Faculty of Mathematic Handbook,1987 - University of Newcastle

Text
Churchill, R V., Brown, J. W.
& Verhey, RF.
or.
Kreysig, E.
References
Grove, E.A. &
Ladas, G.
Kreysig, E.
Levinson, N. & Reelheffer,RM.
O'Neill, P.V.
Spiegel, M.R
Tall, D.O.
Complex Variables and Applications
(McGraw-Hill 1984)
Advanced Engineering Mathematics
Introduction to Complex Variables
(Houghton Mifflin 1974)
Advanced Engineering Mathematics (Wiley 1979)
Complex Variables (Holden-Day 1970)
Advanced Engineering Mathematics(Wadsworth 1983)
Theory and Problems of Complex Variables
(McGraw-Hill 1964)
Functions of a Complex Variable I and II
(Routledge and Kegan Paul 1970)
662109 Topic CO - Vector Calculus & Differential Equations - W. Summerfield
Prerequisite Nil
Hours 2 lecture hours per week and 1 tutorial hour per week
Examination
Content
One 3-hour paper
Differential and integral calculus of functions of several variables: partial derivatives,
directional derivative, chain rule, Jacobians, multiple integrals, Gauss' and Stokes'
theorems (with Green's theorem as a special case), gradient, divergence and curl.
Conservative vector fields. Taylor's polynomial, stationary points. Fourier series:
generalisation. First order ordinary differential equations: separable, homogeneous, linear.
Applications. Higher order (mainly second) linear differential equations: general solution,
initial (and boundary) value problems, solution by Laplace transform. Series solution
about ordinary point and regular singular point. A little on Bessel functions, Legendre
polynomials and applications of higher order equations if time permits. Sturm-Liouville
systems. Second order linear partial differential equations: Laplace, Wave and Diffusion
equations.
Text
Kreyszig, E.
or
Greenberg, M.D.
References
Amazigo, J.C. &
Rubenfeld, L.A.
Boyce, W.E. &
Di Prima, RC.
Churchill, R.Y. &
Brown, J.W.
Courant, R.
Edwards, C.H. & Penney, D.E.
Advanced Engineering Mathematics 5th edn
(paperback, Wiley 1979)(5th edn is preferable but 4th
eeln will suffice)
Foundations of Applied Mathematics (prentice-Hall)
(1978)
Advanced Calculus and its Applications
to the Engineering and Physical Sciences
(Wiley 1980)
Elementary Differential Equations and Boundary
Value Problems (Wiley 1986)
Fourier Series and Boundary Value Problems
(McGraw-HilI 1978)
Differential and Integral Calculus Vol.1I (Wiley 1968)
Calculus and Analytic Geometry (Prentice-Hall 1982)
66
Finizio, N. &
Ladas, G.
Greenspan, H.D. &
Benney, D.J.
Haberman, R.
O'Neill, P.V.
Piskunov, N.
Powers, D.L.
Spiegel, M.R.
Spiegel, M.R.
Stein, S.K.
Stephenson, G.
662104 Topic D - Linear Algebra - G.W. Southern
Prerequisite Nil
Hours
Examination
Content
Ordinary Differential Equations with Modern
Applications 2nd eeln (Wadsworth 1982)
Calculus - an Introduction to Applied Mathematics
(McGraw-Hill 1973)
Elementary Applied Partial Differential Equations
(Prentice-HaIl 1983)
Advanced Engineering Mathematics
(Wadsworth 1983)
Differential and Integral Calculus VoLl
and II 2nd edn (Mir 1981)
Boundary Value Problems (Academic 1972)
Theory and Problems of Vector Analysis (Schaum 1959)
Theory and Problems of Advanced Calculus
(Schaum 1974)
Calculus and Analytic Geometry 3rd edn
(McGraw-Hill 1982)
An Introduction to Partial Differential Equations for
Science Students 2nd eeln (Longman 1974)
1 lecture hour per week and 1 tutorial hour per
fortnight
One 2-hour paper
First semester: A brief review of some material in the algebra section of Mathematics I.
Linear maps, matrix representations. Diagonalisation, eigenvalues and eigenvectors.
Inner product spaces. Orthogonal, unitary, hermitian and nonnal matrices. Difference
equations. Quadratic forms. Linear programming.
Second semester: Gram-Schmidt process, upper triangular matrices. Characteristic and
minimum polynomials. Cayley-Hamilton theorem. Duality. Jordan form. Some
Euclidean geometry, isometries, dimensional rotations.
Text
References
Anton, H.
Bloom, D.M.
Brisley, W.
Lipschutz, S.
Nering, E,D.
Reza, F.
Roman, S.
Rones, C. & Anton, H.
Nil
Elementary Linear Algebra 4th edn (Wiley 1984)
Linear Algebra and Geometry (Cambridge 1979)
A Basis for Linear Algebra (Wiley 1973)
Linear Algebra (Schaum 1974)
Linear Algebra and Matrix Theory (Wiley 1964)
Linear Spaces in Engineering (Ginn 1971)
An Introduction to Linear Algebra (Saunders 1985)
Applications of Linear Algebra (Wiley 1979)
662201 Topic E - Topic in Applied Mathematics e.g. Mechanics and Potential
Tbeory - C.A. Croxton
Corequisite
Hours
Topic CO
1 lecture hour per week and 1 tutorial hour per
fortnight
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