Verified formula topic
Analysis Formulas
Browse 0 reviewed analysis formulas with concrete inputs, outputs, calculations, applicability checks, and LaTeX.
Browse 3 supporting references
Analysis
Fourier Transform
\hat f(\omega)=\int_{-\infty}^{\infty}f(t)e^{-i\omega t}\,dtTransforms a time- or space-domain function into frequency components.
Open formulaAnalysis
Inverse Fourier Transform
f(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}\hat f(\omega)e^{i\omega t}\,d\omegaReconstructs a function from its angular-frequency representation.
Open formulaAnalysis
Multivariable Taylor Expansion
f(x+h)\approx f(x)+\nabla f(x)^Th+\frac12 h^T H_f(x)hApproximates a smooth multivariable function near a reference point.
Open formula