AMSC/CMSC660, Fall 2021 - SCIENTIFIC COMPUTING I

Course information

SYLLABUS: Information about exams, homeworks, grades

There is no textbook. But many topics in this class are covered in Bindel, Goodman: Principles of Scientific Computing . In many cases I will use a somewhat different approach, so attending class and reading the material below is important.

Additional Course Material

Review of Taylor's theorem with example

Gaussian elimination WITHOUT pivoting: Download m-file lunp.m and put it in the same folder as your other m-files.

Gaussian elimination WITHOUT pivoting , Matlab live script file (download this file and open it with Matlab, then you can modify and rerun the examples, instructions for Matlab Live Scripts)

Solving linear systems

Solving a linear system \(Ax=b\) in Matlab:
[L,U,p] = lu(A,'vector') y = L\b(p) x = U\y
or you can use the shortcut x=A\b.

Errors for linear systems

How to approximate \(\mathrm{cond}_1(A)\) , \(\mathrm{cond}_\infty(A)\) just using \(L,U\):
\(\mathrm{cond}_1(A)\approx\) norm(A,1)*invnormest(L,U),
\(\mathrm{cond}_\infty(A)\approx\) norm(A,Inf)*invnormest(U',L').
You first have to download invnormest.m and put it in the same folder as your other m-files.

Matlab programming

We will use Matlab to see how various algorithms work.

Matlab can be downloaded for free from TERPware.

Matlab Onramp - learn Matlab in two hours with this interactive tutorial

We will NOT use SYMBOLIC Matlab commands (like sym, syms, subs, diff, taylor etc.) in this class.

Matlab Primer gives a concise summary of the most important Matlab commands. It was written for an older version of Matlab, so skip sections 14, 15, 17.

How to hand in Matlab results for homeworks:

You have to write an m-file for each problem. (Typing commands at the >> prompt and printing this out is not allowed)
You have to hand in all m-files together with the generated output and graphics.
- You can use the publish command in Matlab (if you call additional m-files you have to print them out separately).
- You can use Live Scripts and export them as pdf, html or Word
- You can manually combine code, graphics, output e.g. in Microsoft Word.
Comment your code so that another person (or you one week later) can see what you are doing.
Only print out values which are asked for in the problem. (Make sure you have a semicolon at the end of lines.)
Label all numerical output and graphics: How to display and label numerical output and graphics in Matlab
Hand in additional pages (this can be handwritten) which show the "paper and pencil work",
answer all the questions asked in the problem and describe your observations.
Each homework has to be handed in as a SINGLE PDF file on ELMS.

How to use the publish command in Matlab:
Use lines starting with %% for the main title and for each section title.
Lines starting with % right after a section title will be printed at the beginning of each section. Use this for your observations about the problem.

Example 1: Using publish with the m-file sample.m generates sample.html (which you can print out and hand in).

Example 2: this m-file shows how to format each problem. This is the generated output.

More information about publishing markup