Math. 45501, Spring, 1997 Assignments
Math. Math. 45501, Spring, 1997 Assignments
/ Assignments /
Exams /
This list is updated as the assignments are made and exam dates
are set.
After assignments are handed back, copies of the answers
are placed on reserve in Dupré Library.
 Lesson 1: (Due Tuesday, January 21)

 Lessons 12: (Due Thursday, January 23)

 page 10: 12
 page 14: 1a, 2a, 3abc, 4
 Lesson 2: (Due Tuesday, January 28)

 Lesson 3: (Due Thursday, January 30)

 p. 19: 10b
 Supplementary
lesson
 Study the indicated Fortran 90 program.
 Describe what the Fortran 90 program does.
 Describe the bitstructure of each of the
printed floating point numbers, indicating
what the sign bit, exponent number, exponent
bias, and mantissa are.
 Lesson 5: (Due Tuesday, February 4, 1997)
 These may be done by hand, by using the programs that
come with the book, or by writing your own Fortran 90
programs. (See the example Fortran 90 program for
a simple Fortran 90
program for Newton's method that you may use.
 page 29: 4, 8, 13
 Do 4 on page 29, but using the secant method
instead of the method of bisection.
 Do 4 on page 29, but using Newton's method instead
of the method of bisection.
 Lesson 10: (Due Thursday, February 20)

 Lesson 11: (Due Thursday, March 6)

 page 83:

No. 12. Do using the program ncubsp34.for from
the book, or other natural cubic spline program.

Also do the same problem with a polynomial
interpolant obtained with neville31.for or
other polynomial interpolation program.

Extra credit (15 points
added to your last exam score): Draw graphs
of both the polynomial interpolant and the spline
interpolant over the interval of interest.
Analyze these graphs carefully, stating both your
reasoning and your conclusions.
 page 89: 3a (Do it by hand, and show all of your work.)
 For Tuesday, March 11:

 p. 98: 1a, 2a, 3a, 4a, 5a, 6a. Also compute an enclosure
to the integral in 1b using the Simpson's rule and bounding
the error term with interval arithmetic.
 p. 105, no. 6.
 Compute the integral from 0 to 0.1 of cos(x)
with a 2point Gaussian quadrature rule.
Bound the error in the formula. Also compute an
enclosure to the solution by evaluating the error
term with interval arithmetic. Carry out eight
digits in these computations.
 For Tuesday, March 18:

 Evaluate the integral from 0 to 1 of cos(x) to within
an error of .0001, by hand. To do this, step through
the adaptive quadrature procedure with Simpson's rule.
You may use either the heuristic error estimate or
the rigorous bound based on interval arithmetic.
 p. 124, no. 7. (You may use adapq43.for from
the routines supplied with the text, quanc8.for
from the Forsythe / Malcolm / Moler routines, or other
adaptive quadrature routine, including one you write
yourself.)
 For Tuesday, March 25:

 For Tuesday, April 1:

 pp. 159160, nos. 3a and 4a.
 pp. 159160, nos. 3a and 4a, except use a fourth order
Runge Kutta method.
 p. 167, no. 14.
 For Tuesday, April 15:

 p. 167, no. 14, but use the RungeKuttaFehlberg 45
method with TOL=1E2 and TOL=1E4.
Graph the iterates.
 pp. 193194, nos. 2a and 6.
 Try solving #14, p. 167, but with k=6.22E10,
using an implicit Euler method, with 20, 100, and
1000 steps. Graph the approximate solutions.
 For Thursday, April 17:

 p. 209, nos. 2cf, 4cf, 6cf
 For Thursday, April 24:

 Do two iterations, by hand, of the multivariate
Newton method, with the system:
x(1)**2  x(2)**2 = 0,
2*x(1)*x(2)  2 = 0
and starting values
x(1)=0.9, x(2)=1.1.
(Note that the first iteration was done
in class.)
 For Thursday, April 24:

 p. 215, nos. 2cf, 4cf, 6cf
 For Tuesday, April 29:

 Compute the condition number in the infinity norm
of a 3 by 3 Hilbert matrix.
 Do five iterations of the power method for the matrix
A = [1,2; 3 4], starting with initial vector
v = [1;1]. (MATLAB notation is used for A and v.)
 For a later date:
 Solve
problem 3c on page 9 with an interval Newton method
After exams are handed back, copies of the exam and answers
are placed on reserve in Dupré Library.
 First exam:
 The first and second exams will be combined, and will
be given on Thursday, February 13. The material will be
from lessons 1 through 7.
 Second exam:
 The third and fourth exams will be combined, and will be
on Thursday, March 13, over what was covered in interpolation
and quadrature.