421-204 Mathematics for Engineers Unit 2.1B (Basic)

Credit Points

Coordinator

Prerequisites

Mathematics 618-181 and 618-182 (or equivalents)

Semester

Contact

Subject Description

The objective of this subject is to give students a working knowledge of basic matrix methods for use in solving linear problems, and calculus when applied to functions of more than one variable.

Topics covered include:

Part 1 Sequences, Series and Matrices: Convergence and divergence of sequences and series, tests for convergence. Taylor's theorem and series representation of elementary functions. Eigenvectors and eigenvalues, linear independence, factorisation of matrices, diagonal, real-symmetric, Hermitian, unitary and orthogonal matrices, quadric surfaces, quadratic forms, definiteness of matrices.

Part 2 Multivariable Calculus: Functions of several variables, level curves, heights. Partial derivatives, total derivative, gradient vector, directional derivatives and applications. Chain rules. Coordinate transformations, Jacobi matrix and determinant. Maxima and minima of functions of several variables with constraints. Lagrange multipliers. Area and volume integrals, iterated integrals, Cartesian and polar coordinates in two and three dimensions.

Assessment

One written examination not exceeding three-hours at the end of first semester. Plus additional tests and assignments to a maximum value of 10%