Section 1. Getting Started: Maple as a Calculator
The following exercises provide practice using Maple to make simple calculations like the ones in the manual. Compare the output to what you can get from your calculator.
0. Pull down the Help menu, choose New Users/Full Tour, then click on the second item: Numerical Calculations and work through the examples in that worksheet.
Open a new Maple worksheet and to the following.
1. Enter the following sequence of square roots.
Then enter and execute
evalf(%);
Now execute
evalf[5](%%);
Now execute
add(k,k=%%%);
Read the Help page for add and then comment on what Maple did to get the last output.
2. Execute the following entry
x = 4/(1+sqrt(2)) + exp(3) - ln(4);
Execute
evalf[4](%);
Now execute
x;
and note that x is still a free variable. This illustrates the fact that
Equations do not assign values.
3. Make the same entry that starts exercise 2. Then execute
simplify(%);
Is the output any simpler, in your opinion?
4. Make the same entry that starts Exercise 2. Then execute the following two entries. They can be entered at the same input prompt.
rationalize(%); expand(%);
Comment on what Maple did to get the two outputs. (Remember what "rationalize the denominator" means from high school algebra.)
5. Execute the following entry.
(1 + sqrt(3))/(1 - sqrt(3));
Then execute
rationalize(%); expand(%);
6. Use the sequence operator, $, to make the following sequences.
a. 2, 4, 6, 8, 10, 12
b. 20, 40, 60, ... , 260 Hint. 20 + 20*k $ k=
c. The 30 prime numbers starting with 11 and ending with 139. Hint. Use ithprime
7.* Add the numbers in the sequence in 6 c.. Hint. If you just did 6 c, then execute add(k,k=%).
8. Multiply the numbers in the sequence in 6 c. Then execute
length(%);
to find out how many digits there are in the product.
9. Use the sequence procedure, seq, to obtain the same sequences that were obtained in Exercise 6 using $.
10. Use seq to obtain the sequence of the cubes of the numbers in the list [2, 5, 6, 9, 12, 44]. Add the numbers in the sequence of cubes and then obtain the prime factorization of the sum.
What do you notice about the prime factorization? (Hint. The integer 87990 is called "square free".)
11.* Obtain the prime factorization of the product of the integers in the sequence of cubes described in Exercise 10.
12. Use the factor procedure to factor the following polynomial expressions.
a. x^3 - x^2 + x - 1
b. x^7 - x^6 + x^5 - ... -1 Hint. Enter this as -add( (-x)^k,k=0..7) then execute factor(%).
13. Use factor/real to factor the two polynomials in Exercise 12 over the real field.
14. Use the factor/complex to factor the two polynomials in Exercise 12 over the complex field.
15.* Use solve to obtain the zeros of the polynomials in Exercise 12.
16.* Add the zeros of the polynomial in 12 a and the zeros of the polynomial in 12 b.
17. Multiply the zeros of the polynomial in 12 a and the zeros of the polynomial in 12 b.