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## Calculus and Analysis Math Symbols

### Introduction:

Delving into the realm of Calculus and Analysis requires a solid understanding of the mathematical symbols that convey complex concepts. This comprehensive table serves as a valuable resource, offering a quick reference guide to symbols used in differentiation, integration, limits, series, and other fundamental aspects of mathematical analysis. Whether you're a student embarking on a calculus course or an enthusiast exploring advanced mathematical concepts, this guide will assist you in deciphering the symbolic language of calculus and analysis.

### Calculus & analysis math symbols table

 Symbol Symbol Name Meaning / definition Example \lim_{x\to x0}f(x) limit limit value of a function ε epsilon represents a very small number, near zero ε → 0 e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞ y ' derivative derivative - Lagrange's notation (3x3)' = 9x2 y '' second derivative derivative of derivative (3x3)'' = 18x y(n) nth derivative n times derivation (3x3)(3) = 18 \frac{dy}{dx} derivative derivative - Leibniz's notation d(3x3)/dx = 9x2 \frac{d^2y}{dx^2} second derivative derivative of derivative d2(3x3)/dx2 = 18x \frac{d^ny}{dx^n} nth derivative n times derivation \dot{y} time derivative derivative by time - Newton's notation Dx y derivative derivative - Euler's notation Dx2y second derivative derivative of derivative \frac{\partial f(x,y)}{\partial x} partial derivative ∂(x2+y2)/∂x = 2x ∫ integral opposite to derivation ∬ double integral integration of function of 2 variables ∭ triple integral integration of function of 3 variables ∮ closed contour / line integral ∯ closed surface integral ∰ closed volume integral [a,b] closed interval [a,b] = {x | a ≤ x ≤ b} (a,b) open interval (a,b) = {x | a < x < b} i imaginary unit i ≡ √-1 z = 3 + 2i z* complex conjugate z = a+bi → z*=a-bi z* = 3 + 2i z complex conjugate z = a+bi → z = a-bi z = 3 + 2i Re(z) real part of a complex number z = a+bi → Re(z)=a Re(3 - 2i) = 3 Im(z) imaginary part of a complex number z = a+bi → Im(z)=b Im(3 - 2i) = -2 | z | absolute value/magnitude of a complex number |z| = |a+bi| = √(a2+b2) |3 - 2i| = √13 arg(z) argument of a complex number The angle of the radius in the complex plane arg(3 + 2i) = 33.7° ∇ nabla / del gradient / divergence operator ∇f (x,y,z) vector unit vector x * y convolution y(t) = x(t) * h(t) Laplace transform F(s) = {f (t)} Fourier transform X(ω) = {f (t)} δ delta function ∞ lemniscate infinity symbol

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