Homework 1, due September 4, 2008.

[goodwine]

Reading: Chapters 1 and 2 from the course text.

Collaborative problems:

1. Choose the text editor you plan to use to write your FORTRAN programs. Indicate somewhere on your homework which one you picked and why you picked it. Justify your decision by indicating which specific features of the editor you liked. If you don't provide a justification, you will not receive credit for this problem.
2. Compute the Taylor series of the exponential function, exp(t) about t=0.
3. Write a FORTRAN program that uses the Taylor series to compute the exponential of a specified value. The program should:
   1. prompt the user for how many terms should be used in the series;
   2. prompt the user for the value of t that should be used in exp(t); and,
   3. print the answer.
4. Investigate how accurate the approximation is for different values of t and for different numbers of iterations. Submit a table that tabulates to how many digits the approximation is valid for different numbers of iterations and different ranges of t. You may use the exp() function in FORTRAN to check the accuracy of your iterative computation.
5. Upload your program as an attachment in the uploads section of the forum for homework 1. Your program should have your name at the top as a comment as well as which problem it is.

Individual Problems:

1. Register for the course web page. You will be required to upload programs during the semester so if you do not register you will not be able to submit part of each homework assignment and possibly parts of each exam. Registration will be disabled on Wednesday, September 3, 2008.
2. Repeat the problem above but for the sine function instead of the exponential function. You may use the sin() function in FORTRAN to check the accuracy of your iterative computation.
3. Upload your program as an attachment in the uploads section of the forum for homework 1. Your program should have your name at the top as a comment as well as which problem it is.

What to Submit:
Submit everything in class including any written work and printouts of any computer code. Also, upload every FORTRAN program that you write for this assignment.

[goodwine]

Someone asked me:

Hey Professor,
Just a little confusion about the homework- for problem one, do we have to make
the table you asked for as an array in fortran or can we just make one out of
an excel spreadsheet? If we do need to use fortran, you should probably let
everyone know soon because i know a few people who have made theirs with excel
already. Thanks.

You may make the table by hand even. I just want it to be a representation of how accurate the series approximation is for different t values and a different number of terms in the series -- sort of a users' manual: if I want to use t=1.5 and an have the answer accurate to, say, four digits, how many terms do I need to use in the series? The ranges for t and the number of terms is up to you, but try to exercise some judgment to make it useful.

[bcastel1]

Prof Goodwine,

Is there a limit to the size of numbers that fortran can count to? Once our numbers get too big, around 1 E 9, fortran does not want the number to get any bigger, and tells us that it is NaN (not a number) and this is causing problems.

[goodwine]

Prof Goodwine,

Is there a limit to the size of numbers that fortran can count to? Once our numbers get too big, around 1 E 9, fortran does not want the number to get any bigger, and tells us that it is NaN (not a number) and this is causing problems.

Yes there is a limit, so if a part of the computation becomes too large it will not work.