AM9561, Graduate Introductory Numerical Methods Autumn 2012

Rob Corless

Middlesex College Room 272

Meeting Times

TA: Piers Lawrence

Course Textbook:

A Graduate Introduction to Numerical Methods and Backward Error, By Rob Corless and Nic Fillion, to be published by Springer

Resources

Topics so far

Maple Worksheets

These worksheets are displayed here in web format, using MathML 2.0 which your browser ought to recognize... Let me know. Ok, this seems to have failed utterly. I put links now to pdf versions.

Old course material below this line

Assignments

    Assignment 2 .pdf version Deadline extended till Monday 15.11.10.
  1. Assignment 1 (worth 5% of your mark). .pdf version , and the LaTeX source , which you will need for question 8.
  2. Assignment 0 (not for credit) Write a short description of your scientific background and interests. Include contact email for inclusion in the course mailing list.

Labs

Topics so far


2009 Course Lectures Tuesday and Thursday 9:30--10:30 MC204

Computer Lab Tuesday 12:30--13:30 North Campus Building 105

In the scheduling meeting we had discussed a preference for the time 13:30--14:30, but balancing different needs I chose this time.

Office Hour: Thursday 10:30--11:30 (right after class)

TA Office Hour: Monday 11:30, MC 275B or Rotunda. (Roman Naryshkin)

Midterm

SSC 2110 has been booked for your AM 9561 midterm on Thursday, November 5 from 5:00 to 7:00pm.

Topics: Condition numbers in all contexts: arithmetic, matrix eigenproblems, solution of linear systems of equations, interpolation, quadrature. NEW : Results are in. Exams handed back 10.11.2009. Solutions

Extension to Assignment 2

Several people have requested more time for Assignment 2. I will at least extend the deadline till Thursday, and we will discuss tomorrow if it makes sense to extend it till next Tuesday. This will be announced also by email (I have finally created the class mailing list). Assignment 1 has now been marked (..except I am double-checking that all of them got marked) and so you should get them back soon.

Resources

Assignments

  1. Assignment 4 (worth 5% of your mark). .pdf version . Helper files first.m and second.m and the file mypoisson.m .
  2. Assignment 3 (worth 5% of your mark). .pdf version due Tuesday November 16, 2009. For interest, .tex source and I have updated the .bib file in the link below. For those of you who wish to use
  3. Assignment 2 (worth 5% of your mark). .pdf version due Tuesday October 20, 2009. For interest, .tex source and I have updated the .bib file in the link below. For those of you who wish to use Maple partly for this assignment, I include a helpful command below.
    
    V := Matrix(7, 7, shape = Vandermonde[[tau[0], tau[0], tau[1], tau[1], tau[1], tau[2], tau[2]], confluent = true]);
    
  4. Assignment 1 (worth 5% of your mark). .pdf version , and the LaTeX source , which you will need for question 8. Oh, yes, the .bib file , too.
  5. Assignment 0 (not for credit) Write a short description of your scientific background and interests. Include contact email for inclusion in the course mailing list. Due 17.9.2009.

Tutorials

Topics so far

Old course material from 2008 and earlier below this line

Course Lectures 2008 Monday 9:30--11:30 MC204

Final Exam

The final exam will take place in HSB 13, Monday Dec 8, 9:00AM--noon. The computers will allow you to use Matlab but not email or web browsing. After you finish the exam, email will be turned back on and you can send me your results. The tutorial Tuesday December 2 will be a "dry run" of the software, with a prototype question.

Course Text and other online references

On the Midterm

Solutions

The midterm will take place in MC 204, Monday November 3, 2008, from 7:00pm until 10:00pm. Extra time will be available for those who need it (some of the questions take a long time to state, and so if English is your second (or third or fourth) language, maybe it's reasonable to take a little extra time to read them. I believe, though, that the questions themselves are straightforward to do, once you've read them.

Calculators or computers will not be necessary. The exam is closed-book, so no notes or text either.

I hope to have your assignments marked by the end of tomorrow, so you may have them back on the weekend to look at.

Observations on the assignment

The midterm material is directly from my notes and from Moler's book, though the problems may involve new situations for what you have learned. The topics covered are: (in six multi-part questions in this order)

  1. Floating-point arithmetic
  2. Numerical Linear Algebra
  3. Interpolation and Least-Squares Approximation
  4. Quadrature
  5. Finite Differences
  6. Rootfinding

Tutorials on Matlab and LaTex

Tuesdays 9:30am, North Campus Building 105

  1. Found them...
  2. 11.11.2008 Residual Example
  3. 28.10.2008 ode solving Three-body problem. orbitodejac.m
  4. 21.10.2008 more on rootfinding: basins of attraction.
  5. 14.10.2008 Guest Tutorial, Prof. David Jeffrey, Chair, Dept. Applied Mathematics. Office Hours Postponed.
  6. 30.9.2008 Kahan on quadrature and my version of Kahan's proof that quadrature is impossible. Also, transcript of the Matlab session 29.9.2008.
  7. 23.9.2008 svdgraphs in matlab

Upcoming Lectures

  1. FFT (Moler 8, fourier.pdf) and PDE (Moler 11, pdes.pdf)

Assignments

  1. Assignment 4: Conditioning . Helper files first.m and second.m.
  2. Assignment 3: Rootfinding and ODEs Due 10.11.2008. If you get this today, ask Audrey or Karen for a printout, don't print it yourself
  3. (draft version 2.0) Assignment 2, Due 20.10.2008

    Possible transcription error in B coefficients? Two students have reported a potential problem with the compact finite difference question. Here is a (Maple) code fragment: you can check the numbers here.

    
       c := 2.0 + sqrt(3.0);
       alpha := 1.0/c;
    
       b := Array(0..n); # same as u
       b[0] := (-(25*c+3)*u[0] + (48*c-10)*u[1] + (18-36*c)*u[2] + (16*c-6)*u[3]
                 +(1-3*c)*u[4] )/12/h;
       for k to n-1 do
          b[k] := 3*(u[k+1]-u[k-1])/h;
       end do;
       b[n] := (11*u[n-4] - 58*u[n-3] + 126*u[n-2] - 182*u[n-1] + 103*u[n])/12/h;
    
    1. genbarywts.m
    2. hermiteval.m
    3. runge2example.m
  4. Assignment 1, Due 29.9.2008
  5. Assignment 0 (not for credit) Write a short description of your scientific background and interests. Due 15.9.2008.

Topics so far

Material from previous years

David Jeffrey's web page for AM561