Mathematics

These studies are provided by academic units within Monash University's Faculty of Science.

General summary

Subject outlines

Enhancement Mathematics

This study consists of the units MAT1055 Mathematics 1A and MAT1085 Mathematics 1B. The two units will be taught as a whole-year sequence. The successful completion of this study will allow students to enrol in second-year mathematics units at Monash University.

MAT1055 Mathematics 1A

On completion of this unit, students will be able to use the basic analytical and computational methods of calculus and apply them to scientific and engineering problems; carry out calculations using matrices, determinants and vectors in three-dimensional space; use matrices to represent transformations; and use geometric interpretation with vector algebra in three dimensions to solve problems.

Topics covered include functions and their inverses and graphs; limits and continuity; differentiation techniques and applications including approximation of functions, optimisation, and rate problems; the integral and methods of integration, with applications in calculating areas, volumes, and centres of mass; elementary differential equations with applications; algebra of matrices, including partitioned matrices; homogeneous linear transformations; determinants and matrix inversion; operation counts for matrix computations; vectors in three-dimensional space, scalar and vector products; and applications of vector algebra in geometry, statics and dynamics.

Assessment

• Assignments: 30%
• Examination (3 hours): 70%

Prescribed textbook

• Ostebee, A, and Zorn, P, Calculus: From Graphical, Numerical and Symbolic Points of View , 2nd edn, Saunders College Publishing, 2002.

Recommended reading (for students who do not attend regular classes)

• Anton, H, and Busby, R, Contemporary Linear Algebra , Wiley, 2003.
• Varsavsky, C, with Carr, A, and Adlem, R, Epsilon 2.0 – Calculus and Linear Algebra (interactive mathematics courseware), Monash University, 2002 (supplied by the university).

MAT1085 Mathematics 1B

On completion of this unit, students will have extended their skills in calculus to include partial differentiation, solving a wider range of differential equations, numerical integration and further methods for analytic integration, and the construction and use of Taylor and Maclaurin series for functions. They will also be able to use several techniques to solve systems of linear equations.

Topics include partial differentiation and application to finding local extrema or saddle points of functions of two variables; numerical integration using several algorithms, and use of error bounds for each of these; applications of integration to arc length, moment of inertia and work done; systematic indefinite integration; exact calculation and estimation for convergent improper integrals; solution of first and second-order ordinary differential equations, including linear and homogeneous equations, and interpretation of initial conditions and solution behaviour; convergence of sequences and tests for convergence of series; obtaining Taylor and Maclaurin series representing functions and applications of these series; row reduction algorithms (Gaussian elimination and Gauss Jordan complete elimination) for the solution of linear systems, and analysis of solution sets; and further matrix inversion.

Assessment

• Assignments: 30%
• Examination (3 hours): 70%

Prescribed textbook

• Ostebee, A, and Zorn, P, Calculus: From Graphical, Numerical and Symbolic Points of View , 2nd edn, Saunders College Publishing, 2002.