CS3005:03
Statistics and Numerical Methods
Townsville
Prerequisites: MA2000
39 lectures, 39 tutorials. Second semester.
Available to civil engineering and engineering technology students.
Probability – Concepts of probability; sample spaces; theorem of total probability; Bayes’ theorem; random variables; probability distributions; normal, binomial and poisson; extreme value distributions.
Data Analysis – Statistical concepts; sampling and estimation; sampling distributions and confidence intervals; linear models; use of probability paper; goodness of fit tests. Statistical quality control.
Properties of time-series; autocorrelation; power spectrum; sampling and aliasing; auto-regressive and moving average models. Signal detection in the presence of noise.
Numerical Methods - Systems of linear algebraic equations; Gauss-Seidel iteration; acceleration of convergence (S.O.R.); condition: condition number; use of MATLAB. Systems of non-linear algebraic equations; Newton-Rapson algorithm. Least-squares fitting. Numerical integration; ordinary differential equations; initial value problems.
Learning Objectives:
- the ability to deal with simple problems of applied probability, including use of the common distributional models;
- the basic ideas of sampling and estimation;
- the ability to carry out a variety of simple statistical analyses of data, including time series data;
- some insight into the procedures and pitfalls associated with the numerical solution of a variety of engineering problems.
Assessment by examination (50%-70%); on-course assessment (30%-50%).