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所在平台: Udemy |
课程主页: https://www.udemy.com/course/vector-calculus-with-applications/
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课程名称：全面指南：矢量与多变量微积分 课程概述：多变量微积分（或称矢量微积分，有时被称为微积分3）是应用数学、物理或工程学高级研究中最重要的学科之一。该课程的核心内容包括“积分定理”，这些定理在这些学科中有广泛的应用。课程内容涵盖以下主题： - 线积分（包括标量和矢量场的线积分） - 线积分的功 - 路径独立的线积分 - 保守场 - 简单连通域与多重连通域（配有动画演示） - 线积分与保守场路径独立性的定理（包括五个定理及其证明） - 线积分的应用（计算围绕曲线C的围栏面积、计算一根线的质量、质心和惯性矩） - 双重积分及其应用（计算平面图的质量、质心和惯性矩） - 曲面的参数表示 - 曲面积（包含替代公式） - 曲面的切平面与法线 - 标量与矢量场的曲面积分 - 积分定理（格林定理、斯托克斯定理、高斯（散度）定理） - 积分定理的应用（热方程、波动方程、拉普拉斯方程、连续性方程的推导等） 本课程包含超过70个示例，以帮助说明这些主题。绝大多数内容以幻灯片和动画形式呈现，部分例题在数字白板（One Note）上演示。每节视频课后附有讲义PDF，此外还提供学习者练习材料和必要提示。大部分讲座采用幻灯片形式，节省学习者的时间。课程还可能根据学习者的需求提供更多例题。 希望学生们能够从这门多变量微积分或矢量微积分课程中学到知识，并享受学习的过程。如发现任何讲座中的错误，欢迎指正；也欢迎提出建议，以促进课程的不断改进。 #多变量微积分 #矢量微积分 #微积分3
Multivariable Calculus or Vector Calculus (also some times called as Calculus 3) is one of the most important subject for advanced studies in applied mathematics, physics or engineering. The core of the subject contains the "Integral Theorems" as they have a wide range of applications to these disciplines. Keeping in view the course outlines Multivariable Calculus or Vector Calculus or Calculus-3 by most of the (local) institutes and universities, the following topics are included in this course Multivariable Calculus or Vector Calculus or Calculus-3:Line Integrals (of both scalar and vector fields) Work done as a Line integralPath Independent Line integralsConservative FieldsSimply Connected and Multiply Connected Domains (with Animations for illustration)Theorems (with proofs) on Path independence of Line Integrals and Conservative Fields (five theorems)Applications of Line integrals (Calculating the area of fence whose base is a curve C in space, calculating the Mass, the Center of Mass, and Moment of inertia of a wire)The Double Integrals with applications (calculating mass, c.o.m, moment of inertia of a lamina)Parametric Representation of SurfacesSurface area (with alternative formulas)Tangent Plane and Normal to a Surface Surface Integrals (of vector and scalar fields)Integral Theorems (Green's Theorem, Stokes's Theorem, Gauss's (Divergence) Theorem)Applications of Integral Theorems Derivation of Heat equation, Wave Equation, Laplace Equation, Continuity Equation etc. More than 70 worked examples are included in this course Multivariable Calculus or Vector Calculus or Calculus-3 to illustrate these topics. Most of the topics are illustrated with Slides and Animations (where needed), and a few examples are worked on digital white board (One Note) using Tablet.PDFs of lectures are also attached with the video lectures, Student Practice Material is also included with necessary hints. Most of the lectures are in the form of slides so that the learners time is marginally saved as compared to the white board lectures. More examples will be included (some examples can be included on demand of the learners).Hopes the students may learn and enjoy from this course Multivariable Calculus or Vector Calculus or Calculus-3.There may be mistakes and I will be extremely thankful to those who point out mistakes in any lecture (Check out the description of each video for corrections). Suggestions are always welcomed because we always need improvements.#Multivariable Calculus #Vector Calculus #Calculus-3
