Linear Algebra and Applications

Overview

Linear algebra and applications is the second of two mathematics core units and builds upon and expands the mathematical concepts developed in Calculus and Applications. It will provide a grounding and further understanding of mathematics and mathematical processes essential in underpinning the skill and knowledge necessary to carry out more complex computations.

Learning outcomes

Teaching methods

Hawthorn

Assessment

Content

• Matrices: basic matrix algebra, multiplication of matrices, special matrices, determinants, inversion, rank, null space, basis, linear independence.
• Linear transformations: matrix of linear transformations, examples: rotations, inversions and projections. Applications to fundamental examples 
• Matrices: 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 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. 
• Elements of differential geometry: curvilinear coordinates, curves and their properties, curvature, velocity and acceleration. Quadric Surfaces. The stationary points of a function of two variables 
• 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.