Overview
This course develops numerical methods for formulating and solving engineering problems that are difficult or impossible to treat analytically. It establishes the foundations of numerical representation, floating-point arithmetic, conditioning, truncation and round-off error, convergence, stability, and algorithm selection.
Students study numerical techniques for nonlinear equations, systems of linear equations, interpolation, polynomial approximation, least-squares regression, numerical differentiation and integration, and ordinary differential equations. Topics may also include boundary-value problems, eigenvalue problems, numerical optimization, Fourier methods, and introductory finite-difference methods for partial differential equations.
Through lectures, tutorials, and computational laboratories, students implement algorithms in a suitable programming environment and apply them to engineering models involving heat transfer, fluid flow, structural response, dynamics, and circuit systems. Emphasis is placed on accuracy assessment, convergence analysis, verification against analytical or benchmark solutions, visualization, interpretation, and clear communication of engineering assumptions and limitations.
Learning Outcomes
- Formulate engineering problems as computational models suitable for numerical solution.
- Evaluate floating-point effects, truncation and round-off errors, conditioning, convergence, and algorithmic stability.
- Select appropriate numerical methods for nonlinear equations, linear systems, approximation, integration, and differential equations.
- Implement and test numerical algorithms for engineering applications in a suitable programming environment.
- Diagnose convergence failure, instability, ill-conditioning, and discretization errors in computational results.
- Verify numerical solutions against analytical, manufactured, or benchmark solutions and quantify their accuracy.
- Visualize and interpret numerical outputs in relation to physical engineering behavior.
- Synthesize computational findings into clear technical reports that communicate assumptions, limitations, verification evidence, and engineering conclusions.
Timetable
| Type | Length | Frequency | Period |
|---|---|---|---|
| Lecture | 2 hours | Weekly | All semester |
| Lab | 2 hours | Weekly | All semester |
| Tutorial | 1 hour | Fortnightly | All semester |
Assessment Schedule
| Type | Description | Weighting |
|---|---|---|
| Assignment | Error analysis and nonlinear equation methods assignment | 15.00% |
| Assignment | Linear algebra and approximation methods assignment | 15.00% |
| Quiz | Short computational quizzes (5 × 2%) | 10.00% |
| Deliverable | Computational laboratory portfolio (5 × 4%) | 20.00% |
| Test | In-semester numerical methods test | 15.00% |
| Capstone | Engineering computational modelling project | 10.00% |
| Exam | Final examination | 15.00% |
Prerequisites
Teaching Staff & Programs
This course is delivered jointly by faculty from the participating programs listed below. In line with the Douchewater Way, the University of Sexology tailors core instruction directly to each cohort's specific discipline — adapting curriculum to program needs rather than forcing students into a one-size-fits-all model. Learn more about our approach at The Douchewater Way.
