Maple Introduction

Notes on Maple:

1. " > pp := 512989" means "set pp = 512989 and store the value of pp in Maple's memory".

2. ";" means "execute the command between ">" and ";" and display the result (if any) on the screen.

3. ":" means "execute the command between ">" and ":" but do not display the result (if any) on the screen.

4. Always check that the cursor is between ">" and (";" or ":") and then press Return or Enter to execute the operation.

5. Do not use the return key to enter data over more than one line. You CAN use "shift - return" to do this. Alternatively, Maple will automatically carry your entry to the next line as needed.

6. "restart" clears all values from Maple's memory.

7. Additional spaces in the command are for clarity

Clear any values from Maple's memory.

restart;

Multiplication is * and powers are ^

238 + 17 + 99*158;

What is 100!, i.e. what is 1*2*3*4* ... *98*99*100?

100!;

How many digits in 100! ?

length(100!);

Q: How many ways can I arrange my 60 books on my bookshelf?

Evaluate the result in floating point arithmetic.

One estimate of the number of atoms in the universe is 10^80. Which is greater?

60! ; evalf(60!); verify(60!, 10^80, greater_than);

Store a=5 and b=8 in memory.

a := 5; b := 8;

a + b;

Redefine and store a and b as the characters a and b.

a := 'a' ; b := 'b';

Print the first 100 elements of the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...

( In Maples's memory set a[1]=1, a[2]=1 and a[i] = a[i-1] + a[i-2] for i from 3 to 100.

Note the use of := in the command.

Do not print the intermediate results, hence use : and not ;

"od" means "end do".

Finally convert a into a list (from an "array").

The result of this is printed because of the final ";" )

a[1] := 1: a[2] := 1 : for i from 3 to 100 do a[i] := a[i-1] + a[i-2]: od: convert(a,'list');

What is the 100000th prime?

ithprime(1000000);

Is a given number a prime?

isprime(4896276498678467893766480764);

Factorise a number.

( i.e. "integer factor")

ifactor(987098398654098299877430953245);

What is the next prime after a given number?

p = nextprime(48962764986784678937);

What is the formula for the sum of the first k integers? Sum of their squares?

( That is sum j^2 from j=1 up to k.

Simplify the resulting expression.)

simplify(sum(j, j=1..k)) ; simplify(sum(j^2, j=1..k));

Is there a formula for the sum of the 10th powers of the first k integers?

simplify(sum(j^10, j=1..k)) ;

Integrate x^3 (ln(x))^2 with respect to x .

int(x^3 * (ln(x))^2 , x );

Find a formula for the integral of e^(ax) + cos(bx) with respect to x.

int(exp(a*x) * cos(b*x) , x);

Plot x^2 sin (1/x) from -0.1 to 0.1 and compare with x^2 and -x^2

plot([x^2, -x^2, x^2 * sin(1/x)] , x = -0.1..0.1 );

Plot sin(xy) for x and y each between -Pi and Pi and put the axes in a box.

plot3d( sin(x*y) , x=0..Pi, y=0..Pi , axes = boxed );