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上海枫泾古镇一角_20240824上海枫泾古镇一角_20240824
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张朝阳物理课:深入浅出讲解二阶张量的协变导数

搜狐科技讯 4月7日消息,在4月6日播出的《张朝阳的物理课》第二百零七期中,搜狐创始人、董事局主席兼CEO、物理学博士张朝阳继续带领网友们探索微分几何中的张量世界,重点讲解了二阶张量的协变导数。

张朝阳首先回顾了一阶张量的协变导数,并解释了其下指标分量表达式中克氏符前面出现负号的原因。他指出,一阶张量的协变导数由两部分组成:第一项是张量分量随坐标的变化率,第二项则是基矢随坐标的变化率对张量分量的修正,而克氏符正是用来描述这种修正的。

接着,张朝阳开始介绍二阶张量的协变导数。他强调,要理解二阶张量的协变导数,首先需要了解二阶张量的基底展开式。他以两个矢量的张量积为例,展示了如何将二阶张量展开成基矢张量积的线性组合。

为了更清晰地说明二阶张量协变导数的推导过程,张朝阳详细分析了二阶张量的微分变化,并将其展开成下基矢的线性组合。通过对微分变化进行点乘操作,他推导出二阶张量协变导数的上指标分量表达式。

对于二阶张量协变导数的下指标分量,张朝阳鼓励网友们自行推导,并指出其表达式与一阶张量的情况类似,克氏符前面同样存在负号。

值得一提的是,张朝阳在讲解过程中始终注重与网友的互动,并耐心解答网友提出的问题。例如,当有网友质疑协变导数下指标分量表达式中克氏符前面为什么是负号时,张朝阳就通过基矢的正交关系,一步步推导出该结论,并最终消除网友的疑惑。

《张朝阳的物理课》每周周五、周日中午12时在搜狐视频直播,网友可以在搜狐视频APP“关注流”中搜索“张朝阳”,观看直播及往期完整视频回放。此外,还可以在搜狐新闻APP的“搜狐科技”账号上,阅览每期物理课程的详细文章。

总结

张朝阳在《张朝阳的物理课》中,以深入浅出的方式讲解了二阶张量的协变导数,并通过生动的例子和清晰的推导过程,帮助网友们更好地理解这一重要的微分几何概念。他的讲解不仅体现了深厚的物理学功底,更展现了对知识传播的热情和耐心。相信通过他的讲解,更多人能够领略到微分几何的魅力,并对物理世界有更深刻的理解。


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