#### Leader: C Hough, E Chu, Y O Tan (M'sia)

#### Offered

Clayton First semester 2007 (Day)

Clayton Second semester 2007 (Day)

Malaysia First semester 2007 (Day)

Malaysia Second semester 2007 (Day)

Os-iran First semester 2007 (Day)

#### Synopsis

Vector algebra and geometry: equations of lines and planes. Linear algebra: matrix operations, systems of linear equations, eigenvalues and eigenvectors. Calculus: logarithmic differentiation, improper integrals, integration by parts. Sequences and series: convergence, power series, Taylor polynomials. Ordinary differential equations: first order, second order with constant coefficients, boundary value problems, systems of ODEs. Multivariable calculus: partial derivatives, directional derivatives, chain rule, maxima and minima.

#### Objectives

On completing this unit, students will be able to calculate cross products of vectors, and use vectors to represent lines and planes; perform matrix algebra; solve systems of linear equations and find eigenvalues and eigenvectors in simple cases; use hyperbolic functions; perform logarithmic differentiation; establish the convergence of improper integrals, and use further techniques of integration, including integration by parts; establish the convergence of numeric and power series, construct Taylor series and use Taylor polynomials to approximate functions; solve first order ordinary differential equations, including the techniques of exact integration, separable variables and integrating factor; and systems of ordinary differential equations; solve 2nd order linear differential equations with constant coefficients; set up differential equations with initial or boundary conditions to model simple engineering problems; calculate partial derivatives, use the grad vector to find directional derivatives, use chain rule, calculate small error using the total differential, and find maximum and minimum values of two-variable functions.

#### Assessment

Assignments and test: 30%

Examination (3 hours): 70%

#### Contact hours

3 hours lectures, 2 hours practice classes and 7 hours of private study per week

#### Prerequisites

VCE Specialist Mathematics (or ENG1090 or equivalent)

#### Prohibitions

ENG1902, MTH1030, MAT1085