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所在平台: Udemy |
课程主页: https://www.udemy.com/course/multivariable-calculus-drsteve/
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Coursera多变量微积分课程概述 本课程是关于多变量微积分的完整学习。多变量微积分是单变量微积分的扩展，涉及两个或多个变量的函数。学习本课程需要具备单变量微积分的基础知识，包括极限、连续性、微分和积分。 本课程将教授如何处理多变量函数和向量值函数。具体内容涵盖： * **三维空间与向量**：包括三维空间中的坐标、向量、点积、叉积、直线方程、平面方程以及二次曲面。 * **向量值函数**：包括向量值函数的弧长、TNB 坐标系、曲率，以及向量值函数的求极限、微分和积分。 * **多变量函数与偏微分**：包括多变量函数的概念、极限与连续性、偏导数、可微性、链式法则、方向导数，以及二元函数的最大值和最小值。 * **重积分**：包括二重积分（包括非矩形区域和极坐标下的二重积分）、三重积分，以及柱坐标和球坐标下的三重积分。 * **向量微积分**：包括向量场、线積分、路径无关性、格林公式、参数化曲面、曲面积分、可定向曲面与通量，以及斯托克斯定理和散度定理。 **先修要求**: 单变量微积分。
This is a complete course in Multivariable calculus. Multivariable calculus is an extension of single variable calculus to calculus with functions of two or more variables. It is expected that anyone taking this course has already knows the basics from single variable calculus: limits and continuity, differentiation and integration.In this course you will learn how to perform calculus on functions of two or more variables, as well as vector-valued functions. In particular, the topics covered include the basics of three dimensional space and vectors, vector-valued functions including the calculus of vector-valued functions (limits, differentiation, and integration), differentiation of functions of two or more variables, integration of functions of two or more variables, and vector calculus.Single variable Calculus is a prerequisite for this course. Here is a complete list of the topics that will be covered: Three-dimensional Space and VectorsRectangular Coordinates in 3-spaceVectorsDot ProductCross ProductEquations of LinesEquations of PlanesQuadric SurfacesVector-valued FunctionsArc Length and the TNB-FrameCurvatureFunctions of Multiple Variables and Partial DifferentiationFunctions of Two or More VariablesLimits and ContinuityPartial DerivativesDifferentiabilityChain RuleDirectional DerivativesMaxima and Minima of Functions of Two VariablesMultiple IntegralsDouble Integrals Double Integrals over Nonrectangular RegionsDouble Integrals over Polar RegionsTriple IntegralsCylindrical and Spherical CoordinatesTriple Integrals in Cylindrical and Spherical CoordinatesVector CalculusVector FieldsLine IntegralsIndependence of PathGreen's TheoremParametric SurfacesSurface IntegralsOrientable Surfaces and FluxStoke's TheoremDivergence Theorem
