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help for twikoo add ssl verify
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@WindyDante
WindyDante committed Dec 2, 2024
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142 changes: 140 additions & 2 deletions public/markdowns/高等数学.md
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Expand Up @@ -1076,11 +1076,11 @@ Cxx的求解方式

### 右侧不为0求通解(第一类)

<img src="C:/Users/Administrator/AppData/Roaming/Typora/typora-user-images/image-20241130223640020.png" alt="image-20241130223640020" style="zoom:50%;" />
<img src="https://s2.loli.net/2024/12/01/18bwQ9s274NIqxM.png" alt="image-20241130223640020" style="zoom:50%;" />

根据类型设特解形式

<img src="C:/Users/Administrator/AppData/Roaming/Typora/typora-user-images/image-20241130223609211.png" alt="image-20241130223609211" style="zoom:50%;" />
<img src="https://s2.loli.net/2024/12/01/Q7ANLaYd3DoOfBU.png" alt="image-20241130223609211" style="zoom:50%;" />

求出y*对其求导就可以得到原式带入解出其他结果值

Expand All @@ -1096,3 +1096,141 @@ Cxx的求解方式

在之前通解的情况下，解出c1c2带回原式即可

## 求解关于变限积分的等式

解法

对其求导计算求微分方程即可

# 二重积分

## 基本概念与性质

概念

<img src="https://s2.loli.net/2024/12/01/cMHkDruWs1J6LTq.png" alt="image-20241201151158437" style="zoom:50%;" />

性质

<img src="https://s2.loli.net/2024/12/01/YEazftk2cPuSlKA.png" alt="image-20241201152820335" style="zoom:50%;" />

<img src="https://s2.loli.net/2024/12/01/ANQLGRmbxYnWe5T.png" alt="image-20241201153102293" style="zoom:50%;" />

## 比大小

<img src="https://s2.loli.net/2024/12/01/bSdlKuUgP5HhRtM.png" alt="image-20241201153258192" style="zoom:50%;" />

## 估值定理

<img src="https://s2.loli.net/2024/12/01/UAO3FyHm6xcuPvY.png" alt="image-20241201153531386" style="zoom:50%;" />

## 圆的表达式

<img src="https://s2.loli.net/2024/12/01/9TGhaorKD1g4d3R.png" alt="image-20241201161852983" style="zoom:50%;" />

## 椭圆表达式

<img src="https://s2.loli.net/2024/12/01/qGk8BzNyLCf9gSj.png" alt="image-20241201162003774" style="zoom:50%;" />

## 直角坐标系下的计算公式

将二重积分化为定积分来计算

公式

<img src="https://s2.loli.net/2024/12/01/UvweRJYnLNciHF5.png" alt="image-20241201165504629" style="zoom:50%;" />

<img src="https://s2.loli.net/2024/12/01/HpL3fIveok4Yhla.png" alt="image-20241201165732355" style="zoom:50%;" />

<img src="https://s2.loli.net/2024/12/01/i8jvrV2lZI5N39D.png" alt="image-20241201170014292" style="zoom:50%;" />

### 解法

<img src="https://s2.loli.net/2024/12/01/8irRej9TahLMF4c.png" alt="image-20241201170940881" style="zoom:50%;" />

## 超越积分顺序选择

题型，根据对应的x或y确定是哪个型，然后和基本的二重积分一样画图来写

<img src="https://s2.loli.net/2024/12/01/S369QDByLeE58ZX.png" alt="image-20241201194700389" style="zoom:50%;" />

## 交换积分次序

x型与y型的顺序交换

<img src="https://s2.loli.net/2024/12/01/4ZO5PmtH9Ld8ajb.png" alt="image-20241201210102993" style="zoom:50%;" />

根据题目已知条件确定类型，然后画图确定范围

## 极坐标系的二重积分

极坐标如下图所示

<img src="https://s2.loli.net/2024/12/01/RZn5U4xYFzl2qaG.png" alt="image-20241201212222125" style="zoom:50%;" />

