Module MA1263: Introduction to numerical analysis

Credit weighting (ECTS)

5 credits

Semester/term taught

Michaelmas term 2014-15

Contact Hours

11 weeks, 3 lectures including tutorials per week. Lecture notes will be published on the following link http://www.maths.tcd.ie/~odunlain/

Lecturer

Prof. Colm Ó Dúnlaing

Learning Outcomes

On successful completion of this module students will have;

• Familiarity with numerical methods for finding roots of polynomials, solving linear equations, and solving some differential equations.
• Knowledge of the IEEE standard and some knowledge of its impementation
• Ability to estimate the accuracy of some numerical methods

Module Content

• Euclid's gcd algorithm, Sturm Sequences, Newton-Raphson.
• Format of single and double-precision floating point numbers and hexadecimal notation.
• The IEEE 754 standard and its implementation.
• Accuracy of summation.
• Gaussian elimination, LU factorisation: accuracy of same.
• ODEs: Euler, Runge-Kutta.
• Condition numbers (time permitting)

Module Prerequisite

 

Assessment Detail

This module will be examined in a 2 hour exam in Trinity term. 20% of the final mark will be based on coursework (quizzes) and the other 80% on the exam. There will, most likely, be five quizzes.