Homework assignment: structure of a program
1. Write FORTRAN90 code that converts temperature in Fahrenheit to Celsius. Plot
Fahrenheit vs. Celsius between -20C and +45C. On the graph note the average
temperatures for Phoenix metropolitan area between January and March (1), April – June
(2), July – September (3), and October – December (4).
2. Write FORTRAN90 code to generate data files with two columns. First column should
correspond to x and the second to y that satisfy the following equation
[called folium of Descartes]: . Generate three data files for a = 2, a = 3, and
a = 4. Plot all three curves in a single figure. Hint: you need to find parametric representation of
this curve [do online research].
3. Write FORTRAN90 code that calculates π using Gregory series:
Plot your result as a function of N to demonstrate numerical convergence. In the same
figure plot horizontal line corresponding to the exact value of π. Note that if you start
with huge values of N your result is most likely already converged. Begin with small N.
4. Write FORTRAN90 code that generates the following function
Note that in actual calculations you cannot use infinite number of terms in the series.
You thus need to ensure you have enough terms for each x. Plot this function for several
values of N to demonstrate numerical convergence. Also note that if you do plot this
3 3 x y axy + -××× 3 0 =
( ) 1
N n n
æ ö – = × ç ÷ ç ÷ × – è ø
( ) 2
lim , 0 20
n fx x
p ®¥ =
æ ö æ ö ç ÷ ç ÷ è ø = ç ÷ ££ × ç ÷ ç ÷ è ø
function for N = 10000 and N = 100000000 your results are most likely to show nearly
identical curves you thus need to experiment to see the minimum number of terms
needed and take a few N that are also smaller than that. Ultimately you want to show
how several lines begin to approach converged data.
5. Write FORTRAN90 code that calculates the product of two matrices. Check if the code is
properly written by calculating the following:
3 2 1, 1 2 3,
[, ] .
C AB A B B A
æ öæ ö ç ÷ç ÷ = =
è øè ø
= ! ×-×
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