https://juemuren.github.io/blog/series/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/「流形上的微积分」下的最新文章Hugozh-cn© Copyright 2026, RaindWed, 28 Oct 2026 14:32:55 +0800https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/Tue, 23 Jun 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/引言，讲解学习路线和知识体系。https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/01-%E7%82%B9%E4%B8%8A%E7%9A%84%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0/Sat, 26 Sep 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/01-%E7%82%B9%E4%B8%8A%E7%9A%84%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0/补充线性代数中的基本概念，包括向量、余向量、矩阵、张量、楔积等。https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/02-%E6%B5%81%E5%BD%A2%E7%9A%84%E9%80%90%E7%82%B9%E7%BA%BF%E6%80%A7%E5%8C%96/Sun, 27 Sep 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/02-%E6%B5%81%E5%BD%A2%E7%9A%84%E9%80%90%E7%82%B9%E7%BA%BF%E6%80%A7%E5%8C%96/补充流形几何中的基本概念，包括流形、子流形、切空间、余切空间、张量空间、外幂空间、纤维、丛、截面等。https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/03-%E5%BE%AE%E5%88%86%E5%BD%A2%E5%BC%8F/Mon, 28 Sep 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/03-%E5%BE%AE%E5%88%86%E5%BD%A2%E5%BC%8F/介绍微分形式，以及外微分和对微分形式的积分。https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/04-%E5%B9%BF%E4%B9%89%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%AE%9A%E7%90%86/Tue, 29 Sep 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/04-%E5%B9%BF%E4%B9%89%E6%96%AF%E6%89%98%E5%85%8B%E6%96%AF%E5%AE%9A%E7%90%86/推导广义斯托克斯定理，并用其统一微积分基本定理、曲线积分基本定理、格林定理、高斯定理和斯托克斯定理。https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/05-%E9%BB%8E%E6%9B%BC%E5%BA%A6%E9%87%8F/Tue, 13 Oct 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/05-%E9%BB%8E%E6%9B%BC%E5%BA%A6%E9%87%8F/介绍黎曼度量，以及与之相关的音乐同构、霍奇星算子、法空间和余法空间。https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/06-%E7%BB%8F%E5%85%B8%E5%90%91%E9%87%8F%E5%88%86%E6%9E%90/Wed, 14 Oct 2026 00:00:00 +0000https://juemuren.github.io/blog/posts/math/%E6%B5%81%E5%BD%A2%E4%B8%8A%E7%9A%84%E5%BE%AE%E7%A7%AF%E5%88%86/06-%E7%BB%8F%E5%85%B8%E5%90%91%E9%87%8F%E5%88%86%E6%9E%90/将经典向量分析中的点积、叉积、梯度、密度、散度、旋度用微分形式的语言重新定义。