Department of Applied Mathematics and Theoretical Physics

Numerical Analysis Course

Part IB

An important aspect of the application of mathematics to problems in the real world is the ability to compute answers as accurately as possible subject to the errors inherent in the data presented and the limits on the accuracy of calculation. Numerical analysis is the branch of mathematics studying such computations.

Contents

The course commences with approximation theory, focussing on the approximation of functions and data by polynomials, continues with the numerical solution of ordinary differential equations and concludes with the solution of linear algebraic systems. Although computational algorithms form a central part of the course, so do mathematical theories underlying them and investigating their behaviour: computation and approximation at their best should be done with proper mathematical justifcation.

Lecture Notes

Available on collection from the lectures.

For an older set of notes, see http://www.damtp.cam.ac.uk/user/na/PartIB/.

NOTE: the syllabus has changed!

The ODEs section of the course was previously in lectures 9-14 of Part II; see:

http://www.damtp.cam.ac.uk/user/na/PartII/Handouts.html

Example Sheets

From http://www.damtp.cam.ac.uk/user/examples/