麻省理工开放课程:18.02SC 多变量微积分 OCW Scholar Multivariable Calculus 英文无字幕版70集更新完毕！[MP4]

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资源信息： 中文名: 麻省理工开放课程:18.02SC 多变量微积分 英文名: OCW Scholar Multivariable Calculus 资源格式: MP4 课程类型: 数学 学校: MIT 主讲人: Christine Breiner,David Jordan,Joel Lewis 版本: 英文无字幕版70集更新完毕！ 发行日期: 2011年01月01日 地区: 美国 对白语言: 英语 概述:

本课程涵盖多个变量的函数的微分积分和矢量计算。这些数学工具和方法被广泛使用在物理科学，工程学，经济学和计算机图形学。 目录: 1_Coordinate free proofs_ centroid of a triangle 2_Dot products and angles 3_Components of a vector 4_Area of a parallelogram 5_Determinants 6_Volume of a parallelepiped 7_Finding area using cross products 8_Matrix multiplication practice 9_Solve a linear system using matrices 10_Equations of planes 11_Distance of a point to a plane 12_Systems of linear equations 13_Parametrized lines and intersections 14_Parametric line intersecting a plane 15_Differentiating a vector valued function 16_Parametric curves_ velocity, acceleration,length 17_Graphing surfaces 18_Level curves 19_Level curves and critical points 20_Partial derivatives 21_Tangent plane approximation 22_Least squares 23_Second derivative test 24_Max_Min 25_Total differentials and the chain rule 26_Tangent planes 27_Gradient and directional derivative 28_Lagrange multipliers 29_Lagrange multipliers (3 variables) 30_The chain rule with constraints 31_Gradients - composition 32_Regions of integration 33_Changing the order of integration 34_Integration in polar coordinates 35_Integrals with density 36_Change of variables 37_Integral of exp(-x^2) 38_Change of variables 39_Line integrals_ path dependence 40_Line integrals_ parametrization independence 41_Line integrals by geometric reasoning 42_Fundamental theorem of line integrals 43_Non-conservative vector fields 44_Potentials of gradient fields 45_Green's Theorem_ an off center circle 46_Green's Theorem_ area under an arch 47_Application of Green's theore 48_Flux across a curve 49_Green's Theorem in normal form 50_Extended Green's Theorem 51_Domains of vector fields 52_Volume in cylindrical coordinates 53_Average height 54_Moment of inertia of a cylinder 55_Average distance on a sphere 56_Gravity and a half-sphere 57_Flux through easy surfaces 58_Flux through a square 59_Flux through surfaces 60_Flux 61_Flux and the divergence theorem 62_Extended Gauss' Theorem 63_Del and the product rule 64_Line integral on a helix 65_Conservative fields and exact differentials 66_Stokes' Theorem 67_Extended Stokes' Theorem 68_Simply connected regions 69_More Stokes' Theorem 70_Consequences of Stokes' Theorem