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学习笔记:广义积分·瑕积分

  • 2026-03-28 12:01:19
学习笔记:广义积分·瑕积分
最近持续关注美以袭击伊朗，这个恃强凌弱的世界真的越来越没有公平正义了。
各位当自强！
前天得知张雪峰猝死，年仅41岁，扼腕叹息，生命真的是太无常！
他是一个时代的代表符号，我尊敬他！
人生就是一场修行！
觉正净，可这人皆有之的自性三宝，能化作觉己，觉行，觉他的雨心吗？
写公众号，其实也是写给自己人生的作文或自白，爱数学的你，有可能偶尔看到，那就打扰了。
言归正传，继续整理听课笔记。
广义积分也可以称为非正常积分
我们通常采用的是第一种定义！
注意第一种定义要求的两个独立条件
在第二种定义下
奇怪不？这是因为少了独立条件。
再看一例
其实有一个发散就可以判定不收敛了。
但上面例子满足柯西主值收敛！
下面的习题，其实有解答，特意留白，数学人都懂！
瑕积分
离开大学太久了，这些内容都似曾相识。
计算方法
太晚了，先停手。
明天继续
晚安
一片禅心于2026年3月26日夜23:27
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  1. CONNECT:[ UseTime:0.000454s ] mysql:host=127.0.0.1;port=3306;dbname=no_67808;charset=utf8mb4
  2. SHOW FULL COLUMNS FROM `fenlei` [ RunTime:0.000630s ]
  3. SELECT * FROM `fenlei` WHERE `fid` = 0 [ RunTime:0.000322s ]
  4. SELECT * FROM `fenlei` WHERE `fid` = 63 [ RunTime:0.000323s ]
  5. SHOW FULL COLUMNS FROM `set` [ RunTime:0.000588s ]
  6. SELECT * FROM `set` [ RunTime:0.000247s ]
  7. SHOW FULL COLUMNS FROM `article` [ RunTime:0.000658s ]
  8. SELECT * FROM `article` WHERE `id` = 477939 LIMIT 1 [ RunTime:0.000486s ]
  9. UPDATE `article` SET `lasttime` = 1774698693 WHERE `id` = 477939 [ RunTime:0.012827s ]
  10. SELECT * FROM `fenlei` WHERE `id` = 65 LIMIT 1 [ RunTime:0.000237s ]
  11. SELECT * FROM `article` WHERE `id` < 477939 ORDER BY `id` DESC LIMIT 1 [ RunTime:0.000383s ]
  12. SELECT * FROM `article` WHERE `id` > 477939 ORDER BY `id` ASC LIMIT 1 [ RunTime:0.001178s ]
  13. SELECT * FROM `article` WHERE `id` < 477939 ORDER BY `id` DESC LIMIT 10 [ RunTime:0.001956s ]
  14. SELECT * FROM `article` WHERE `id` < 477939 ORDER BY `id` DESC LIMIT 10,10 [ RunTime:0.000636s ]
  15. SELECT * FROM `article` WHERE `id` < 477939 ORDER BY `id` DESC LIMIT 20,10 [ RunTime:0.000767s ]
0.090581s