RHIT MA113/Equation Sheet

Equation Sheet

Name	Function
Vectors
Magnitude	$\Vert \overrightarrow{a}\Vert =\sqrt{a_x^2+a_y^2}$
Dot Product	$⟨a,b⟩\cdot ⟨c,d⟩=ac+bd$
Angle between 2 vectors	$\cos (\theta )=\frac{\overrightarrow{a}\cdot \overrightarrow{b}}{\Vert \overrightarrow{a}\Vert \Vert \overrightarrow{b}\Vert }$
Cross Product	$\Vert \overrightarrow{a}\times \overrightarrow{b}\Vert =\Vert \overrightarrow{a}\Vert \Vert \overrightarrow{b}\Vert \sin (\theta )$
Vector Functions
Velocity	$\overrightarrow{v}=\frac{d}{dt}\overrightarrow{r}$
Tangent Vector	$\overrightarrow{T}=\frac{\overrightarrow{v}}{\Vert \overrightarrow{v}\Vert }$
Normal Vector	$\overrightarrow{N}=\frac{\frac{d\overrightarrow{T}}{dt}}{\Vert \frac{d\overrightarrow{T}}{dt}\Vert }$
Acceleration	$\overrightarrow{a}=\frac{d}{dt}\overrightarrow{v}$
Partial Derivatives
A	B
Multiple Integrals
Average Value	$\frac{\underset{R}{\iint }f(x)dA}{\underset{R}{\iint }dA}$
Area	$\underset{R}{\iint }dA$
Volume	$\underset{R}{\iiint }dV$
Mass	$\underset{R}{\iiint }\sigma dV$
First Moment	$\underset{R}{\iiint }r\sigma dV$
Second Moment	$\underset{R}{\iiint }{r}^2\sigma dV$