# Glossary of Notations

 i The square root of minus one. $$f(x)$$ The value of the function $$f$$ at argument $$x$$. $$\sin x$$ The value of the sine function at argument $$x$$. $$\exp x$$ The value of the exponential function at argument $$x$$. This is often written as $$e^x$$. a^x The number a raised to the power $$x$$; for rational $$x$$ is defined by inverse functions. $$\ln x$$ The inverse function to $$\exp x$$. $$a^x$$ Same as a^x. $$\log_b a$$ The power you must raise $$b$$ to in order to get $$a$$: $$b^{\log_ba} = a$$. $$\cos x$$ The value of the cosine function (complement of the sine) at argument $$x$$. $$\tan x$$ Works out to be $$\frac{\sin x}{\cos x}$$. $$\cot x$$ The value of the complement of the tangent function or $$\frac{\cos x}{\sin x}$$. $$\sec x$$ Value of the secant function, which turns out to be $$\frac{1}{\cos x}$$. $$\csc x$$ Value of the complement of the secant, called the cosecant. It is $$\frac{1}{\sin x}$$. $$\text{asin}\, x$$ The value, $$y$$, of the inverse function to the sine at argument $$x$$. Means $$x = \sin y$$. $$\text{acos}\, x$$ The value, $$y$$, of the inverse function to cosine at argument $$x$$. Means $$x = \cos y$$. $$\text{atan}\, x$$ The value, $$y$$, of the inverse function to tangent at argument $$x$$. Means $$x = \tan y$$. $$\text{acot}\, x$$ The value, $$y$$, of the inverse function to cotangent at argument $$x$$. Means $$x = \cot y$$. $$\text{asec}\, x$$ The value, $$y$$, of the inverse function to secant at argument $$x$$. Means $$x = \sec y$$. $$\text{acsc}\, x$$ The value, $$y$$, of the inverse function to cosecant at argument $$x$$. Means $$x = \csc y$$. $$\theta$$ A standard symbol for angle. Measured in radians unless stated otherwise. Used especially for $$\text{atan}\, \frac{x}{y}$$ when $$x$$, $$y$$, and $$z$$ are variables used to describe point in three dimensional space. $$\hat{i}$$, $$\hat{j}$$, $$\hat{k}$$ Unit vectors in the $$x$$, $$y$$ and $$z$$ directions respectively. $$(a, b, c)$$ A vector with $$x$$ component $$a$$, $$y$$ component $$b$$ and $$z$$ component $$c$$. $$(a, b)$$ A vector with $$x$$ component $$a$$, $$y$$ component $$b$$. $$\left(\vec{a},\vec{b}\right)$$ The dot product of vectors $$\vec{a}$$ and $$\vec{b}$$. $$\vec{a} \cdot \vec{b}$$ The dot product of vectors $$\vec{a}$$ and $$\vec{b}$$. $$\left(\vec{a} \cdot \vec{b}\right)$$ The dot product of vectors $$\vec{a}$$ and $$\vec{b}$$. $$|\vec{v}|$$ The magnitude of the vector $$\vec{v}$$. $$|x|$$ The absolute value of the number $$x$$. $$\sum$$ Used to denote a summation, usually the index and often their end values are written under it with upper end value above it. For example the sum of $$j$$ for $$j = 1$$ to $$n$$ is written as $$\sum_{j=1}^{n}j$$ or $$\sum^{n}j$$. This signifies $$1 + 2 + ... + n$$. $$M$$ Used to represent a matrix or array of numbers or other entities. |v> A column vector, that is one whose components are written as a column and treated as a $$k$$ by $$1$$ matrix.