echw (Eytan Chong’s Homework Class) is a $\LaTeX$ class file for homework and assignments based on Justin Wilson’s Homework Class
and Pascal Michaillat’s latex-math
.
Documentation
Packages
echw automatically loads the following packages (with libraries in brackets):
Brackets
| Bracket |
Example Usage |
Example Output |
| Parenthesis |
\bp{x} |
$(x)$ |
| Square Brackets |
\bs{x} |
$[x]$ |
| Curly Brackets |
\bc{x} |
$\{x\}$ |
| Absolute Value |
\abs{x} |
$\lvert x \rvert$ |
| Norm |
\norm{x} |
$\lVert x \rVert$ |
| Floor |
\floor{x} |
$\lfloor x \rfloor$ |
| Ceiling |
\ceil{x} |
$\lceil x \rceil$ |
| Parenthesis for Function Arguments |
f \of{x} |
$f{(x)}$ |
Functions and Operators
Common Functions
| Command |
Example Usage |
Example Output |
| Logarithm |
\ln{x + 1} |
$\ln(x + 1)$ |
| Exponential |
\exp{x + 1} |
$\exp(x + 1)$ |
| Sine |
\sin[n]{x} |
$\sin^n(x)$ |
| Cosine |
\cos[n]{x} |
$\cos^n(x)$ |
| Tangent |
\tan[n]{x} |
$\tan^n(x)$ |
| Cosecant |
\csc[n]{x} |
$\csc^n(x)$ |
| Secant |
\sec[n]{x} |
$\sec^n(x)$ |
| Cotangent |
\cot[n]{x} |
$\cot^n(x)$ |
| Arcsine |
\arcsin[n]{x} |
$\arcsin^n(x)$ |
| Arccosine |
\arccos[n]{x} |
$\arccos^n(x)$ |
| Arctangent |
\arctan[n]{x} |
$\arctan^n(x)$ |
Functional Operators
| Command |
Example Usage |
Example Output |
| Inverse |
\inv f |
$f^{-1}$ |
| Range |
\ran f |
$R_{f}$ |
| Domain |
\dom f |
$D_{f}$ |
| Indicator |
\ind{X} |
$\mathbf{1}_{X}$ |
| Maximum |
\max[x]{y} |
$\operatorname{max}_x\{y\}$ |
| Supremum |
\sup[x]{y} |
$\operatorname{sup}_x\{y\}$ |
| Argmax |
\argmax |
$\operatorname{argmax}$ |
| Minimum |
\min[x]{y} |
$\operatorname{min}_x\{y\}$ |
| Infimum |
\inf[x]{y} |
$\operatorname{inf}_x\{y\}$ |
| Argmin |
\argmin |
$\operatorname{argmin}$ |
Geometry
| Command |
Example Usage |
Example Output |
| Area |
\area |
$\operatorname{Area}$ |
| Length |
\length |
$\operatorname{Length}$ |
| Volume |
\volume |
$\operatorname{Volume}$ |
Complex Numbers
| Command |
Example Usage |
Example Output |
| Real Part |
\Re{z} |
$\operatorname{Re}(z)$ |
| Imaginary Part |
\Im{z} |
$\operatorname{Im}(z)$ |
| Argument |
\Arg{z} |
$\operatorname{arg}(z)$ |
| Complex Conjugate |
z\cconj |
$z^\ast$ |
Calculus
| Command |
Example Usage |
Example Output |
| Differential |
\d x |
$\mathrm{d} x$ |
| Ordinary Derivative (display) |
\der[n]{y}{x} |
$\dfrac{\mathrm{d}^n y}{\mathrm{d}x^n}$ |
| Ordinary Derivative (text) |
\derx[n]{y}{x} |
$\mathrm{d}^n y / \mathrm{d}x^n$ |
| Partial Derivative (display) |
\pder[n]{y}{x} |
$\dfrac{\partial^n y}{\partial x^n}$ |
| Partial Derivative (text) |
\pderx[n]{y}{x} |
$\partial^n y / \partial x^n$ |
| U-Substitution |
\usub{u &= 2x\\du &= 2dx} |
$$\begin{aligned}u &= 2x \\ du &= 2dx\end{aligned}$$ |
| Evaluation of Derivative |
\evalder{\der{y}{x}}{y = 0} |
$\left. \dfrac{\mathrm{d} y}{\mathrm{d} x} \right|_{y = 0}$ |
| Evaluation of Integral |
\evalint{F(x)}{a}{b} |
$\left[F(x)\right]_{a}^{b}$ |
Linear Algebra
| Command |
Example Usage |
