MA3201 - Numerical Methods

Numerical linear algebra: LU, QR, SVD factorisations, eigenvalue computations, least squares; numerical partial differential equations: finite differences, stability analysis, iterative solutions for elliptic equations.

Learning Outcomes

• manipulate advanced algebraic expressions and equations using appropriate techniques;
• factorise systems of linear equations (A=LU, A=LDU, PA=LU, A=AT=LDLT);
• understand fundamental theorems and definitions of linear algebra (operation counts, vector norms, matrix norms, condition numbers, Gerschgorin's Theorem, left and right inverses);
• apply linear algebra methods to solve eigenvalue and eigenvector problems, including QR algorithms and SVD factorisation;
• solve continuous and discrete least squares problems;
• classify partial differential equations and analytically solve certain types;
• construct numerical algorithms for different classes of partial differential equations (parabolic, hyperbolic);
• communicate mathematical thinking incorporating the concepts and methods presented in the course.

Note: Minor variations might occur due to the continuous Subject quality improvement process, and in case of minor variation(s) in assessment details, the Subject Outline represents the latest official information.