LaTex Rendering

LaTeX Math Examples

Practiced various math equations rendered using LaTeX

Algebra - Slope-Intercept Form

The equation of a straight line, where m is the slope and b is the y-intercept

y=mx+by = mx + b

Linear Algebra - Matrix Multiplication

The product of two 2×2 matrices

(abcd)(efgh)=(ae+bgaf+bhce+dgcf+dh)\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} e & f \\ g & h \end{pmatrix} = \begin{pmatrix} ae+bg & af+bh \\ ce+dg & cf+dh \end{pmatrix}

Calculus - Chain Rule

The chain rule for differentiation

ddx[f(g(x))]=f′(g(x))⋅g′(x)\frac{d}{dx}[f(g(x))] = f'(g(x))\cdot g'(x)

Vector Calculus - Divergence Theorem

The relationship between volume integral and surface integral

∭V(∇⋅F) dV=∯SF⋅n dS\iiint_V (\nabla \cdot \mathbf{F})\,dV = \oiint_S \mathbf{F} \cdot \mathbf{n}\,dS

Complex Analysis - Cauchy's Integral Formula

Formula for the value of a holomorphic function inside a contour

f(a)=12πi∮Cf(z)z−a dzf(a) = \frac{1}{2\pi i} \oint_C \frac{f(z)}{z-a}\,dz

Differential Equations - Wave Equation

The one-dimensional wave equation

∂2u∂t2=c2∂2u∂x2\frac{\partial^2 u}{\partial t^2} = c^2\frac{\partial^2 u}{\partial x^2}

Linear Algebra - Eigenvalue Equation

The characteristic equation for finding eigenvalues

det(A−λI)=0, where Av=λvdet(A - \lambda I) = 0, \text{ where } A\mathbf{v} = \lambda\mathbf{v}

Statistics - Normal Distribution

The probability density function of the normal distribution

f(x)=1σ2πe−12(x−μσ)2f(x) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{1}{2}(\frac{x-\mu}{\sigma})^2}

Quantum Mechanics - Schrödinger Equation

The time-independent Schrödinger equation

−ℏ22m∇2ψ+Vψ=Eψ-\frac{\hbar^2}{2m}\nabla^2\psi + V\psi = E\psi