# MAT1085 - Mathematics 1B

## 6 points, SCA Band 2, 0.125 EFTSL

#### Offered

Gippsland Second semester 2007 (Day)

Gippsland Second semester 2007 (Off-campus)

#### Synopsis

Topics covered include the following. Calculus: complex numbers; extension of systematic indefinite integration beyond MAT1055; extension of differential equations including homogeneous and linear ODEs; convergence of series; Taylor's theorem; partial differentiation and local extrema of functions of two variables. Linear algebra: linear systems of equations, row-reduction algorithms; linear dependence of vectors and subspace of Euclidean n-space; eigenvalues and eigenvectors; diagonalisation of matrices; applications to population growth models and mechanical systems.

#### Objectives

On completion of this unit the student is expected to demonstrate an understanding of the basic computational techniques of calculus, including those involving infinite series representation of functions and partial differentiation of functions of two variables; understand sufficient of the conceptual basis of calculus to be able to apply it to derive formulations of scientific and engineering problems; demonstrate facility in computations involving row-reduction algorithms for solution of linear systems, and eigenvalues and eigenvectors of a small square matrix; demonstrate an understanding of the structure of the solution set of a linear system and of the interpretation and uses of eigenvalues and eigenvectors.

#### Assessment

Assignments (and a class test for on-campus students): 30%

Examination (3 hours): 70%

#### Contact hours

3 hours of lectures and one 1-hour tutorials per week

#### Prerequisites

MAT1055

#### Prohibitions

MTH1030, ENG1902