Monash University Handbook 2010 Undergraduate - Unit

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%

Chief examiner(s)

Dr Andrew Prentice (First semester)
Dr Eric Chu (Second semester)

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