Course overview
This course will develop students' knowledge of mathematics (multivariable calculus) and statistics, and mathematical software in the context of engineering problems. Calculus. Partial differentiation of multivariable functions, multiple integration. Curves in space. Curve fitting, optimization, formulation and solution of differential equations relating to engineering problems with analytical and software solutions. Statistics. Graphical and numerical description of data sets. Probability models, confidence intervals, prediction and tolerance intervals, significance tests, statistical process control, linear regression, statistical software. Computer assisted modelling and problem solving. Apply mathematical principles and tools to selected examples of modelling specific to each of the engineering discipline areas.
Course learning outcomes
- Use the techniques of differential calculus of functions of two or more variables to identify critical points and rates of change of functions.
- Use the techniques of integral calculus of functions of two or more variables to calculate areas, volumes, and masses.
- Use the techniques of parametrized curves in two and three dimensional space to calculate velocity, speed, arc length and curvature.
- Use the techniques associated with hypothesis testing and statistical inference for means and proportions applied to engineering situations.
- Use the technique of least squares regression to analyse relationships between quantitative variables for engineering applications.
- Develop, in a team, a model of a practical problem in mechanical engineering, and solve using appropriate software.
- Develop, in a team, a model of a practical problem in civil engineering, more independently than in Objective 6, and solve using appropriate software.