Faculty of Mathematic Handbook,1987 - University of Newcastle

Examination
Content
This topic will introduce basic concepts of the local theory of differentiable manifolds.
Vector fields, differential forms, and their mapping. Frobenius' theorem. Fundamental
properties of Lie groups and Lie algebras. General linear group. Principle and associated
fibre bundles. Connections. Bundle of linear frames, affine connections. Curvature and
torsion. Metric, geodesics. Riemannian manifolds.
Text
References
Auslander, L.
Chevalley, C.
Kobayashi, S. & Nomizu. K.
Nil
664165 Mathematical Physiology - W. Summerfield
Prerequisite Nil
Hours About 27 lecture hours
Examination
Content
Differential Geometry (Harper & Row 1967)
Theory of Lie Groups, Vol. I (princeton 1946)
Foundations of Differential Geometry, Vol. I
(Interscience 1963)
One 2·hour paper
Physiology " the study of how the body works based on the knowledge of how it is
constructed - essentially dates from early in the seventeenth century when the English
physician HalVey showed that blood circulates constantly through the body. The
intrusion of engineering into this field is well know through the wide pUblicity given to
(for example) heart by-pass and kidney dialysis machines. cardiac assist pace-makers. and
prosthetic devices such as hip and knee joints; the obviously beneficial union has led to
the establishment of Bioengineering Departments within Universities and Hospitals.
Perhaps the earliest demonstration of mathematics' useful application in (some areas of)
physiology is the mid-nineteenth century derivation by Hagen, from the basic equations
of continuum motion, of Poiseuille's empirical formula for flow through narrow straight
tubes; detailed models of the cardiovascular circulatory system have recently been
developed. Mathematical models have also been formulated for actions such as
coughing, micturition and walking, as well as for the more vital processes involved in gas
exchange in the lungs, mass transport between lungs and blood and blood and tissue,
metabolic exchanges within tissues, enzyme kinetics, signal conduction along nelVe
fibres. sperm transport in the cervix, ..... Indeed, mathematical engineering might now. be
said to be part of the conspiracy to produce super humans (e.g. see "Fast Runnmg
Tracks" in Dec. 1978 issue of Scientific American).
This course will examine in some detail a few of the previously mentioned mathematical
models; relevant physiological material will be introduced as required.
Text
References
Bergel, D.H. (ed.)
Care, C.G., Pedley, T.J.,
Schroter, R.D. & Seed, W.A.
Christensen, H.N.
Nil
Cardiovascular Fluid Dynamics (Vols I & II)
(Academic 1972)
The Mechanics of the Circulation (Oxford 1978)
Biological Transport (W.A. Benjamin, 1975)
,
I
Fung, Y.C
Fung, Y.C
Fung, Y.C, Perrone, N. &
Anliker, M. (eds.)
Lightfoot, E.N.
Margaria, R.
Pedley, T.J.
West, J.B. (ed.)
664105 Combinatorial Designs· (not offered in 1987)
Prerequisites
Hours
Examinatioli
Content
Biodynamics: Circulation (Springer· Verlag 1984)
Biomechanics: Mechanical Properties of Living
Tissues (Springer-Verlag 1981)
Biomechanics Its Foundations and Objectives
(Prentice· Hall 1972)
Transport Phelwmena and Living Systems (Wiley 1974)
Biomechanics and Energetics of Muscular Exercise
(Clarendon 1976)
The Fluid Mechanics of Large Blood Vessels
(Cambridge 1980)
Bioengineering Aspects of the Lung
(Marcel Dekker 1977)
Topics D and K
About 27 lecture hours
One 2·hour paper
An introduction to various types of designs and their properties. Pairwide balanced
designs: the basic theory, some existence theorems, Wilson's theorems. Latin squares
and balanced incomplete block designs; the existence theory using pairwise balanced
designs, and various constructions. Partial balance. Room squares. Hadamard matrices.
Block designs on graphs, such as handcuffed designs.
Text
Street, A.P. & Wallis, W.D.
References
Denes, J. & Keedwell, A.D.
Hall, M. Jr.
Mann, H.B.
Raghavarao. D.
Ryser, H.J.
Wallis, W.D. et al.
Wallis, W.D.
Combinatorial Theory: An Introduction (CBRe 197)
Latin Squares and their Applications
(English and Akademiai Kiado 1974)
Combinatorial Theory (Blaisdell 1967)
Additioll Theorems. The Addition Theorems of Group
Theory and Number Theory (Interscience 1965)
Constructions and Combinatorial Problems in Design
of Experiments (Wiley 1971)
Combinatorial Mathematics (Wiley 1963)
Combinatorics: Room Squares, Sum·Free Sets,
Hadamard Matrices (Springer 1972)
Combinatorial Designs (Vniv. of Surrey 1977)
664168 Asfrophysical Applications of Magnetohydrodynamics . W.P. Wood
Prerequisites
Hours
Examination
Content
Topics CO and PD
About 27 lecture hours
One 2-hour paper
The nonnal state of matter in the universe is that of a plasma, or ionized gas, permeated.
by magnetic fields. Moreover, these fields (unlike that of the earth) may be dominant, or
at least Significant, in controlling the structure of the region. The aim of this course is to
investigate the effects of astrophysical magnetic fields, ranging from 10-6 gauss in the
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