|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/covariant-formulation-of-classical-electrodynamics/
课程评论：没有评论
课程名称：经典电动力学的协变形式 课程概述：该课程旨在以简明、完整且在数学上直观的方式描述电磁学的基本法则，包括麦克斯韦方程、洛伦兹力、电磁能动量张量等。课程中广泛使用了张量、闵可夫斯基度量和拉格朗日力学等概念，这些在讲师之前的课程“特殊与一般相对论背后的数学直觉”中已被介绍。经典电磁学的协变形式是指以明确不变的方式书写经典电磁学法则（特别是麦克斯韦方程和洛伦兹力），以符合特殊相对论的形式（因此使用惯性坐标系）。这些表达式清楚地证明了经典电磁学法则在任何惯性坐标系中保持相同的形式，并提供了在不同参考系中处理场和力的方法。然而，这种表达形式并不如在弯曲时空中的麦克斯韦方程（即非直线坐标系）一般。事实上，麦克斯韦方程也可以毫不费力地扩展到弯曲时空。 课程中，我们将推导真空中的麦克斯韦方程，此时可以将其写成两个张量方程（而非四个向量方程）。我们还将展示如何从直观的拉格朗日方法出发推导出电磁张量，并计算与电磁场相关的能量-动量张量，回顾在“特殊与一般相对论背后的数学直觉”课程中得出的一些表达式。 注意：我在2021年9月提升了整门课程的语言流畅性，现在应该更容易理解。在创建这门课程时，我更注重概念的传达而非课程外观或语言的流畅性。然而，概念的呈现方式同样重要，因此我认为这次改进是有必要的。
This course aims to give a concise, complete and mathematically intuitive description of the fundamental laws of electromagnetism, namely: Maxwell's equations, Lorentz force, electromagnetic energy momentum tensor, etc.The following concepts are used extensively: tensors, Minkowski metric, lagrangian mechanics, which were introduced by the instructor in the course "Mathematical intuition behind Special and General Relativity".The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is clearly invariant under Lorentz transformations, in the formalism of special relativity (therefore using inertial coordinate systems). These expressions simply prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, as well as provide a way to treat the fields and forces in different reference frames. However, this is not as general as Maxwell's equations in curved spacetime (i.e. non-rectilinear coordinate systems). Maxwell's equations can also be extended to curved spacetime without great effort.We will derive Maxwell's equations in vacuum, where they can be written as two tensor equations (instead of 4 vector equations).We will also see how to derive the electromagnetic tensor, starting from an intuitive Lagrangian approach, and also calculate the energy-momentum-tensor related to electromagnetic fields, by recalling some expressions derived in the course on General Relativity ("Mathematical Intuition behind Special and General Relativity").Note (September 2021): I have improved the speaking fluency of the entire course, which should now be easier to follow. When I created this course, I focused more on the concepts rather than on the appearance of the course or speech fluency. However, the way concepts are delivered is also very important, so I deem this improvement to be relevant.
