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所在平台: Udemy |
课程主页: https://www.udemy.com/course/vector_calculus/
课程评论：没有评论
**课程名称：** 向量微积分第一部分：梯度、散度和旋度 **课程概述：** 本课程将带领学生深入学习向量微积分的基础知识，包括： * **向量基础概念：** 详细介绍标量和向量场，常向量，以及相关的基本定理。 * **微分与连续性：** 证明可微向量函数必然是连续函数。 * **常向量条件：** 证明向量场取常值与否的充要条件，以及向量函数具有常数模长时，该函数与其对时间导数垂直的充要条件。 * **方向与模长：** 探讨向量函数具有常数方向和常数模长的充要条件。 * **方向导数与场：** 学习方向导数及其在切平面、法线和等值面中的应用。 * **几何解释：** 深入理解向量的几何意义，特别是梯度、散度和旋度的几何解释。 * **算子与场：** 介绍Del算子和Laplacian算子，以及它们在定义无散度（Solenoidal）向量场和无旋（Irrotational）向量场中的应用。 * **重点定理与习题：** 课程将包含大量基于例题和定理的习题，并辅以证明。 **学习支持：** 如果您在学习过程中遇到任何问题或有任何疑问，请随时提问。讲师会尽力提供帮助。 **感谢与致意！**
In course , Vector Calculus Part 1 the student will learn about the following topics: Basic concepts of Vectors and detailed definitions Scalar and Vector point functions Constant Vectors and all Based Theorems.The proof of the Theorem that every Differentiable vector function is Continuous.The proof of the result that_The Necessary and sufficient condition for a vector point function to be Constant.The proof of the result that _If vector function has a Constant magnitude then f and df/dt are perpendicular. The Necessary and sufficient condition for a vector function to have Constant magnitude. The Necessary and sufficient condition for a vector function to have Constant direction. Directional Derivatives with examples Tangent Plane and Normal, Level Surfaces with definitions and detailed explanation Geometrical interpretation of vectors Geometrical Interpretation of Gradient of scalar point function Gradient, Divergence, and Curl of a vector and Many more Based examples and assignments with Theorems and proofs. Del Operator & Laplacian operator with examples. Solenoidal vector & Irrotational vector Important various Results, Expected Theorems, and Based AssignmentIf you need any help in understanding the topics or If you have any queries, feel free to revert back. The instructor is always there to help you. Thanks and Regards!
