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Appendix A Notation

Notation refers to the symbols we use to represent physical quantities and variables in mathematical expressions. Notation is a tool for communication and the symbols themselves carry meaning. You will find it easier to understand the contents of engineering textbooks if you are familiar with the notation used, and can pronounce the symbols to yourself when studying the equations.

\begin{equation*} \text{Symbol} \end{equation*}
\begin{equation*} \text{Notes} \end{equation*}
\begin{equation*} \vec{F}, \text{ or } \vecarrow{F} \end{equation*}

Vectors are written in a bold serif font. For handwritten vectors, a superimposed arrow is used.

\begin{equation*} F \end{equation*}

Magnitudes and other scalar values are rendered in an regular italic serif font. \(F\) is the magnitude of \(\vec{F}\text{.}\)

\begin{equation*} | \vec{F} | \end{equation*}

Vertical bars indicate absolute value. The absolute value of a vector is its magnitude.

\begin{equation*} \vec{F}_x, \vec{F}_y \end{equation*}

Vector component of \(\vec{F}\) in the \(x\) and \(y\) directions. Subscripts are used to distinguish different related values.

\begin{equation*} F_x, F_y \end{equation*}

Scalar components of vector \(\vec{F}\) in the \(x\) and \(y\) directions. These are signed numbers, not vectors. Together, the sign and subscript define a vector component.

\begin{equation*} \left \langle F_x, F_y \right \rangle \end{equation*}

An ordered pair of scalar components enclosed in angle brackets defines a vector.

\begin{equation*} (F; \theta) \end{equation*}

An ordered pair of magnitude and direction separated with a semicolon defines a vector.

\begin{equation*} \ihat, \jhat, \khat \end{equation*}

Unit vectors in the \(x\text{,}\) \(y\text{,}\) and \(z\) directions. Pronounced ‘i hat’, ‘j hat’, etc.

\begin{equation*} \hat{\vec{A}}, \hat{\vec{\lambda}} \end{equation*}

A hat indicates a unit vector in the vector’s direction.

\begin{align*} \vec{F}_x \amp = F_x\, \ihat\\ \vec{F}_y \amp = F_y\, \jhat \end{align*}

Scalar components multiplied by unit vectors are vector components.

\begin{align*} \vec{F} \amp = \vec{F}_x + \vec{F}_y\\ \amp = F_x\, \ihat + F_y\, \jhat \end{align*}

A vector is the sum of its vector components.

\begin{align*} \vec{F} \amp = \left \langle F_x, F_y \right \rangle\\ \amp = \vec{F}_x + \vec{F}_y\\ \amp = F_x\, \ihat + F_y\, \jhat\\ \amp = (F \cos \theta)\, \ihat + (F \sin \theta)\, \jhat \\ \amp = F \left (\ihat\, \cos \theta + \jhat\, \sin \theta \right ) \\ \amp =|\vec{F}| \langle \cos \theta,\ \sin \theta \rangle \end{align*}

These are all equivalent representation of vector \(\vec{F}\text{.}\)

Figure A.0.1. Notation used in this book