Faculty of Mathematic Handbook,1987 - University of Newcastle

Kolmogorov, A.N. &
Fomin, S.Y.
Munroe, M.E.
663204 Topic W • Functional Analysis - J.R. Giles
Prerequisites
Hours
Examination
Content
Introductory Real Analysis (prentice-Hall 1970)
Introduction to Measure and Integration (Addison
Wesley 1953)
Topics B, CO, D, K. L
2 lecture hours and 1 tutorial hour per week for
1st half year
One 2-hour paper
Hilbert space, the geometry of the space and the representation of continuous linear
functionals. Operators on Hilbert space, adjoint, self-adjoint and projection operators.
Complete orthonormal sets and Fourier analysis on Hilbert space.
Banach spaces, topological and isometric isomorphisms, finite dimensional spaces and
their properties. Dual spaces, the Hahn-Banach Theorem and reflexivity. Spaces of
operators, conjugate operators.
Text
Giles, J.R.
References
Banach, S.
Brown, A.L. & Page, A.
Giles, J.R.
Kolmogorov, A.N. &
Fomin, S.Y.
Kceysig, E.
Liustemik, L.A. & Sobolev, U.l.
Simmons, G.F.
Taylor, A.E.
Wilansky, A.
Analysis of Normed Linear Spaces (University of
Newcastle 1978)
663217 Topic X • Fields and Equations - R.F. Berghout
Prerequisites
Hours
Examination
Content
Theorie des Operations Lineaires 2nd edn (Chelsea)
Elements of Functional Analysis (Van Nostrand 1970)
Analysis of Metric Spaces (University of Newcastle 1975)
Elements of the Theory of Functions and Functional
Analysis Yoll (Grayloch 1957)
Introductory Functional Analysis with Applications
(WHey 1978)
Elements of Functional Analysis (Frederick Unger 1961)
Introduction to Topology and Modern Analysis
(McGraw-Hill 1963)
Introduction to Functional Analysis (Wiley 1958)
Functional Analysis (Blaisdell 1964)
Topics D & K
1 lecture hour per week and 1 tutorial hour per
fortnight
One 2-hour paper
In this topic we will study the origin and solution of polynomial equations and their
relationships with classical geometrical problems such as duplication of the cube and
trisection of angles. It will further examine the relations between the roots and
coefficients of equations, relations which gave rise to Galois theory and the theory of
extension fields. We will learn why equations of degree 5 and higher cannot be solved
by radicals, and what the implications of this fact are for algebra and numerical analysis.
7.
Text
References
Bickhoff, G.D. & Macl.ane, S.
Edwards, H.M.
Herstein, IN.
Kaplansky, 1
Stewart, 1
Nil
A Survey of Modern Algebra (Macmillan 1953)
Galois Theory (Springer 1984)
Topics in Algebra (Wiley 1975)
Fields and Rings (Chicago 1969)
Galois Theory (Chapman & Hall 1973)
663207 Topic Z • Mathematical Principles of Numerical Analysis· W.P. Wood
Prerequisites
Hours
Examination
Content
Topics CO and 0; High-level language programming
ability is assumed.
2 lecture hours and 1 tutorial hour per week for
2nd half year
One 2-hour paper
Solution of linear systems of algebraic equations by direct and linear iterative methods;
particular attention will be given to the influence of various types of errors on the
numerical result, to the general theory of convergence of the latter class of methods and
to the concept of "condition" of a system. Solution by both one step and multistep
methods of initial value problems involving ordinary differential equations. Investigation
of stability of linear marching schemes. Boundary value problems. Finite-difference and
finite-element methods of solution of partial differential equations. If time permits, other
numerical analysis problems such as integration, solution of non-linear equations etc. will
be treated.
Text
Burden, R.L. &
Faires, J.D.
References
Atkinson, K.E.
Ames, W.F.
Cohen, A.M. et al.
Conte, S.D. &
de Boor, C.
Forsythe, O.E., Malcolm, M.A.
& Moler, C.B.
Isaacson, E. & Keller, H.M.
Lambert, J.D. &
Wait, R.
Mitchell, A.R. &
Wait, R.
Pizer, S.M. &
Wallace, V.L.
Smith, G.p.
Numerical Analysis 3rd edn (Prindle,
Weber & Schmidt 1985)
An Introduction to Numerical Analysis (Wiley 1978)
Numerical Methods for Partial Differential Equations
(Nelson 1969)
Numerical Analysis (McGraw-HilI 1973)
Elementary Numerical Analysis 3rd edn
(McGraw-Hill 1980)
Computer Methods for Mathematical Computations
(prentice-Hall 1977)
Analysis of Numerical Methods (Wiley 1966)
Computational Methods in Ordinary Differential
Equations (Wiley 1973)
The Finite Element Method in Partial
Differential Equations (Wiley 1977)
To Compute Numerically: Concepts and Strategies
(Little, Brown & Co. 1983)
Numerical Solution of Partial Differential Equations:
Finite Difference Methods (Oxford 1978)
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