Please note - Swinburne University of Technology

Vector Calculus - scalar and vector fields, gradient of a
scalar field, the potential, surface integrals, flux of a vector
field, divergence Gauss' theorem, continuity of fluid flow,
line integrals. curl, Stokes theorem, introduction to fluid
dynamics.
Linear algebra - orthogonal matrices, eigenvalued problems,
real symmetric matrices and applications.
Statistics - review of data analysis, probability distributions
for discrete variates and continuous variates, sampling
distributions. The t distribution, F and Chi-Square hypothesis
testing, goodness of fit, ANOVA (One and Two-way),
correlation and simple regression, experimental design.
Minitab package used.
Operations research chosen from queuing theory and linear
programming.
Textbook
Smith, P.J. lntro Statistics. Melbourne, Australia: Thomas Nelson, 1993
References
Bajpai, A.C., Calus, J.M. and Fairley, J.A. Statistical Methods for
Engineerr and Scientists. New York: Wiley, 1978
Hogg, R.V. and Ledolter, J. Engineering Statistics. New York:
Macrnillan, 1989
Kreyszig. E. Advanced Engineering Mathematics 7th ed, New York:
Wiley, 1993
Rade, L. and Westergren, B. Beta Mathematics Handbook. 2nd ed,
Lund: Studentlitteratur, 1990
Ryan, B.F. Joiner, B.L. and Ryan, T.A. Minitab Handbook. 2nd ed,
Boston: Duxbury Press, 1992
Stroud, K.A. Further Engineering Mathematics. London: MacMillan,
1986
Thomas, B.T. Jr. and Finney, R.L. Cakulus and Analytical Geometry.
8th ed, Reading, Mass.: Addison Wesley, 1992
SM294
Engineering Mathematics
No. of hours per week: four hours for two
semesters
Prerequisite: SM199 (or SM199A) Engineering
Mathematics
Instruction: lectures and tutorials
Assessment: examination and tests
F
n
c Engineering (Electrical- unstreamed).
0
A second-year subject in the degree of Bachelor of
K Subject aims
This subject aims to provide the necessary mathematical
background and analytical techniques essential for the
%.
understanding of the engineering course and for further
m research.
2.
2 Subject description
" Integration: integration techniques, infinite integrals. Double
integrals, triple integrals, occurrence. Plane polar, cylindrical
and s~herical coordinates.
bplace transforms: calculation of transforms and inverse
transforms, shift theorems, transforms of derivatives and
integrals, solution of differential equations, initial and final
value theorems. Step function and dirac delta, circuit
differential equations, convolution.
Fourier series: orthogonality. Trigonometric Fourier series,
Euler formulas, half range series, Dirichlet's theorem,
Parseval's formula, power spectrum, transmission of periodic
waveforms by two port networks, transfer functions.
Fourier transforms: frequency spectrum of a non-periodic
function. Fourier transforms, inversion integral, convolution.
Two port networks, impulse response.
Vector fields: line and surface integrals, grad, div and curl,
the formulas of Gauss and Stokes, combinations of vector
operators, scalar potential, the equations of Laplace and
Poisson.
Special functions: the Gamma function and its properties.
Definition of Bessel functions of the first kind, properties.
Bessel's differential equation and its solution, the Weber
functions and their properties. Orthogonality, Fourier-Bessel
series. Partial differential equations: solution by direct
integration and by separation or variables. Application of
boundary and initial conditions. Use of Fourier series and
Fourier-Bessel series.
Probability and statistics: combinational reliability, series and
parallel systems, redundancy, statistical dependence. Discrete
distributions, the binomial distribution, the Poisson
distribution. Continuous distributions, probability density
functions, the normal, chi-square, Rayleigh and gamma
distributions, sum of two random variables, characteristic
functions, the central limit theorem. Confidence limits and
hypothesis testing for the mean and variance. Goodness of
fit.
References
Kreyzig, E. Advanced Engineering Mathematics. 7th ed, New York:
Wiley. 1993
O'Neil. F! Advanced Engineering Mathematics. 3rd ed, Belmont:
Wadsworth, 1991
Rade. 1. and Westergren. 8. Beta Mathematics Handbook. 2nd ed,
Lund: Yudentlineratur, 1990
Thomas, G.B. and Finney, R.L. Calculus and Analytic Geometry. 8th
ed, Reading, Mass.: Addison-Wesley, 1992
SM295 Engineering Mathematics
No. of hours per week: six hours for five weeks,
seven hours for nine weeks
A subject in the bridging program for engineering students
from S.E. Asia.
Subject aims and description
Vector geometry, functions of more than one variable, partial
differentiation, differential equations.
Statistics, multiple integration, vector calculus, linear algebra.
References
Hogg. R.V. and Ledolter, 1. Engineering Statistics. N.Y.: MacMillan,
1989
Krepzig, E. Advanced Engineering Mathematics 7th ed, New York:
Wiley, 1993
Rade, L. and Westergren, 8. Beta Mathematics Handbook. 2nd ed.
Lund: Studentlitteratur, 1990
sM299
Engineering Mathematics
No. of hours per week: three hours for two
semesters
Instruction: integrated instruction and practice
A second-year subject in the degree of Bachelor of
Engineering (MechanicallManufacturing).
Subject aims and description
Integration-integration methods, plane polar coordinates,
double integrals and applications, cylindrical and spherical
coordinates, triple integrals and applications.
Vector calculus - scalar and vedor fields, gradient of a
scalar field, the potential, surface integrals, flux of a vector
field, divergence Gauss' theorem, continuity of fluid flow,
line integrals, curl, Stokes theorem, introduction to fluid
dynamics, introduction to tensors and tensor notation.
Linear algebra - orthogonal matrices, eigenvalue problems,
real symmetric matrices and applications.
Statistics - review of data analysis, probability, probability
distributions for discrete variates and continuous variates,
sampling distributions. The t distribution, F and Chi-Square,
hypothesis testing, goodness of fit, ANOVA (One and Twoway),
correlation and simple regression, experimental design.
Minitab package used.