Everyone should read Chapter 2.

Collaborative problems:

- Compute the Taylor series of the exponential function, exp(t) about t=0.
- Write a FORTRAN program that uses the Taylor series to compute the exponential of a specified value. The program should:
- prompt the user for how many terms should be used in the series;
- prompt the user for the value of t that should be used in exp(t); and,
- print the answer.

- 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.

- Repeat the problem above but for the cosine function instead of the exponential function. You may use the cos() function in FORTRAN to check the accuracy of your iterative computation.
- Write a program that prompts a user to enter an integer. Print out the integer cubed (you may just multiply it by itself three times). Use this program to determine an approximate value for the maximum and minimum integer values. Based on this, how many bits does remote2.helios.nd.edu use to represent an integer?

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. The first line of every program should have your ND ID number and what problem it is, e.g., homework 1, problem 2a.

Extra Credit:

- Do all the problems again in C, C++ or java.
- Re-write the logistic map problem from class (in FORTRAN) so that it does the computation in integers and works up to the largest possible integer value.