### FALL SEMESTER 1998

#### FINAL EXAMINATION

Tuesday, December 15, 7:00-9:00 PM in Room 158 Van Allen. The final test will be mainly on Chapters 8 and 9, with some other questions from other chapters, so consider it as being comprehensive. The test will be done with open books and open notes. Bring a scientific calculator. Only under exceptional circumstances will a student be permitted to shift the time of this examination.

#### UNIX CLASS ACCOUNTS

• Class directory: /group/class/m72002. I will put the codes by chapter, e.g., the codes for chapter 1 are under /group/class/m72002/chap1.
• Class submit directory: /group/submit/m72002. You must submit course work via the coursework submission tools.
• Group you belong to and class mailing list: m72002.
• If you do not know your password go to 303A MLH.
• Accounts for students who are not majors within the Division of Mathematical Sciences will be deleted after the term has ended! Note the expiration date at the top of your Unix Account Information form.
• The directory for this class will be removed before the beginning of the next term! If there is anything in this directory that you would like to save, you must archive it to your own home directory.

#### HOMEWORK ASSIGNMENTS

1. Due Friday, September 4: Problems 1.1.2ac, 1.1.6., 1.2.2, and 1.2.11.
2. Due Friday, September 11: Modify the Matlab code /group/class/m72002/chap1/Gregory_Taylor.m by using nested iterations (Horner's algorithm) and minimize the number of arithmetic operations within the loop. You may have to use one of the following functions in Matlab: ceil, fix, floor, mod, or round. Submit your work into /group/submit/m72002/homework2 via the coursework submission tools.
3. Due Friday, September 18: Problems 2.1.1.b, 2.1.3.bc, 2.1.5. In problem 2.2.10 write the given single precision Fortran code and run it. Modify the code to double precision and run it. Rewrite the same code in Matlab and run it. Comment on your results.
4. Due Friday, September 25: Problems 3.1.1.d, 3.1.6.b, 3.1.14.a, 3.2.5, 3.3.1. For problem 3.1.14.a, do not submit your work via the coursework submission tools, but plot the graphs (Matlab is recommended). In problem 3.3.1 write a Fortran or Matlab code and submit your work into /group/submit/m72002/homework4 via the coursework submission tools.
5. Due Friday, October 9: Use the subroutine BISECT to solve 4.1.1ad, 4.1.6. Solve the same problems, but this time using the subroutine NEWTON. Do problems 4.2.3abc, 4.2.9.
6. Due Monday, October 19: Do problems 4.3.7, 4.5.1, 5.1.1abc, 5.1.7. Use the subroutine DIVDIF to solve 5.2.7. Print out your codes and the results.
7. Due Friday, October 30: Do problems 5.3.4, 5.3.7 (use Matlab, print out your code and the pictures), 5.4.3, 5.4.9. Using the Fortran code SIMPSON compute the following integrals: e^{-x^2} between -1 and 1; x^3 between 4 and 8; x^4 between 4 and 8; 1/(1+cos(x)^2) between 0 and pi, print out just your results.
8. Due Wednesday, November 11: Do problems 7.1.6a, 7.1.8, 7.2.1ab, 7.2.5ac, 7.2.12, 7.3.5, 7.4.1a, and 7.4.2 (repeat only 7.4.1a).
9. Due Friday, December 4: Do problem 8.1.1. Use the double precision routines DGETRF, DGETRS from LAPACK (see copies to be distributed in class) on HP machines to solve this problem 8.1 for the data (-1,1), (0,2), (1,1), (3,2). To link LAPACK and BLAS routines in Fortran when compiling, type for example the command f90 myprogram.f -L/usr/pkg/lapack/LAPACK/ -llapack -lblas to compile the program myprogram.f under UNIX. Solve 8.2.7b using these same routines. Do problems 8.3.1ac, 8.3.19a, 8.4.6a, 8.5.3a (consider the 1-norm only for this exercise), 8.8.1b (iterate until the error is less than 0.01 in the (Euclidean) 2-norm).
10. Due Friday, December 11: Do problem 9.1.1ad, 9.1.2, 9.2.3. Apply the code DOPRI5 in FORTRAN to find y(1) the solution at x=1 of the initial value problem y'=sin(y), y(0)=0.1. You can also apply instead the Matlab routine ode23 to solve this problem.

#### SOME INTERESTING LINKS

Two disasters due to floating-point errors. The Flight 501 Failure (more technical details on that).
Laurent O. Jay
Department of Mathematics
14 MacLean Hall
The University of Iowa
Iowa City, IA 52242-1419
USA
Tel: (319)-335-0898
Fax: (319)-335-0627
E-mail: ljay@math.uiowa.edu