MAT1085

Mathematics 1B

Dr John Arkinstall, Dr Alistair Carr and Dr Jill Wright

6 points - Second semester: Gippsland and distance - First semester: distance only - 3 hours of lectures and 2 hours of tutorials per week - Prerequisites: MAT1055 or GAS1613 - Prohibitions: GAS1642, MAT1010, MAT1020, MAT1050, MAT1080, GAS1615 (to 1997) Note: Optional weekend school sessions are offered for distance education students.

Objectives On completion of this subject 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.

Synopsis Topics covered include the following. Calculus: complex numbers; extension of systematic indefinite integration beyond MAT1055; extension of differential equations including homogenous 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 and row-reduction algorithms; linear dependence of vectors and subspaces of Euclidean n-space; eigenvalues and eigenvectors; diagonalisation of matrices; applications to population growth models and mechanical systems.

Assessment Assignments (and a class test for on-campus students): 30% - Examination (3 hours): 70%

Prescribed texts

Ostebee A and Zorn P Calculus from graphical, numerical and symbolic points of view vol. 2, Saunders, 1997
Grossman S I Elementary linear algebra 5th edn, Saunders, 1994

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