### 极坐标的三角关系

<img src="https://s2.loli.net/2024/12/01/VU9AftylYING41D.png" alt="image-20241201212531854" style="zoom:50%;" />

在极坐标下：x平方+y平方=r平方

### 二重积分计算

解法

<img src="https://s2.loli.net/2024/12/01/hR78ZLodvFj4NVi.png" alt="image-20241201213357114" style="zoom:50%;" />

上下限的确定方法

<img src="https://s2.loli.net/2024/12/01/6CG7bcitje2HvOp.png" alt="image-20241201214042472" style="zoom:50%;" />

半径r的取值范围

<img src="https://s2.loli.net/2024/12/01/pzCHGU4c5Dda2XM.png" alt="image-20241201220202398" style="zoom:50%;" />

常见的积分图像

<img src="https://s2.loli.net/2024/12/01/jwqBHrgPZibkfh9.png" alt="image-20241201220756013" style="zoom:50%;" />

<img src="https://s2.loli.net/2024/12/01/Z1G9L8IrEHzkUya.png" alt="image-20241201221128351" style="zoom:50%;" />

<img src="https://s2.loli.net/2024/12/01/cdhe3Q7uImDUOaf.png" alt="image-20241201221347282" style="zoom:50%;" />

## 二重积分对称性

条件,偶倍奇零，画图，看关于哪个轴对称，然后看对应函数的奇偶性来算

<img src="https://s2.loli.net/2024/12/01/9CnH7jtIGT4gosF.png" alt="image-20241201232156107" style="zoom:50%;" />

注：若D对称，首选对称性

# 多元函数微分学

## 基本概念

<img src="https://s2.loli.net/2024/12/02/jUgeVMJGwa25Zky.png" alt="image-20241202151422828" style="zoom:50%;" />

## 定义域

<img src="https://s2.loli.net/2024/12/02/65yFOn8vSNxIj1w.png" alt="image-20241202152756449" style="zoom:50%;" />

## 二元函数对应法则

解法

<img src="https://s2.loli.net/2024/12/02/HhpiCatMsKmdNoQ.png" alt="image-20241202160223137" style="zoom:50%;" />

例题

<img src="https://s2.loli.net/2024/12/02/JzZ1saX3V468oSn.png" alt="image-20241202160541099" style="zoom:50%;" />

## 二元函数极限

<img src="https://s2.loli.net/2024/12/02/4927A5kdxFfYXCG.png" alt="image-20241202161011693" style="zoom:50%;" />

例题

<img src="https://s2.loli.net/2024/12/02/T9bFaoV3zvYws6S.png" alt="image-20241202162143839" style="zoom:50%;" />

## 一阶偏导

1 change: 0 additions & 1 deletion src/components/Main.vue
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Expand Up @@ -77,7 +77,6 @@ const goToArticle = (file) => {
name: "Content",
params: {
title: file.title,
date: file.date,
},
});
};
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2 changes: 1 addition & 1 deletion src/components/RSSGenerator.vue
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Expand Up @@ -35,7 +35,7 @@ const generateRSS = () => {
// 遍历文章并生成 RSS 条目
articles.value.forEach((article) => {
console.log(article);
// console.log(article);
// 生成每篇文章的链接，基于当前页面的 URL
const articleLink = `${baseURL}#/content/${encodeURIComponent(
article.name
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2 changes: 1 addition & 1 deletion src/components/Twikoo.vue
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Expand Up @@ -21,7 +21,7 @@ export default {
script.onload = () => {
// 在加载完成后初始化 Twikoo
twikoo.init({
envId: "http://124.223.88.171:7070/", // 替换为你的环境 ID 或 Vercel 地址
envId: "https://twikoo.windydante.top/", // 替换为你的环境 ID 或 Vercel 地址
el: "#tcomment",
lang: "zh-CN",
});
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2 changes: 1 addition & 1 deletion src/router/index.js
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Expand Up @@ -31,7 +31,7 @@ const router = createRouter({
component:()=>import("@/views/FriendLinks.vue")
},
{
path: "/content/:title/:date",
path: "/content/:title",
name: "Content",
component: () => import("@/components/Content.vue")
},
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