x^2+3*x+4; #F is an expression.

F(1); # You cannot use this notation for expressions

G:=x -> x^2+3*x+4; #G is a function, so you can use function notation.

G(1);

G(t);

You can create a function from an expression using the "unapply" command:

H:=unapply(F,x);

H(3);

int(F,x); #Integration uses an expression.

int(G,x); #G is a function, so this doesn't work.

int(G(x),x); #However, G(x) is an expression in x, so this works.

Solving Equations: Maple can solve them exactly (using algebra, where possible), or numerically.

solve(x^2+3*x+4,x);

solve({3*x+2*y=1, -x+3*y=2},{x,y});

g:=x ->exp(x)+x^2-10*x;

plot(g(x),x=-1..4);

solve(g(x)=0,x);

fsolve(g(x)=0,x=0..1);

fsolve(g(x)=0,x=2..4);

Some Plotting Commands: Plot using expressions (it's more intuitive).

H:=sin(3*x)-exp(1/2*x);

plot(H,x=-3..3);

?plot

A:=<<1, 2, 3, 4, 5, 6>|<6, 5, 4, 4, 1, 2>>; #An array of ordered pairs

plot(A,style=point); #Plot the ordered pairs

plot([sin(t),cos(t),t=0..Pi],scaling=constrained); # Example of a parametric plot.

plot([t,t^2+1],t=-3..3); # This is a plot with two functions.

plot([t,t^2+1,t=-3..3]); #This is a parametric plot

plot([1+2*sin(t),t,t=-Pi..Pi],coords=polar);

plot({[t,t^2+1,t=-2..2],[t,1+3*t,t=-2..2]},x=-5..5); #Example of two parametric plots