<div class="directories"> <!-- Generate directories listing --> <!-- Generate posts listing --> <div class="post-preview"> <a href="/skill/math/equivalent-infinitesimal.html"> <h2 class="post-title"> 数学笔记 - 等价无穷小 </h2> <sub>-「Skill / Math」</sub> <h3 class="post-subtitle"> 考研中常用的一些等价无穷小 </h3> <div class="post-content-preview"> \[\begin{align*} \sin x &amp;\sim x \\ \arcsin x &amp;\sim x \\ \tan x &amp;\sim x \\ \arctan x &amp;\sim x \\ e^x-1 &amp;\sim x \\ \ln(1+x) &amp;\sim x \\ \s... </div> </a> <p class="post-meta"> Posted by Oscaner on September 9, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/derivation-formula.html"> <h2 class="post-title"> 数学笔记 - 求导公式 </h2> <sub>-「Skill / Math」</sub> <h3 class="post-subtitle"> 考研中常用的一些求导公式 </h3> <div class="post-content-preview"> \[\begin{align*} ( c )^\prime &amp;= 0 \\ ( x^a )^\prime &amp;= ax^{a - 1} \\ ( \log_a x )^\prime &amp;= \dfrac{1}{x \ln a} \\ ( \ln x )^\prime &amp;= \dfrac{1}{x} \\ ( a... </div> </a> <p class="post-meta"> Posted by Oscaner on September 9, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/taylor-formula.html"> <h2 class="post-title"> 数学笔记 - 泰勒公式 </h2> <sub>-「Skill / Math」</sub> <h3 class="post-subtitle"> 考研中的泰勒公式 </h3> <div class="post-content-preview"> 公式 \[f_{( x )} = f_{( x_0 )} + f^\prime_{( x_0 )} ( x - x_0 ) + \dfrac{f^{\prime \prime}_{( x_0 )}}{2!} ( x - x_0 )^2 + \dots + \dfrac{f_{( x_0 )}^{( n )}}{n!} ( x - x_0 )^n + R_n ( x )\] 标准公式... </div> </a> <p class="post-meta"> Posted by Oscaner on September 14, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/integral-formula.html"> <h2 class="post-title"> 数学笔记 - 积分公式 </h2> <sub>-「Skill / Math」</sub> <h3 class="post-subtitle"> 考研常用的一些积分公式 </h3> <div class="post-content-preview"> 基本积分公式 \[\begin{align*} &amp; \int x^k dx = \dfrac{1}{k + 1} x^{k + 1} + C \\ &amp; \int \dfrac{1}{x} dx = \ln \lvert x \rvert + C \\ &amp; \int a^x dx = \dfrac{1}{\ln a} a^x + C \;... </div> </a> <p class="post-meta"> Posted by Oscaner on September 17, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/differential-operators.html"> <h2 class="post-title"> 数学笔记 - 微分算子法 </h2> <sub>-「Skill / Math」</sub> <h3 class="post-subtitle"> 微分算子法主要用于求微分方程的特解 </h3> <div class="post-content-preview"> 【公式】 \[\begin{align*} &amp;设 \; D = \dfrac{d}{dx}, \; 则 \; y^\prime = D y, \; y^{\prime \prime} = D^2 y \\ &amp;( 1 ) \begin{cases} F_{( D )} e^{kx} = F_{( k )} e^{kx} \\ \d... </div> </a> <p class="post-meta"> Posted by Oscaner on September 22, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/inequality.html"> <h2 class="post-title"> 数学笔记 - 不等式 </h2> <sub>-「Skill / Math」</sub> <div class="post-content-preview"> 柯西不等式 普通形式 简记：平方和的乘积 ≥ 乘积和的平方 \[( a_1^2 + a_2^2 + \cdots + a_n^2 ) ( b_1^2 + b_2^2 + \cdots + b_n^2 ) \geqslant ( a_1 b_1 + a_2 b_2 + \cdots + a_n b_n )^2\] \[\sum_{i = 1}^n a_i^2 \sum_{i =... </div> </a> <p class="post-meta"> Posted by Oscaner on October 1, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/mean-value-theorem.html"> <h2 class="post-title"> 数学笔记 - 中值定理 </h2> <sub>-「Skill / Math」</sub> <div class="post-content-preview"> 罗尔定理 f(x) 在 [a,b] 内连续，在 (a,b) 内可导 \[f_{( a )} = f_{( b )} =&gt; f_{( \xi )} = 0\] 拉格朗日中值定理 f(x) 在 [a,b] 内连续，在 (a,b) 内可导 \[f_{( b )} - f_{( a )} = f_{( \xi )} ( b - a )\] 柯西中值定理 f(... </div> </a> <p class="post-meta"> Posted by Oscaner on October 1, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/gamma-function.html"> <h2 class="post-title"> 数学笔记 - 伽玛函数 </h2> <sub>-「Skill / Math」</sub> <div class="post-content-preview"> 积分形式 \[\begin{cases} \Gamma_{( x + 1 )} = \int_0^{+\infty} t^x e^{-t} dt \\ \\ \Gamma_{( x )} = \int_0^{+\infty} t^{x - 1} e^{-t} dt \end{cases}\] 【注】 考研中常见 t = x^2 , 即 \[\Gamma_{( u ... </div> </a> <p class="post-meta"> Posted by Oscaner on October 1, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/normal-line.html"> <h2 class="post-title"> 数学笔记 - 法线 </h2> <sub>-「Skill / Math」</sub> <div class="post-content-preview"> 切线法线 切线斜率 * 法线斜率 = -1 \[\begin{cases} f_{( x_0 )}^\prime * k = -1 \\ \\ y - y_0 = k ( x - x_0 ) \end{cases}\] 曲面法线 \[设曲线方程: z = f_{( x, y )} = 0\] 点(x0, y0)处的法线 \[\dfrac{x - x_0... </div> </a> <p class="post-meta"> Posted by Oscaner on October 6, 2018 </p> </div> <div class="post-preview"> <a href="/skill/math/distance-formula.html"> <h2 class="post-title"> 数学笔记 - 距离公式 </h2> <sub>-「Skill / Math」</sub> <div class="post-content-preview"> 点到点 \[\begin{cases} 点A: ( x_0, y_0 ) \\ \\ 点B: ( x_1, y_1 ) \\ \\ \mid AB \mid = \sqrt{( x_1 - x_0 )^2 + ( y_1 - y_0 )^2} \end{cases}\] 点到线 \[\begin{cases} 点A: ( x_0, x_1 ) \\ \\ ... </div> </a> <p class="post-meta"> Posted by Oscaner on October 6, 2018 </p> </div> </div>