Example Output |
| Boldface Vector |
\vec{v} |
$\mathbf{v}$ |
| 2D Column Vector |
\cvecii{x}{y} |
$\begin{pmatrix}x\\ y\end{pmatrix}$ |
| 3D Column Vector |
\cveciii{x}{y}{z} |
$\begin{pmatrix}x\\ y \\ z\end{pmatrix}$ |
| Dot Product |
\vec{u} \dotp \vec{v} |
$\mathbf{u} \cdot \mathbf{v}$ |
| Cross Product |
\vec{u} \crossp \vec{v} |
$\mathbf{u} \times \mathbf{v}$ |
| Boldface Matrix |
\matr{A} |
$\bm{A}$ |
| Trace |
\tr{X} |
$\operatorname{tr}(X)$ |
| Determinant |
\det{X} |
$\det(X)$ |
Statistics
| Command |
Example Usage |
Example Output |
| Variance |
\var[t]{X} |
$\operatorname{var}_t (X)$ |
| Covariance |
\cov[t]{X} |
$\operatorname{cov}_t (X)$ |
| Correlation |
\corr[t]{X} |
$\operatorname{corr}_t (X)$ |
| Standard Deviation |
\sd[t]{X} |
$\operatorname{sd}_t (X)$ |
| Standard Error |
\se[t]{X} |
$\operatorname{se}_t (X)$ |
| Expectation |
\E[t]{X} |
$\mathbb{E}_t (X)$ |
| Probability |
\P[t]{X} |
$\mathbb{P}_t (X)$ |
Misc
| Command |
Example Usage |
Example Output |
| Degree Symbol |
180 \deg |
$180^{\circ}$ |
| Significant Figures |
\tosf n |
$\text{ ($n$ s.f.)}$ |
| Decimal Places |
\todp n |
$\text{ ($n$ d.p.)}$ |
| Reject |
\reject{\because x > 0} |
$\qquad \text{(rej. $\because x > 0$)}$ |
| Newton-Raphson Method |
\nrm{x_0}{f} |
$x_0 - \dfrac{f(x_0)}{f’(x_0)}$ |
| Cases |
\case{1}{$x$ is odd} |
$\textbf{Case 1: $x$ is odd}$ |
Accents
| Accent |
Example Usage |
Example Output |
| Overline |
\ol{x} |
$\overline{x}$ |
| Over Right Arrow |
\oa{x} |
$\overrightarrow{x}$ |
| Underline |
\ul{x} |
$\underline{x}$ |
| Hat |
\wh{x} |
$\widehat{x}$ |
| Tilde |
\wt{x} |
$\widetilde{x}$ |
Letters
Calligraphic Letters
| Command |
Output |
\Ac |
$\mathcal{A}$ |
\Bc |
$\mathcal{B}$ |
\Cc |
$\mathcal{C}$ |
\Dc |
$\mathcal{D}$ |
\Ec |
$\mathcal{E}$ |
\Fc |
$\mathcal{F}$ |
\Gc |
$\mathcal{G}$ |
\Hc |
$\mathcal{H}$ |
\Ic |
$\mathcal{I}$ |
\Jc |
$\mathcal{J}$ |
\Kc |
$\mathcal{K}$ |
\Lc |
$\mathcal{L}$ |
\Mc |
$\mathcal{M}$ |
\Nc |
$\mathcal{N}$ |
\Oc |
$\mathcal{O}$ |
\Pc |
$\mathcal{P}$ |
\Qc |
$\mathcal{Q}$ |
\Rc |
$\mathcal{R}$ |
\Sc |
$\mathcal{S}$ |
\Tc |
$\mathcal{T}$ |
\Uc |
$\mathcal{U}$ |
\Vc |
$\mathcal{V}$ |
\Wc |
$\mathcal{W}$ |
\Xc |
$\mathcal{X}$ |
\Yc |
$\mathcal{Y}$ |
\Zc |
$\mathcal{Z}$ |
Blackboard Letters
| Command |
Output |
\Q |
$\mathbb{Q}$ |
\N |
$\mathbb{N}$ |
\Z |
$\mathbb{Z}$ |
\R |
$\mathbb{R}$ |
\C |
$\mathbb{C}$ |
Greek Letters
| Command |
Output |
\a |
$\alpha$ |
\b |
$\beta$ |
\c |
$\chi$ |
\de |
$\delta$ |
\D |
$\Delta$ |
\e |
$\epsilon$ |
\ve |
$\varepsilon$ |
\f |
$\phi$ |
\vf |
$\varphi$ |
\g |
$\gamma$ |
\G |
$\Gamma$ |
\h |
$\eta$ |
\i |
$\iota$ |
\k |
$\kappa$ |
\vk |
$\varkappa$ |
\l |
$\lambda$ |
\L |
$\Lambda$ |
\m |
$\mu$ |
\n |
$\nu$ |
\o |
$\omega$ |
\O |
$\Omega$ |
\p |
$\psi$ |
\r |
$\rho$ |
\vr |
$\varrho$ |
\s |
$\sigma$ |
\vs |
$\varsigma$ |
\S |
$\Sigma$ |
\t |
$\theta$ |
\u |
$\upsilon$ |
\U |
$\Upsilon$ |
\x |
$\xi$ |
\X |
$\Xi$ |
\z |
$\zeta$ |