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[latexpage]
At first, we sample $f(x)$ in the $N$ ($N$ is odd) equidistant points around $x^*$:
[
f_k = f(x_k),: x_k = x^*+kh,: k=-frac{N-1}{2},dots,frac{N-1}{2}
]
where $h$ is some step.
Then we interpolate points ${(x_k,f_k)}$ by polynomial
begin{equation} label{eq:poly}…Read More

\begin{tikzpicture}
[+preamble]
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
[/preamble]
\begin{axis}
\addplot3[surf,domain=0:360,samples=40] {cos(x)*cos(y)};
\end{axis}
\end{tikzpicture}

[mathjax]
\begin{aligned}
\textbf{1. Gauss’s Law:} & \quad \nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \\
\textbf{2. Gauss’s Law for Magnetism:} & \quad \nabla \cdot \mathbf{B} = 0
\end{aligned}
[/mathjax]

[latex]
\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} &= 0
\end{aligned}
[/latex]

[latex]
begin{aligned}
textbf{1. Gauss’s Law (Electricity):}quad
& nabla cdot mathbf{E} = frac{rho}{varepsilon_0}, \
& oint_{partial V} mathbf{E} cdot dmathbf{A} = frac{Q_text{enc}}{varepsilon_0} \[6pt]
textbf{2. Gauss’s Law (Magnetism):}quad
& nabla cdot mathbf{B} = 0, \
& oint_{partial V} mathbf{B} cdot…Read More

$$ begin{aligned}
textbf{1. Gauss’s Law (Electricity):}quad
& nabla cdot mathbf{E} = frac{rho}{varepsilon_0}, \
& oint_{partial V} mathbf{E} cdot dmathbf{A} = frac{Q_text{enc}}{varepsilon_0} \[6pt]
textbf{2. Gauss’s Law (Magnetism):}quad
& nabla cdot mathbf{B} = 0, \
& oint_{partial V} mathbf{B} cdot dmathbf{A}…Read More

Getting Started with IoT: Your Comprehensive Beginner’s Guide