# RHIT MA113/Equation Sheet

 RHIT MA113 Equation Sheet

# Equation Sheet

Name Function
Vectors
Magnitude ${\displaystyle \left\Vert {\vec {a}}\right\|={\sqrt {a_{x}^{2}+a_{y}^{2}}}}$
Dot Product ${\displaystyle \left\langle a,b\right\rangle \,\cdot \,\left\langle c,d\right\rangle =a\,c+b\,d}$
Angle between 2 vectors ${\displaystyle \cos {(\theta )}={\frac {{\vec {a}}\cdot {\vec {b}}}{\left\Vert {\vec {a}}\right\|\,\left\Vert {\vec {b}}\right\|}}}$
Cross Product ${\displaystyle \left\Vert {\vec {a}}\times {\vec {b}}\right\|=\left\Vert {\vec {a}}\right\|\,\left\Vert {\vec {b}}\right\|\,\sin {(\theta )}}$
Vector Functions
Velocity ${\displaystyle {\vec {v}}={\frac {d}{dt}}\,{\vec {r}}}$
Tangent Vector ${\displaystyle {\vec {T}}={\frac {\vec {v}}{\left\Vert {\vec {v}}\right\|}}}$
Normal Vector ${\displaystyle {\vec {N}}={\frac {\frac {d{\vec {T}}}{dt}}{\left\Vert {\frac {d{\vec {T}}}{dt}}\right\|}}}$
Acceleration ${\displaystyle {\vec {a}}={\frac {d}{dt}}\,{\vec {v}}}$
Partial Derivatives
A B
Multiple Integrals
Average Value ${\displaystyle {\frac {\iint \limits _{R}\,f(x)\,dA}{\iint \limits _{R}\,dA}}}$
Area ${\displaystyle \iint \limits _{R}\,dA}$
Volume ${\displaystyle \iiint \limits _{R}\,dV}$
Mass ${\displaystyle \iiint \limits _{R}\,\sigma \,dV}$
First Moment ${\displaystyle \iiint \limits _{R}\,r\,\sigma \,dV}$
Second Moment ${\displaystyle \iiint \limits _{R}\,r^{2}\,\sigma \,dV}$