Engineering Mathematics in LaTeX: Signals, Systems, and Control

Engineering fields have their own mathematical notation conventions. This guide covers the essentials.

Fourier and Laplace Transforms

Fourier transform: \\hat{f}(\\xi) = \\int_{-\\infty}^{\\infty} f(x) e^{-2\\pi i x \\xi}\\,dx. Laplace transform: F(s) = \\int_0^{\\infty} f(t) e^{-st}\\,dt.

Differential Equations

First order: \\frac{dy}{dx} + P(x)y = Q(x). Second order: a\\frac{d^2y}{dx^2} + b\\frac{dy}{dx} + cy = 0.

Control Systems

Transfer function: G(s) = \\frac{Y(s)}{U(s)}. Block diagram notation uses \\xrightarrow and \\xleftarrow for signal flow.