1997 QUT Handbook

tions to random processes and regression; power; goodnessof-fit;
introduction to non-parametric tests.
Courses: BS50, BS56, ED50, IF34, IF42, IF44, IF58, IF71,
IT20, MA34, SC30
Prerequisites: MAB347 or credit in MAB237 or EFB101
Corequisites: MAB301
Credit Points: 12 Contact Hours: 4 per week
■ MAB422 TOPICS IN MATHEMATICS
Topics in geometry, recreational mathematics, and the history
of mathematics, including fractals, iterative maps, map projections,
Euclidean constructions, tesselations and mathematical
puzzles
Courses: ED50, IF34, IF71, SC30
Prerequisites: MAB222 or MAB301, MAB303
Credit Points: 12 Contact Hours: 4 per week
■ MAB485 ENGINEERING MATHEMATICS 2C
Differential equations, Laplace transform methods; orthogonal
functions; solution of systems of linear equations; vector analysis;
functions of a complex variable; limits, continuity; exponential,
circular, hyperbolic and logarithmic functions;
Cauchy-Riemann equations; Fourier transforms.
Courses: EE44, IF23 Prerequisites: MAB187, MAB188
Credit Points: 8 Contact Hours: 3 per week
■ MAB486 ENGINEERING MATHEMATICS 2D
Probability: events and sample spaces; independence; discrete
random variables and probability functions; continuous random
variables; mean, variance; examples of distributions.
Partial differential equations: the simultaneous partial differential
equations of Maxwell; the three-dimensional wave equation.
Laurent’s theorem. Residue theory, application to complex
integration.
Courses: EE44, IF23 Prerequisites: MAB485
Credit Points: 8 Contact Hours: 3 per week
■ MAB487 ENGINEERING MATHEMATICS 2A
Solution of large scale systems of linear equations by direct
and indirect methods; solution of second order differential
equations with constant coefficients; numerical solution of
differential equations; polynomial interpolation.
Courses: CE42, EE43, IF56, ME45, ME46
Prerequisites: MAB187, MAB188
Credit Points: 8 Contact Hours: 3 per week
■ MAB488 ENGINEERING MATHEMATICS 2B
Quadrature, determination of eigenvalues and eigenvectors of
large scale linear systems, power method, inverse iteration,
acceleration techniques; interpolation by cubic splines; Fourier
series and harmonic analysis; convergence of infinite series.
Laplace transforms.
Courses: EE43, IF56, ME45, ME46
Prerequisites: MAB487
Credit Points: 8 Contact Hours: 3 per week
■ MAB494 SURVEY MATHEMATICS 1
Spherical trigonometry: definition of sphere, circles on sphere
and spherical triangles; columnar, antipodal and polar triangles;
sine, cosine and half-angle formulae, Napier’s and
Delembre’s analogies; solution of spherical triangles, spherical
excess, area of spherical triangle; relation between plane
and spherical trigonometry. Differential calculus; Taylor and
Maclaurin series for functions of a single variable; extension
to functions of several variables; maxima and minima with
constraints, Lagrange multipliers; positional astronomy.
Courses: IF54, PS47 Prerequisites: MAB188
Credit Points: 6 Contact Hours: 3 per week
■ MAB496 SURVEY MATHEMATICS 2
Linear algebra: systems of linear equations in two and three
dimensions, the no solution, many solution and unique solution
cases, geometric interpretation; extension of concepts to
large scale systems, matrix formulation. Matrices: elementary
matrix algebra, equality, addition, multiplication by a
scalar, matrix products, inverse matrix, transpose matrix; types
of matrix, elementary matrices, identity matrices, singular and
non-singular matrices, symmetric matrices; orthogonal ma-
752
trices; reduction of a matrix to echelon form. Eigenvalue problem:
solution of characteristic equation in two and three dimensions,
corresponding eigenvectors; reality of eigenvalues
in symmetric cases; quadratic forms, principal axes; geometrical
applications, (classification of conics), extension of concepts
to large scale system.
Courses: IF54, PS47 Prerequisites: MAB188
Credit Points: 6 Contact Hours: 3 per week
■ MAB601 MULTIVARIABLE CALCULUS
Differentiation, extrema; double integrals, triple integrals,
surface integrals; functions of a complex variable, analyticity,
complex integration.
Courses: ED50, IF34, IF42, IF44, IF58, IF71, MA34, SC30
Prerequisites: MAB303, MAB304
Credit Points: 12 Contact Hours: 4 per week
■ MAB602 VECTOR FIELD THEORY
Vector analysis; scalar and vector fields; line integrals; surface
integrals; differential field operators; the integral properties
of fields. Tensor analysis; curvilinear coordinates; application
to potential theory; hydrodynamic theory, electromagnetic
theory; calculus of variations; functionals; Euler’s differential
equation; problems with subsidiary conditions.
Courses: IF42, IF44, MA34, SC30
Prerequisites: MAB601
Credit Points: 12 Contact Hours: 4 per week
■ MAB612 DIFFERENTIAL EQUATIONS
Mathematical modelling with differential equations;
wellposedness of first order differential equations and graphical
methods; theory of linear systems and nth order differential
equations, solutions for constant coefficients; series; Laplace
Transform; boundary value problems; Fourier series; separation
of variables method for partial differential equations.
Courses: ED50, IF34, IF42, IF44, IF58, IF71, MA34 SC30
Prerequisites: MAB303, MAB304
Credit Points: 12 Contact Hours: 4 per week
■ MAB618 COMPUTATIONAL MATHEMATICS 2
Linear equations; numerical solution of a single non-linear
equation; interpolation; quadrature; numerical solution of a
single first order differential equation.
Courses: IF42, IF44, IF58, IF71, IT20, MA34, SC30
Prerequisites: MAB321
Credit Points: 12 Contact Hours: 4 per week
■ MAB620 FINITE MATHEMATICS
Logic; axioms, proofs, truth-table decidability; set theory, relations,
functions; number theory: primes and divisibility,
Fermat’s and Euler’s theorems; greatest common divisor, Euclid’s
algorithm; primitive roots; arithmetic functions; abstract
algebra: Boolean algebras, groups, rings, fields; automata: finite
state machines.
Courses: ED50, IF58, IF71, IT20, MA34, SC30
Prerequisites: MAB303
Credit Points: 12 Contact Hours: 4 per week
■ MAB630 LINEAR ALGEBRA & ITS
APPLICATIONS
Concrete and abstract vector spaces; matrices; linear systems
and determinants; inner products and the projection theorem;
linear operators on a unitary space; eigenvalues; applications.
Courses: IF34, IF42, IF44, IF58, IF71, ED50, IT20, MA34,
SC30 Prerequisites: MAB303
Credit Points: 12 Contact Hours: 4 per week
■ MAB632 MATHEMATICAL MODELLING
Models are taken mainly from the areas of medicine and biology,
including cancer research and population growth, and
from mechanics applied to sport. Emphasis is on the mathematical
modelling and not on the development of new mathematical
techniques.
Courses: IF34, IF42, IF58, IF71, ED50, MA34, SC30
Prerequisites: MAB303 or MAB212, MAB222
Corequisites: MAB304
Credit Points: 12 Contact Hours: 4 per week