Course details
Semester
 Autumn 2007
 Monday, October 8th to Friday, December 14th
Hours
 Live lecture hours
 20
 Recorded lecture hours
 0
 Total advised study hours
 0
Timetable
 Tuesdays
 11:05  11:55
 Tuesdays
 13:05  13:55
Description
Prerequisites
No prerequisites information is available yet.
Syllabus
This is a 20 lecture course. The aim of the course is to introduce
students to a number of key ideas and methods in numerical
analysis and for the students to learn to implement algorithms in
Matlab.
Syllabus
Lecture 1: Introduction and prerequisites. Description of the
ideas to be covered and the assessment activities.
Lecture 2: Stable and unstable computation, relative and
absolute error, floating point computation and round off errors.
Lecture 3: Finding roots of nonlinear equations. Bisection,
secant and Newton's methods.
Lecture 4: Approximation
of functions I. Polynomial interpolation, Lagrange and Newton
forms: divided differences.
Lecture 5: Approximation of function II. Piecewise polynomial approximation.
Splines and their generalisations into higher dimensions.
Lecture 6: Approximation of functions III. Least
squares and orthogonal polynomials.
Lecture 7: Numerical integration. NewtonCotes and
Gauss formulae. Integration of periodic functions. Romburg
integration.
Lecture 8: The Fast Fourier transform.
Lecture 9: Numerical differentiation and Richardson
extrapolation.
Lecture 10: Solving systems of linear equations I.
Gauss elimination, pivoting. Cholesky factorisation.
Lecture 11: Solving systems of linear equations II.
Conditioning and error analysis.
Lecture 12: Solving systems of linear equations II.
Iterative methods: Jacobi, GaussSeidel, SOR.
Lecture 13: Least squares solution and the QR
algorithm.
Lecture 14: Solving partial differential equations I.
Finite difference methods for elliptic equations.
Lecture 15: Solving partial differential equations II.
The Galerkin method and finite element methods.
Lecture 16: Solving partial differential equations III.
Parabolic equations, explicit and implicit methhods. The
CrankNicolson method.
Lecture 17: Solving ordinary differential equations I.
Taylor series methods. RungeKutta methods.
Lecture 18: Solving ordinary differential equations II.
Multistep methods. Higher order differential equations.
Lecture 19: Solving ordinary differential equations III.
Boundary value problems: shooting methods, finite difference
methods, collocation.
Lecture 20: Summarising and finishing course. This
lecture also allows some time if other topics take longer than
expected.
Reading list and references
There are a number of excellent books on numerical analysis and you are encouraged to consult these books for alternative and often better accounts of what you have heard in lectures. In the main I have followed Kincaid and Cheney [4] and Higham [2].
Reading list and references
There are a number of excellent books on numerical analysis and you are encouraged to consult these books for alternative and often better accounts of what you have heard in lectures. In the main I have followed Kincaid and Cheney [4] and Higham [2].
 S. D. Conte and C. deBoor, Elementary Numerical Analysis, (3rd Ed) McGrawHill, 1980.
 N. J Higham, Accuracy and Stability of Numerical Algorithms, SIAM, 1996.
 A. Iserles, A First Course in the Numerical Analysis of Differential Equations, CUP, 1996.
 D. R. Kincaid and E. W. Cheney, Numerical Analysis, Brooks/Cole Publishing Company, 1991.
 E. Süli and D. Myers, An Introduction to Numerical Analysis, CUP, 2003.
Lecturer

JL
Professor Jeremy Levesley
 University
 University of Leicester
Bibliography
No bibliography has been specified for this course.
Assessment
Attention needed
Assessment information will be available nearer the time.
Lectures
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