Mathematical Tripos: Part IB

Lecture notes for the course

Numerical Analysis (D3)

The left icon gives a PostScript file and the right icon a LaTEX2e file. You will need a PostScript viewer, e.g. ghostview, to display PostScript files. To compile, view and print LaTEX2e you need the right (and widely available) software, as well as the camnum.sty style file, which you can obtain from this site.

Click here for camnum.sty

Lecture handouts:

Lecture 1 Lecture 7
Lecture 2 Lecture 8
Lecture 3 Lecture 9
Lecture 4 Lecture 10
Lecture 5 Lecture 11
Lecture 6 Lecture 12

Example sheets:

Examples 1 Examples 2

Worked-out examples:

1. LU factorization
2. LU factorization with pivoting
3. Cholesky factorization
3a. Jacobi and Gauss-Seidel methods
4. QR factorization: Gram-Schmidt
4a. QR factorization: Gram-Schmidt
5. QR factorization: Givens rotations
5a. QR factorization: Givens rotations
6. QR factorization: Householder reflections
6a. QR factorization: Householder reflections
7. Least squares
8. Interpolation: the Lagrange formula
9. Interpolation: the Newton formula
10. Orthogonal polynomials
11. Least squares polynomial fitting
12. Gaussian quadrature
13. The Peano Kernel Theorem

Bear in mind, please, that these notes are for the exclusive use of Cambridge University students, supervisors and Directors of Studies only.
Do consult me for any nonstandard use and please let me know any comments, remarks and corrections.

Not all the files here are up-to-date: I am revising the handouts/examples, bringing them up-to-date, during the lecture course. However, I decided to leave last year's material whenever new material isn't available, to allow students an opportunity for an independent study. Always check the date to ascertain whether a handout is up-to-date!

The style file camnum.sty has been written by Prof. A. Iserles for the use by members of the NA group in Cambridge.
Here is what he says: "I do not mind if it is used by others, as long as

  1. It is not placed on web, ftp and gopher sites without my permission;
  2. It is not amended (actually, you are welcome to amend it if you change the name and obliterate all references to Cambridge NA and to me);
  3. No complaints are made to the author for bugs, shortcomings and acts of gross moral turpitude following the use of this style file."
A. Shadrin
DAMTP, University of Cambridge