Please note - Swinburne University of Technology

~~3400 Mathematical Methods
8.0 credit points per semester
No. of hours per week: three hours
Prerequisite: SM 1200 or SM 1215
Assessment: testslexaminations and assignments
A second-year subject of the degree course in instrumentation
and computer science.
Subject description
Linear algebra and vectors
Matrices and matrix algebra. Systems of linear equations:
Guassian elimination; procedures for numerical solution by
direct or iterative methods, (Jacobi and Gauss-Seidel),
transformation matrices.
Real analysis
Partial differentiation, chain rule, approximations. Application
to maximum and minimum problems constrained optima
and Lagrange multipliers. Change of variable. Multiple
integrals. Applications of single, double and triple integrals.
Jacobians. Surface integrals. Fourier series of general periodic
functions. Laplace transforms. Use of tables. Partial
differential equations, solution via separation of variables
(Fourier series).
Vector analysis
Basic vector manipulation including calculus of vector
functions. Space curves, Serret-Frenet formulas. Special
emphasis on gradient of a scalar field, directional derivative,
divergence and curl of a vector field. Line, surface and
volume integrals. Field theory.
Complex analysis
Algebra and geometry of complex numbers. Functions of a
complex variable. Elementary functions such as polynomial,
exponential, trigonometric, hyperbolic, logarithm and power.
Differentiability and Cauchy-Reimann equations. Harmonic
functions. Contour integration, Cauchy integral and residue
theorems. Evaluation of definite integrals. Conformal
mapping and applications.
Random processes
Review of probability, Markw chains, Poisson processes,
birth-death processes, Chapman-Kolmogorw equations.
Steady state probabilities. Simple queueing processes.
Modern algebra with applications
Groups, rings fields (including Galois fields). Vector spaces,
polynomials with binary coefficients. Linear block codes,
parity check matrices and standard arrays. Cyclic codes,
generator polynomials. Hamming codes.
Prescribed text
Semesters 1 and 2
Boas, M.L. Mathematical methods in the physical sciences 2nd ed,
Nw York: Wilq, 1983
Semester 2 only
Hill, R.A. First course in coding theory. Oxford: Oxford University
Press, 1990
SM3415 Mathematical Methods
8.0 credit points for semesters one and two
No. of hours per week: three hours
Prerequisite: SM 1200 or SM1215
Assessment: tests/examinations and assignments
A second-year subject of the degree course in instrumentation
and computer science.
Subject description
Linear algebra and vector;
Matrices and matrix algebra. Systems of linear equations:
Guassian elimination; procedures for numerical solution by
direct or iterative methods, (Jacobi and Gauss-Seidel),
transformation matrices.
Real analysis
Partial differentiation, chain rule, approximations. Application
to maximum and minimum problems constrained optima
and Lagrange multipliers. Change of variable. Multiple
integrals. Applications of single, double and triple integrals.
Jacobians. Surface integrals. Fourier series of general periodic
functions. Laplace transforms. Use of tables. Partial
differential equations, solution via separation of variables
(Fourier series).
kctor analysis
Basic vector manipulation including calculus of vector
functions. Space curws, Serret-Frenet formulas. Special
emphasis on gradient of a scalar field, directional derivative,
divergence and curl of a vector field. Line, surface and
volume ~ntegrals. Field theory.
Complex analysis
Algebra and geometry of complex numbers. Functions of a
complex variable. Elementary functions such as polynomial,
exponential, trigonometric, hyperbolic, logarithm and power.
Differentiability and Cauchy-Reimann equations. Harmonic
functions. Contour integration. Cauchy integral and residue
theorems. Evaluation of definite integrals. Conformal
mapping and applications.
Random processes
Review of probability, Markov chains, Poisson processes,
birth-death processes, Chapman-Kolmogorw equations.
Steady state probabilities. Simple queueing processes.
Modern algebra with applications
Groups, rings fields (including Galois fields). Vector spaces,
polynomials with binary coefficients. Linear block codes,
parity check matrices and standard arrays. Cyclic codes,
generator polynomials. Hamming codes.
Prescribed text
Semesters 1 and 2
Boas, M.L. Mathematical methods in the physical sciences. 2nd ed,
New York: Wiley, 1983
Semester 2 only
Hill. R.A. Fint course in coding theory Oxford: Oxford Univesity
Press, 1990
SP106 Physics
10.0 credit points
No. of hours per week: five hours
Assessment: practical work, assignments and
examination
A first-year subject of the degree courses in applied science
(computer-aided chemistry, computer-aided biochemistry).
Subject description
Motion and forces: relativistic kinematics and dynamics,
rotational kinematics and dynamics, gravitation.
Electricity and magnetism: electric fields, Gauss' Law, electric
potential, energy density of the electric field, magnetic fields,
Biot-Savart Law, Ampere's Law, inductance, AC circuits,
displacement current, DC circuits.
Atomic physics: photoelectric effect, x-rays, Compton effect,
photon-electron interactions, Bohr model, de Broglie matter
waves.
SPIOS Physics
10.0 credit points
No. of hours per week: five hours
Assessment: practical work, assignments and
examination
A first-year subject of the degree course in computer-aided
chemistry and computer-aided biochemistry taken by
students who have not reached Year 12 physics standard.