The Ultimate Crash Course for STEM Majors

Gain lifetime access to thousands of ad free lessons, textbooks, research projects, certificates, and study resources through PLEM Academy.

PLEM Academy

Book Notations

Note: Some symbols may have different meanings in different courses; i.e., never assume.

And	$\land$
Or	$\lor$
In	$\in$
Manipulation or row reduction occurred	$\sim$
Implies	$\Rightarrow$
Becomes	$\Leftarrow$
If and only if	$\Leftrightarrow$
Therefore	$\therefore$
Because	$\because$
Equivalent / defined as	$\equiv$

Euler’s Number

$e=\sum_{n=0}^{\infty}\frac{1}{n!} = \lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n$

Vector Notation

Any other vector (scalar not bold / hat / vec)

$\vec{v}=\mathbf{v}$

Unit Circle

The unit circle is one of the most important diagrams in mathematics, physics, engineering, computer science, and differential equations. Every point on the circle has radius one and corresponds to the ordered pair

$(\cos\theta,\sin\theta)$

Key points:

$(1,0)$ corresponds to $0^\circ$ or $0$ radians.
$(0,1)$ corresponds to $90^\circ$ or $\frac{\pi}{2}$ radians.
$(-1,0)$ corresponds to $180^\circ$ or $\pi$ radians.
$(0,-1)$ corresponds to $270^\circ$ or $\frac{3\pi}{2}$ radians.

$\begin{array}{c|c|c} \text{Degrees} & \text{Radians} & (\cos\theta,\sin\theta)\\ \hline 30^\circ & \frac{\pi}{6} & \left(\frac{\sqrt3}{2},\frac12\right)\\ 45^\circ & \frac{\pi}{4} & \left(\frac{\sqrt2}{2},\frac{\sqrt2}{2}\right)\\ 60^\circ & \frac{\pi}{3} & \left(\frac12,\frac{\sqrt3}{2}\right) \end{array}$

Continue Your STEM Journey

Join PLEM Academy for ad free lessons, research opportunities, certificates, textbook writing projects, and thousands of educational resources designed for STEM majors.

Visit PLEM Academy