36 Volume 7 — Engineering mathematics
This volume is the core mathematics sequence that first- and second-year engineering students usually experience as separate courses: ordinary differential equations, linear algebra, multivariable calculus, vector calculus, Fourier methods, PDEs, complex analysis, numerical methods, optimisation, and probability.
The build is intentionally broad before it becomes specialised. The aim is not to imitate a single textbook chapter order, but to give readers the mathematical objects that upper-year engineering courses assume they can already use: state equations, eigenmodes, fields, transforms, discretised systems, feasible regions, and distributions.
Volume 8 extends this into the mathematics that appears inside third- and fourth-year discipline courses: control and feedback, discrete-time systems, continuum models, computational simulation, estimation, reliability, and nonlinear design optimisation.
36.1 Sections
| Section | Core move |
|---|---|
| ODEs | Model change by relating a system to its own rates |
| Linear algebra and vector calculus | Move from single equations to spaces, fields, and operators |
| Fourier analysis and PDEs | Decompose signals and solve distributed physical systems |
| Complex analysis | Use the complex plane as a practical computational tool |
| Numerical methods | Replace exact formulas with controlled approximation |
| Optimisation and probability | Decide and infer under constraints and uncertainty |