math

$$\frac{\sin(\text{A})}{\text{a}} = \frac{\sin(\text{B})}{\text{b}} = \frac{\sin(\text{C})}{\text{c}}$$

$$\frac{f(x+h) - 2f(x) + f(x-h)}{h^2}$$

$$\scriptsize \nabla \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\\\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\\\ F_x & F_y & F_z \end{vmatrix}$$

$$\nabla \cdot \mathbf{F} = \frac{\partial F_x}{\partial x} + \frac{\partial F_y}{\partial y} + \frac{\partial F_z}{\partial z}$$

$$\nabla f = \frac{\partial f}{\partial x} \mathbf{i} + \frac{\partial f}{\partial y} \mathbf{j} + \frac{\partial f}{\partial z} \mathbf{k}$$

$$\scriptsize \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} w & x \\ y & z \end{pmatrix} = \begin{pmatrix} aw + by & ax + bz \\ cw + dy & cx + dz \end{pmatrix}$$

$$\\ {x^2 \over a^2} + {y^2 \over b^2} + {z^2 \over c^2} = 1$$

$$ax + by + cz = d$$

$$\small R^2 = (x-x_0)^2 + (y-y_0)^2 + (z - z_0)^2$$

$$X(\omega) = \int_{-\infty}^{\infty}x(t)e^{-j\omega t}\,dt$$

$$\scriptsize P = A \left[\frac{(1+i)^n-1}{i(1+i)^n}\right] + G \left[\frac{(1+i)^n-in-1}{i^2(1+i)^n}\right]$$

$$A = P \left[\frac{i(1 + i)^n}{(1 + i)^n - 1}\right]$$

$$F = P(1 + i)^n$$

$$\int_0^{\infty} x^n e^{-tx} dx = \frac{n!}{t^{n+1}}$$

$$S_n = \frac{a(1-r^n)}{1-r}$$

$$(f*g)(t)=\int_{-\infty}^{\infty} f(\tau)g(t-\tau)d\tau$$

$$\lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)}$$

$$\det(A)$$

$$\sin(2\theta) = 2 \cdot \sin(\theta) \cdot \cos(\theta)$$

$$\scriptsize \sin(a \pm b) = \sin(a) \cos(b) \pm \cos(a) \sin(b)$$

$$proj_{\vec{b}}(\vec{a})=\frac{\vec{a}\cdot\vec{b}}{\|\vec{b}\|^2}\vec{b}=(\vec{a}\cdot\hat{b})\hat{b}$$

$$\sinh(x) = \frac{e^x - e^{-x}}{2}$$

$$\vec{a} \times \vec{b} = \begin{vmatrix} \vec{i} & \vec{j} & \vec{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{vmatrix}$$

$$\vec{a} \cdot \vec{b} = \sum_{i=1}^n a_i b_i$$

$$c^2 = a^2 + b^2 - 2 \cdot a \cdot b \cdot \cos(\theta)$$

$$\frac{d}{dx}f(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$$

$$\sin^2(x) + \cos^2(x) = 1$$

$$\oint_C f(z)dz = 0$$

$$\nabla^2 f = \nabla \cdot \nabla f = 0$$

$$\int_a^b f(x) dx = F(b) - F(a)$$