Linear Algebra and Applications

Overview

This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies.

Learning outcomes

Teaching methods

Hawthorn

Assessment

(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.

Content

• Matrices: basic matrix algebra, multiplication of matrices, special matrices, determinants, inversion, Cramer's rule, rank, null space, basis, linear independence
• Vectors: direction and magnitude, vector spaces, sub-spaces spanning and bases, linear dependence / independence, length of a vector and the scalar product, area of a parallelogram and the vector product. Examples and applications to simple models
• Elements of linear geometry: equation of a line, equation of a plane, intersection between lines and planes, distance from a point to a plane, distance from a point to a line, distance between two lines
• Systems of linear equations: elementary row operations, augmented matrix, row echelon form, Gaussian elimination, Cramer’s rule, inversion method, solution in the parametric form. Examples and applications to relevant models
• Elements of differential geometry: curvilinear coordinates, curves and their properties, curvature, velocity and acceleration
• Linear transformations: system of linear equations in the matric form, matrix of linear transformations, examples: rotations, inversions and projections. Applications to fundamental examples.
• Complex numbers and their properties: imaginary numbers, complex conjugates, Argand plane in Cartesian and polar forms, de Moivre’s theorem, roots of complex numbers, complex exponential form and applications