| symbol | latex code | explanation | |
|---|---|---|---|
f'(x) | f'(x) | First derivative of f(x) | |
f''(x) | f''(x) | Second derivative of f(x) | |
df/dx | \frac{df}{dx} | Derivative of f with respect to x | |
∂f/∂x | \frac{\partial f}{\partial x} | Partial derivative of f with respect to x | |
Dⁿf(x) | D^n f(x) | nth derivative of f(x) | |
dy/dx | \frac{dy}{dx} | Rate of change of y with respect to x | |
∇f | \nabla f | Gradient of a scalar field f | |
∫ f(x) dx | \int f(x)\, dx | Indefinite integral of f(x) | |
∫ₐᵇ f(x) dx | \int_a^b f(x)\, dx | Definite integral of f(x) from a to b | |
∬ f(x,y) dA | \iint f(x,y)\, dA | Double integral over a region A | |
∭ f(x,y,z) dV | \iiint f(x,y,z)\, dV | Triple integral over a volume V | |
∮ f(x) dx | \oint f(x)\, dx | Line integral of f(x) | |
∫ₓ f ds | \int_C f\, ds | Integral along a curve C | |
limₓ→c f(x) | \lim_{x \to c} f(x) | Limit of f(x) as x approaches c | |
limₓ→∞ f(x) | \lim_{x \to \infty} f(x) | Limit of f(x) as x approaches infinity | |
limₓ→c⁻ f(x) | \lim_{x \to c^-} f(x) | Left-hand limit of f(x) as x approaches c | |
limₓ→c⁺ f(x) | \lim_{x \to c^+} f(x) | Right-hand limit of f(x) as x approaches c | |
∑ₙ₌₁ⁿ₌∞ aₙ | \sum_{n=1}^\infty a_n | Infinite series | |
∑ₙ₌₀ⁿ₌N aₙ | \sum_{n=0}^N a_n | Finite series up to N terms | |
Πₙ₌₁ⁿ₌∞ aₙ | \prod_{n=1}^\infty a_n | Infinite product | |
a₀ + ∑ₙ₌₁ⁿ₌∞ aₙxⁿ | a_0 + \sum_{n=1}^\infty a_n x^n | Power series representation of a function | |
∇⋅F | \nabla \cdot \mathbf{F} | Divergence of a vector field F | |
∇×F | \nabla \times \mathbf{F} | Curl of a vector field F | |
∬ₛ F ⋅ dS | \iint_S \mathbf{F} \cdot \mathbf{dS} | Flux of F through a surface S | |
∮ₓ F ⋅ dr | \oint_C \mathbf{F} \cdot \mathbf{dr} | Line integral of F along a curve C | |
|f(x)| | |f(x)| | Absolute value of f(x) | |
sgn(x) | \text{sgn}(x) | Sign function | |
∞ | \infty | Infinity | |
dx | dx | Infinitesimal change in x | |
ε | \epsilon | Epsilon (small positive quantity in limits) | |
δ | \delta | Delta (small positive quantity in limits) | |
∭ₓ f dV | \iiint_V f\, dV | Triple integral over a volume V | |
∯ₓ f dS | \iint_S f\, dS | Surface integral over surface S | |
∮ₓ f dx | \oint_C f\, dx | Closed line integral | |
∫ₐᵦ |f(x)| dx | \int_a^b |f(x)|\, dx | Integral of absolute value of f(x) | |
∫ f(x) δ(x − x₀) dx | \int f(x)\, \delta(x - x_0)\, dx | Integral involving Dirac delta function | |
∇²f | \nabla^2 f | Laplacian of f | |
∂²f/∂x² | \frac{\partial^2 f}{\partial x^2} | Second partial derivative of f with respect to x | |
∂²f/∂x∂y | \frac{\partial^2 f}{\partial x \partial y} | Mixed second partial derivative | |
d²y/dx² | \frac{d^2y}{dx^2} | Second ordinary derivative of y with respect to x | |
κ | \kappa | Curvature of a curve | |
τ | \tau | Torsion of a curve | |
r(t) | \mathbf{r}(t) | Parametric curve | |
T(t) | \mathbf{T}(t) | Unit tangent vector | |
N(t) | \mathbf{N}(t) | Unit normal vector | |
B(t) | \mathbf{B}(t) | Unit binormal vector | |
Γ(n) | \Gamma(n) | Gamma function | |
ζ(s) | \zeta(s) | Riemann zeta function | |
Li(x) | \text{Li}(x) | Logarithmic integral | |
erf(x) | \text{erf}(x) | Error function | |
dy/dx = f(x) | \frac{dy}{dx} = f(x) | Ordinary differential equation | |
∂u/∂t = D∇²u | \frac{\partial u}{\partial t} = D\nabla^2 u | Heat equation | |
∂²u/∂t² = c²∇²u | \frac{\partial^2 u}{\partial t^2} = c^2\nabla^2 u | Wave equation | |
∇²φ = ρ | \nabla^2 \phi = \rho | Poisson's equation |