ENGINEERING MATH REFERENCE

Quick reference for the math that underlies engineering calculations: standard derivatives and integrals, Taylor series expansions for common functions, vector operations (dot, cross, gradient, divergence, curl), matrix operations including inversion and eigenvalues, complex number arithmetic in rectangular and polar form, and Laplace transforms for control-system analysis. Includes common trig identities and the small-angle approximations used in vibration and beam-bending derivations.

• d/dx (sin x) = cos x; d/dx (e^x) = e^x
• ∫ 1/x dx = ln|x| + C
• ∫ sin² x dx = x/2 - sin(2x)/4 + C
• sin x ≈ x - x³/6 (small angle)
• A · B = |A||B|cosθ; |A × B| = |A||B|sinθ
• e^(jωt) = cos(ωt) + j·sin(ωt)

References & StandardsCRC Handbook of Math Tables, Abramowitz & Stegun

Reference page; not a calculator. Use when re-deriving a formula, checking a hand-calc, or remembering the form of a Taylor expansion. Cross-references to the Equations module for complete formula index by discipline.