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					                    Practical Exercise Sheet 1
          Basic Arithmetic and Command Line Exercises



Exercise
All the following should be done in MATLAB .

  1. Multiply 5 and 6.

  2. Let us consider the compound interest program introduced in Lectures:
     Execute the following statements in the Command Window:


      (a) Put the number 1000 into variable balance
     (b) Put the number 0.09 into variable rate
      (c) Multiply the contents of rate by the contents of balance and put the answer
          in interest
     (d) Add the contents of balance to the contents of interest and put the answer in
         balance
      (e) Display (in the Command Window) the message given in single quotes.
      (f) Display the contents of balance
      (g) What values do variables balance, interest, and rate have at the end of the
          program?

  3. Give values to variables a and b on the command line, e.g. a = 3 and b = 5. Write
     some statements to find

      (a) the sum
     (b) the difference
      (c) the quotient

     of a and b respectively.

  4. Enter the following numbers at the command prompt in scientific notation:

      (a) 1.234 × 105 ,
     (b) −8.765 × 10−4 ,
      (c) 1015 ,
     (d) −10−12 .

  5. Use MATLAB to evaluate the following expressions


                                            1
   (a) 1 + 2 × 3
   (b) 4/(2 × 2)
    (c) (1 + 2)/4
   (d) 1 + 2/4
           1
    (e)   2×3
           2×3
    (f) 2
   (g) 1.5 × 10−4 + 2.5 × 10−2
   (h) 1000 (1 + 0.15/12)6 0. What does this mean?
6. Try to avoid using unnecessary brackets in an expression. Can you spot the errors
   in the following expression (test your corrected version with MATLAB ):

  (2 (3+4)/(5*(6+1))^2

7. Find the volume of a cylinder of radius 5cm and height 10cm. Hint: type pi in
   MATLAB .
8. Suppose a and b are defined as follows:

  a = [2 -1 5 0];
  b = [3 2 -1 4];

  Evaluate by hand the vector c in the following statements. Check your answers
  with MATLAB
   (a) c = a − b,
   (b) c = 2 × a + ab (Be careful! )
    (c) c = b/a
   (d) c = b × 2 × a
9. Scientists often have to convert from one unit of measurement to another; this
   can be tricky sometimes. You need to think carefully through the process. For
   example, convert 5 acres to hectares, given that an acre is 4840 square yards, a
   yard is 36 inches, an inch is 2.54cm and a hectare is 10 000m2 . The best approach
   is to develop a formula to convert x acres to hectares. You can do this as follows:
                       one square yard = (36 × 2.54)2 cm2
                           so one acre = 4840 × (36 × 2.54)2 cm2
                                       = 0.4047 × 108 cm2
                                       = 0.4047 hectares
                            so x acres = 0.4047x hectares
  Once you have found the formula (but not until you have found the formula),
  MATLAB can do the best. Convert 5 acres to hectares and display the answer
  on the Command Window.

                                         2
 10. Develop formulae for the following conversions, and use some MATLAB state-
     ments to find the answers

     (a) Convert 22 yards (an imperial cricket pitch) to meters
     (b) One pound (weight) = 454 grams. Convert 75 kg to pounds
     (c) Convert 49 meters/second
     (terminal velocity for a falling person-shaped object) to km/hour
     (d) One calorie = 4.184 joules. Convert 6.25 kilojoules to calories


 Quitting MATLAB
Give the instruction quit or exit (or use the command window’s menu).




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