Differential of Surface Area

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\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{math}
\usepackage{ifthen}
\usepackage[active,tightpage]{preview}
\PreviewEnvironment{tikzpicture}
\setlength\PreviewBorder{1pt}
%
% File name: differential-of-surface-area.tex
% Description: 
% A geometric representation of the differential of surface area is shown.
% 
% Date of creation: October, 23rd, 2021.
% Date of last modification: October, 9th, 2022.
% Author: Efraín Soto Apolinar.
% https://www.aprendematematicas.org.mx/author/efrain-soto-apolinar/instructing-courses/
% Source: page 120 of the 
% Glosario Ilustrado de Matem\'aticas Escolares.
% https://tinyurl.com/5udm2ufy
%
% Terms of use:
% According to TikZ.net
% https://creativecommons.org/licenses/by-nc-sa/4.0/
% Your commitment to the terms of use is greatly appreciated.
%
\begin{document}
%
\begin{center}
\tdplotsetmaincoords{80}{100}
%
\begin{tikzpicture}[tdplot_main_coords,scale=1.5]
    % the function $z = f(x,y)$
    \tikzmath{function funcion(\x,\y) {return 1.125+0.25*sin((0.5*\x + 1.5*\y) r);};}
    \pgfmathsetmacro{\step}{pi/50.0} % step size
    \pgfmathsetmacro{\xi}{0}    % initial value for x
    \pgfmathsetmacro{\xf}{1.0*pi}   % final value for x
    \pgfmathsetmacro{\xe}{\xf+\step}
    \pgfmathsetmacro{\xs}{\xi+\step}
    \pgfmathsetmacro{\yi}{0}    % initial value for y
    \pgfmathsetmacro{\yf}{1.0*pi}   % final value for y
 
 
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