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所在平台: Udemy |
课程主页: https://www.udemy.com/course/intro-to-calculus-2/
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**课程名称：** 微积分入门 2 (Intro To Calculus 2) **课程概述：** 本课程相当于大学二年级的微积分课程，共包含 22 小时的视频讲座、视频测验和最终笔试。课程内容被划分为六个主要部分：积分、积分的应用、微分方程、极坐标函数、参数方程与向量函数、数列与级数。每个部分结束后均设有视频测验。 **课程要求：** * 扎实的微积分 1A 基础 * 一本用来记笔记的笔记本 * 学习的动力 **课程涵盖的主题：** * 黎曼和 * 西格玛符号 * 积分规则 * 指数函数积分 * 三角函数积分 * 反三角函数积分 * 微积分基本定理 * 换元法 * 积分中值定理 * 粒子运动 * 分部积分法 * 三角换元法 * 反常积分 * 两曲线间的面积 * 已知截面的体积 (圆盘法、垫圈法) * 旋转体体积 * 弧长公式 * 功与胡克定律 * 静水压力 * 力矩与质心 * 可分离变量微分方程 * 斜率场 * 指数增长与衰减 * 欧拉法 * Logistic 微分方程 * 极坐标 * 极坐标图 * 极坐标下的切线 * 极坐标面积 * 向量 * 参数方程 * 数列与级数 (通项测试、p 级数、几何级数、极限比较测试、积分测试、伸缩级数、交错级数、比值测试、根值测试、收敛半径与收敛区间、幂级数、泰勒级数、二项级数)
This course is equivalent to second semester college level calculus course. This course has 22 hours of video lectures, video quizzes, and written final exam. This course is broken into six main sections: integrals, application of integrals, differential equations, polar functions, parametric and vector function, sequences and series. Each section is ended with a video quiz.Requirements for this course:Good foundation of calculus 1A notebook to write good notesThe drive to learnTopics that will be covered in this course:Riemann sumSigma notationIntegration rulesIntegral of exponential functionTrig integralsInverse trig integralsFundamental theorem of calculusU-substitutionMean value theorem for integralsParticle motionIntegration by partsTrig substitutionImproper integralsArea between two curvesVolumes with known cross sectionsDisk methodWasher methodSolids of revolutionArc length formula calculusWork and hooke's lawHydrostatic forceMoments and center of massSeparable differential equationsSlope fieldsExponential growth and decayEuler's methodLogistic differential equationsPolar coordinatesPolar graphsTangent line in polar coordinatesArea in polar coordinatesVectorsParametricSequences and seriesNth term testP series TestGeometric seriesLimit comparison testIntegral testTelescoping seriesAlternating seriesRatio testRoot testRadius and interval of convergencePower seriesTaylor seriesBinomial series
