The first aim of Technical Mathematics 4 is to develop the students’ competence in a range of mathematical techniques in probability (as applied to process control), iteration (as applied to numerical integration and the numerical solution of equations) and basic calculus in such a way as to support other engineering modules. The second aim is to deepen the students understanding of key mathematical ideas regarding the application of the normal distribution to engineering problems, sequence and the convergence of a mathematical sequence, basic integration of engineering functions (including indefinite integrals, definite integrals, and numerical integration). The third aim is to extend the students use of software applications in the processing of engineering data (sampling and control) and understanding engineering concepts (numerical integration and limits).
Probability Distributions:
The normal distribution. The standard normal table. Using the standard normal table to solve problems for general normal distributions. Confidence intervals. Statistical Process Control: X-Bar charts.
Software skills:
Control structures (loops), iteration (sequences and series), numerical integration, Newton’s Method
Sequences and Series:
Ordinary, explicit, and recursive forms of sequences. Convergence and divergence of sequences. Newton’s method as an example of convergence of a sequence.Series as a sequence of partial sums.
Integration:
Anti-derivatives of simple functions. The constant of integration. Integration of linear combinations of simple functions. Definite integrals. The area under a graph, including area below the horizontal axis. Integration of the composition of two functions, the first being a linear function. Integration using the tableau method. Integration using partial fractions. Solution of simple variable separable differential equations. Solution of first order differential equations using the integrating factor method.
Numerical Integration:
The trapezoidal rule. Simpson’s rule.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 40 |
| Formal Examination | 60 |