Excercise 1

Basic arithmetic

1. Calculate 10 sin(10)
2. Divide the result by 4
3. Add 10 to the result
4. Calculate the square of the result
5. Add together the two previous results.

Solution

Substitutions

Direct substitution

1. Set the variable x equal to 10 and y equal to 5 using direct substitution
2. Set z equal to 2x+y using direct substitution. Check the value of z.
3. Set x equal to 8
5. What's the value of z now? Try it.

Clear x, y and z

Solution

Delayed substitution

1. Set x and y equal to 3 and 4.
2. Using delayed substitution, set z equal to x*y
3. Check the value of z
4. Set x equal to 5
5. What's the value of z now? Try it.
6. Clear y and check what is z.

Clear x, y and z

Solution

Truth values

1. Evaluate 10 != 11
2. Evaluate 0==0.
3. Evaluate 1<=3.
4. Evaluate 10==a.
5. Evaluate -10 < 10.

Solution

Bonus excercises

Mathematica can check the types of variables and numbers. Evaluate the following:
1. NumberQ[1.24]
2. EvenQ[4]
3. OddQ[6]
4. PrimeQ[7]

Solution

Lists

Elementarities

1. Construct the list {1,2,3,5,7,11} and set it to the variable x.
2. Add together the first and last element of x.
3. Multiply the second element with the third element and add the fourth element to the product.

Clear x.

Solution

More elementarities

1. Construct the list {a,b,c} and set it to variable x.
2. Construct the list {1,2,3} and set it to y.
3. What would x+y give? Try it.

Clear x and y

Solution

Two-dimensional lists

1. Set A equal to the list {{1,2,3}, {4,5,6}}.
2. Extract the second element of A.
3. Extract the third element of the first element of A.
4. Extract the first element of the second element of A.
5. Add together the two previous results.

Clear A.

Solution

Extra excercises

1. Construct the matrix (

Clear A.

Solution

Rules, equations, solving equations

First

1. Calculate +x+1with x equal to 10
2. Calculate x+y with x and y equal to 1 and 2
3. Calculate with a and b equal to 3 and 4
4. Set x equal to 10 using a rule and a substitution operator.

Solution

Second

1. Solve the equation +p x+q=0, and set the result to the variable e.
2. Extract the second element of the solution list.
3. Using the above rule, calculate x+p.
4. Calculate the above with p=1and q=2.
5. Check the numerical value of the above using the function N[...].

Solution

Third

1. Set the variable Y equal to the equation +p +q x+r=0.
2. Solve equation Y.
3. Check the solution by substituting it into the equation and simplifying the resulting expression

Solution

Fourth

1. Set the variable y equal to
2. Apply the functions Expand, Factor, Together, Apart, Cancel, Simplify, Numerator ja Denominator on y.
3. Solve the equation y=0by taking the numerator of y and finding its zeros.
4. Check the solution by substituting it into the equation. What do you see? How could you fix the situation?

Solution

Extra excercise

1. Solve the set of equations {

b x+a y=3

Solution

Created by Mathematica  (April 10, 2007)