如何使矢量中的导数具有更大的字体大小，此外，如何使我的方程式居中？

Question

%\documentclass[12pt]{article}
\documentclass[12pt]{scrartcl}
\title{AE498 SDO - HW1}
\nonstopmode
%\usepackage[utf-8]{inputenc}
\usepackage{graphicx} % Required for including pictures
\usepackage[figurename=Figure]{caption}
\usepackage{float}    % For tables and other floats
\usepackage{verbatim} % For comments and other
\usepackage{amsmath}
\usepackage{physics}% For math
\usepackage{amssymb}  % For more math
\usepackage{fullpage} % Set margins and place page numbers at bottom center
\usepackage{paralist} % paragraph spacing
\usepackage{listings} % For source code
\usepackage{subfig}   % For subfigures
%\usepackage{physics}  % for simplified dv, and 
\usepackage{enumitem} % useful for itemization
\usepackage{siunitx}  % standardization of si units 


\begin{align*}
\nabla \theta &= \begin{pmatrix} \pdv{\theta}{R}\\[6pt] \pdv{\theta}{H}\end{pmatrix}=\begin{pmatrix} 4\pi R+2\pi H\\ 2\pi R\end{pmatrix}\\[6pt] 
\nabla h &= \begin{pmatrix} \pdv{h}{R}\\[6pt] \pdv{h}{H}\end{pmatrix}=\begin{pmatrix} \frac{2(0.001)}{\pi R^3}\\ 1\end{pmatrix}
\end{align*}


Equation (1) yields 2 equations and equation (2) yields 1 equation. Therefore we have 3 equations to solve for 3 unknowns ($R, H,\lambda$).

\begin{align*}
4\pi R+2\pi H\ &= \lambda \frac{0.002}{\pi R^3} \\[6pt]
2\pi R&= \lambda,\qquad R=\frac{\lambda}{2\pi} \\[6pt]
h(R,H)&=H-\frac{0.001}{\pi R^2} =0, \qquad H=\frac{0.004\pi}{ \lambda^2} \\[6pt]
\end{align*}

Answer 1

为了进行比较，我只在第一个方程中增加了向量的大小。为此我\displaystyle之前使用过pdv：

\documentclass[12pt]{scrartcl}
\title{AE498 SDO - HW1}
\nonstopmode
\usepackage[utf8]{inputenc}% <-- corrected
\usepackage{graphicx} % Required for including pictures
\usepackage[figurename=Figure]{caption}
\usepackage{float}    % For tables and other floats
\usepackage{verbatim} % For comments and other
\usepackage{amsmath}
\usepackage{physics}% For math
\usepackage{amssymb}  % For more math
\usepackage{fullpage} % Set margins and place page numbers at bottom center
\usepackage{paralist} % paragraph spacing
\usepackage{listings} % For source code
\usepackage{subfig}   % For subfigures
%\usepackage{physics}  % for simplified dv, and  <-- it is sufficient to load ones
\usepackage{enumitem} % useful for itemization
\usepackage{siunitx}  % standardization of si units

 \begin{document}
\begin{align*}
\nabla\theta    & = \begin{pmatrix}
                        \displaystyle\pdv{\theta}{R}\\[6pt] % corrected size by \displaystyle
                        \displaystyle\pdv{\theta}{H}        % corrected size
                    \end{pmatrix}
                  = \begin{pmatrix}
                    4\pi R+2\pi H\\
                    2\pi R\end{pmatrix}         \\[6pt]
\nabla h        & = \begin{pmatrix}
                        \pdv{h}{R}\\[6pt]                   % not corrected
                        \pdv{h}{H}                          % not corrected
                    \end{pmatrix}
                  = \begin{pmatrix}
                        \dfrac{2(0.001)}{\pi R^3}\\
                        1
                    \end{pmatrix}
\end{align*}
Equation (1) yields 2 equations and equation (2) yields 1 equation. Therefore we have 3 equations to solve for 3 unknowns ($R, H,\lambda$).
\begin{gather*}
4\pi R+2\pi H 
    = \lambda \frac{0.002}{\pi R^3}             \\
2\pi R
    = \lambda,\quad R=\frac{\lambda}{2\pi}     \\
h(R,H)
    = H-\frac{0.001}{\pi R^2} =0, \quad H=\frac{0.004\pi}{ \lambda^2}
\end{gather*}
\end{document}