Please note - Swinburne University of Technology

1.
:.
3
0,
~ ~ 2 9 3 Engineering Mathematics
No. of hours per week: three hours for two
semesters
Instructions: lecturers and practical workshops
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 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 form queueing theory and linear
programming.
Textbook
Smith, P.J. Into Statistics. Melbourne, Nelson, 1993
References
Bajpai, A.C., Calus, I.M. and Fairley, J.A. Statistical Methods for
3. Engineers and Scientists. New York, Wiley, 1978
2 Hogg, R.V. and Ledolter, J. Engineering Statistics. New York, Macmillan,
-% 1987
m Kreyszig, E. Advanced Engineering Mathematics. 7th edn, New York,
4, Wiley, 1993
2 Rade. L. and Westeraren. B. Beta Mathematics Handbook. 2nd edn.
r[)
%. ~und; Studentlitteraiur, i990
3 Ryan, B.F., Joiner, B.L. and Ryan, T.A. Minitab Handbook. 2nd edn,
'fl Boston, PWS-Kent, 1992
L"
Stroud, K.A. Further Engineering Mathematics. London, Macmillan,
? 1986
V
B.
Thomas, G.B. and Finney, R.L. Calculus andAnalytica1 Geometry 8th
edn, Reading, Mass., Addison-Wesley, 1992
3
~ ~ 2 9 4 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
Subject aims
This subiect aims to provide the necessary mathematical
background and analytical techniques essential for the
understanding of the engineering course and for further
research.
Subject description
Integration and Fourier series: integration techniques, infinite
integrals, repeated integrals. 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.
Laplace transforms: calculation of transforms and inverse
transforms, shift theorems, transforms of derivatives and
intearals. solution of differential eauations. initial and final
value theorems. Step function and'dirac delta, circuit
differential equations, convolution.
Fourier transforms: frequency spectrum of a non-periodic
function. Fourier transforms, inversion integral, convolution.
Two port networks, impulse response.
Double and triple integration: double integrals, triple
integrals, occurence. Plane polar, cylindrical and spherical
coordinates.
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.
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, probability density functions, the normal, chisquare,
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 edn, New York,
Wiley, 1993
O'Neil, P. Advanced Engineering Mathematics. 3rd edn, Belmont,
Wadsworth, 1991
Rade, L. and Westergren, B. Beta Mathematics Handbook. 2nd edn,
Lund, Studentlitteratur, 1990
Thomas, G.B. and Finney, R.L. Calculus and Analytic Geometry 8th
edn, Reading, Mass., Addison-Wesley, 1992
~ ~ 2 9 5 Engineering Mathematics
No. of hours per week: six hours for five weeks.
seven hours for nine weeks
Subject aims and description
Vector geometry, functions of more than one variable, partial
differentiation, differential equations.
Statistics, mutiple integration, vector calculus, linear algebra.
References
Hogg, R.V. and Ledolter, J. Engineering Statistics, New York, Macmillan,
1989
LGszig, E. Advanced Engineering Mathematics. 7th edn, New York,
Wiley, 1993
Rade, L. and Westergren. B. Beta Mathematics Handbook. 2nd edn,
Lund, Studentlitteratur, 1990