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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/electrodynamics-introduction
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课程名称：电动力学导论 概述：电磁学是材料科学、电气工程和物理化学等多个领域的基础，深入和广泛的学习曲线要求学生持久而稳步的学习。本课程旨在弥合电磁学中基本原理与其在具体领域（如材料、物理和化学）中的实际应用之间的差距，特别是在能量储存和采集相关的研究中。本课程不仅教授电磁学，还引入了一些解决相关问题所需的数学工具。课程中将复习向量微积分，并解释如何利用场的概念来可视化所讨论的主题。课程内容动态发展，讲座内容不断基于之前的知识，针对每个解法提供多种解释。作为一个基础课程，我们将重点关注静电学的简单概念，探索分子间力和电容器的特性，从而将电磁学与更常规的研究主题及其在能量储存和采集中的应用联系起来。 课程大纲： 1. **静电学导论与基础**：本模块介绍电动力学，考察不同的力，并解释与电力相关的力量。此外，我们定义场，区分标量场和矢量场，并覆盖构成电动力学的定律，特别是麦克斯韦方程组和洛伦兹力，最后探讨相对论与本课程材料的关系。 2. **向量场的微积分导论**：该模块主要讲授微分方程的数学内容，介绍∇运算符及其在数学中的应用，证明∇运算符是一个向量。对麦克斯韦方程进行导数形式改写，并介绍散度和旋度的概念，最后探讨拉普拉斯算子及其他形式的∇运算符。 3. **向量积分微积分导论**：本模块解释线积分及其在某些方程的重要性，概念上解释场的通量和环流，并通过高斯定理和斯托克斯定理获得相关内容，最后讨论无散度和无旋度场的特性。 4. **静电解的导论**：本模块讨论如何在静电学场景中简化麦克斯韦方程，以及电势的使用及其相对值在某些计算中的重要性，展示不同几何体的通量，并讨论电场线和等势面的可视化。 5. **高斯定律的应用**：该模块主要集中在电场上，讨论平衡的数学要求，找到了点电荷的平衡的含义，描述不同几何体产生的电场，最后比较导体内外的电场及其如何产生电屏蔽现象。 此课程为学习电磁学提供了坚实的基础，结合理论与实际应用，适合对电磁学及其应用有兴趣的学习者。
Name:Introduction and Basics of Electrostatics
Description:In this module, electrodynamics is introduced by examining the different forces and explaining which are related to electric forces. Furthermore, fields are defined and we differentiate between scalar and vector fields. We cover laws that constitute electrodynamics, specifically Maxwell's equations and the Lorentz force. After explaining how these topics can be illustrated, we also cover how relativity relates to the subject material.
Name:Introduction to Differential Calculus of Vector Fields
Description:This module mainly covers the mathematics behind differential forms of equations. We introduce the ∇ operator and show how it can be used in mathematics. Then, the ∇ operator is proved to be a vector. The Maxwell equations are rewritten in derivative form, and the concepts of divergence and curl are introduced. Finally, we examine the Laplace operator, and other forms of the ∇ operator applied twice.
Name:Introduction to Vector Integral Calculus
Description:This module explains line integrals and presents some equations where they are important. We explain what the flux and circulation of a field are conceptually and how they can be obtain using the divergence and curl through Gauss' and Stokes' theorems respectively. Finally, we explain the qualities of divergence and curl free fields.
Name:Introduction to Electrostatic Solutions
Description:This module covers how to simplify Maxwell's equations in the scenario of electrostatics. Then, we discuss how the electric potential can be used and why using a relative value is useful for certain calculations. The flux out of different geometries is presented, as well as how to display field lines and equipotential surfaces.
Name:The Application of Gauss' Law
Description:This module focusses primarily on electric fields. First, we talk about the mathematical requirements for equilibrium and the implications of finding equilibrium for point charges. Then we move on to describe the electric field coming from different geometries. Finally, we compare the electric fields inside and outside of a conductor and how they create the phenomenon of electric shielding.
The depth and breadth of electromagnetism, the foundation for many fields including materials science, electrical engineering, and physical chemistry, requires a long, steep, and steady learning curve. This course aims to bridge the gap between the fundamental principles taught in electromagnetism and its practical application to specific fields such as materials, physics, and chemistry related to energy storage and harvesting. The goal of Electrodynamics: An Introduction is to not only teach electromagnetism but also introduce some mathematical tools which can be used to solve problems in the subject. Within these lecture notes, we review vector calculus and explain how to use fields to visualize the topics we cover. This course is dynamic, as the lectures continuously build on previous notes and a variety of explanations are presented for each solution. Since this is a lower level course, we will focus on the simple concept of electrostatics. This has applications in exploring intermolecular forces, and qualities of capacitors. Through this, we relate electromagnetism to more conventionally studied topics and its application to specific research topics related to energy storage and harvesting.
