HOMEWORK AND DUE DATES:
Whenever your assignment includes computer work, attach the printouts
of your Matlab sessions to the work you hand in.
Hw 1, due 9/4:
Page 24 ff: #5, #8, #9.
Page 30 ff: #1, #13.
Page 45 ff: #13.
Page 52 ff: #7, #8, #11
Hw 2, due 9/11:
Page 5 ff: #10.
Page 10 ff: #10, #12, #16
Page 17 ff: #4, #6, #7, #8 (for #8, use horner.m or horner2.m to
evaluate the polynomial you obtained. For the coefficients you may
use fact.m.
Calculate the exponencial using the Matlab function exp. Calculate
the Taylor
polynomial using taynexp.m, compare both results: plot them, check
their maximum
difference with max(abs(y-z)), check the time the computation took
for each method).
Change the range of the variable: what can you say?
Hw 3, due 9/18:
Page 67 ff: #2, #3, #4, #6, #7, #8. Except for #8, use the course's Matlab
package.
Hw 4, due 9/25:
Page 76 ff: #3, #4, #5, #6, #10.
Page 82 ff: #2, #3 ,#5.
Hw 5, due 10/2:
Page 91 ff: #1, #3, #4, #6, #11, #12..
Page 99 ff: #8, # 13. For #13, set up a Matlab routine (adapting the
routine fixpt.m in the course's package as indicated in the exercise).
Hw 6, due 10/9:
Page 108 ff: #1, #2, #8, #16.
Page 118 ff: #5, #6, # 7, #8.
Hw 7, due 10/16:
Page 127 ff: #1, #4, #7, #8.
Page 136 ff: #1, #2, # 7, #8, #9.
When asked to "compare" splines, polynomials or/and other functions,
plot them on the same coordinate system
and write down your observations. To costruct the splines you may use
the programs cubsev.m, cubsplcl.m,
cubsplf.m, cubsplna.m, in the course package. Do howerver compute one
by hand!
Hw 8, due 10/30:
Page 151 ff: #5.
Page 158 ff: #2, # 3 part b), #4, #5, #6.
NOTE: you may use chebyfit.m, chebypts.m, lagr.m, compe.m. Chebyfit
is actually not the near minimax method
developed in 6.3, but closer to 6.1 - it is constructed using a least
square fitting for the polynomials.
In #3 b) and #5, construct the interpolation polynomial with Chebishev
nodes (you can use your package
for this). Chebyfit.m will be close to the minimax approximation. Compare
these two.
Compare the plots of these two functions.
Compe.m shows you a very complete example for the exponential function.
Page 170 ff: # 2, (Use Simp.m, simpp.m, for this exercise, you don't
need to write any
extra program), #3 (Use trap.m, trapp.m for this exercise, you
don't need to write any
extra program). You may pick 3 (instead of all six), make sure to pick
the same three in
#2 and in #3. Make sure to compute the approximate integrals for a
fair sample of numbers
of intevals: a few (say, less than 10), medium (say, of the range of
200), many (say, over 400).
Page 172, # 7. The question after (d) is optional.
Hw 9, due 11/6:
This is our last theoretical work on numerical integration and differentiation.
I would expect this homework to take more time, and I'd like it to
look quite good.
Budget your time accordingly, and do a carefull job.
Page 183 ff: #1, #3, #5, #18. (Compare the result of #18 to the
effect of the error in function values in numerical
differentiation. Notice that #18 tells you that in numerical integration
the change due to error in function values is
independent of the mesh size h.)
Page 203 ff: #1, #2, # 3, #4.
Hw 10, due 11/13:
Page 222 ff: #1, #3, #7.
Use your softaware package for most of this assignment.
For Ex #3, you should solve Ax=b, for A and b given in the exercise.
For this one needs to figure
out how to store the matrix A, for a given n..
Page 246 ff: #6, #8, # 9, #10, #11, #12.
Ex.# 10 will require a modification of the matlab code to eliminate
the pauses!!!!!!!!!!!!!!
There is a bunch of programs to use in your package, most start with
gen, ges, gep, gj. Notice also getrid is very
useful. You will also need to use some instructions of your old handout:
mainly how to combine matrices, to declare
the augmented matrices when you want to solve a system.
Hw 11, due 11/20:
Use your software package for computational work.
Page 255 ff: #1, #3, #4, #7.
In Ex #1, use the software in your package to carry out the steps
the exercise asks for.
Problem c) is an example of very ill-conditioned system, for which
residual correction
will nevertheless converge.
Page 266 ff: #1, #2, # 3, #4, #6.
In Ex. #7, find the inverses of A5 and A6. Cond (An)=n2^(n-1), and
det(An)=det(inv(An))=1.
This problem is ill-conditioned even though all eigenvalues of An are
1.
(You may do all the work for n=5 and n=6 only).
Hw 12, due 12/4:
You will need to rename power.m - call it power2.m. Once renamed it will
run.
Page 193 ff: #1, #2, #3, #5.
Page 279 ff: #12, # 13, #15, #16.
Page 289 ff: #3, #4, #6, #8.
Page 302: #3, #5, #8.
Use power.m, gsit.m, jacit.m, gauss.m from the course's package.
We will be working on some of these
exercises in class.