Model change by relating a system to its own rates. First-order, second-order, systems of ODEs, and the Laplace transform as an algebraic shortcut for solving them.
Volume 7 — Engineering mathematics
Volume 7
Engineering Mathematics
This volume covers the core mathematics sequence that first- and second-year engineering students usually experience as separate courses: ordinary differential equations, linear algebra, vector calculus, Fourier methods, PDEs, complex analysis, numerical methods, optimisation, and probability.
The aim is not to imitate a single textbook chapter order, but to give you the mathematical objects that upper-year engineering courses assume you can already use: state equations, eigenmodes, fields, transforms, discretised systems, and feasible regions.
6 sections
First/second year engineering
Needs Volumes 4–5
Section Map
Move from single equations to spaces, fields, and operators. Eigenvalues, vector differential and integral calculus — the language of multivariable physical systems.
Decompose signals and solve distributed physical systems. Fourier series, Fourier transforms, and partial differential equations for heat, wave, and diffusion problems.
Use the complex plane as a practical computational tool. Analytic functions, contour integration, residues, and conformal mapping — with direct application to transforms and filters.
Replace exact formulas with controlled approximation. Root finding, interpolation, numerical integration, and numerical methods for ODEs and PDEs — what to use when calculus can't give a closed form.
Decide and infer under constraints and uncertainty. Linear programming, graph algorithms, mathematical statistics, and probability theory at engineering depth.