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所在平台: Udemy |
课程主页: https://www.udemy.com/course/mr-sutton-presents-ap-calculus-bc/
课程评论:没有评论
**课程名称:** Mr. Sutton Presents. AP Calculus BC **课程概述:** 本课程旨在提供一种便捷、自主的学习方式,帮助学习者掌握优质的数学内容。讲师 Mr. Sutton 以清晰、简洁、不冗余的教学风格著称,通过精心设计的视频、PDF讲义、分组笔记和大量的练习题(附带答案和视频讲解)来帮助学生理解 AP Calculus BC 的核心概念。 **课程内容亮点:** * **精炼的教学视频:** 视频内容直奔主题,提供必要的背景知识和应用示例,并通过精心挑选的例题模型展示解题过程。 * **多样化的学习材料:** * 提供每节课的PDF版本,方便回顾。 * PPT幻灯片形式的课程内容,告别手写笔记。 * 可打印的引导式笔记,方便学生边学边记,避免重复抄写。 * **丰富的练习资源:** * 每节课提供2-4套练习题。 * 提供打印版练习题和PDF及视频格式的答案解析。 * 包含章节练习测验,帮助复习多个概念。 **课程涵盖的主要主题:** * **极限与连续:** 直观极限、代数极限、无穷极限、连续性、中间值定理。 * **变化率与导数:** 导数定义、求导法则(幂法则、乘积法则、商法则、链式法则)、隐函数微分、指数/对数/反三角函数的导数、高阶导数。 * **导数的应用:** 极值、单调性、凹性、拐点、图形分析、均值定理、线性化、指数增长与衰减、相关率。 * **积分:** 反导数、定积分(几何方法、黎曼和)、梯形法则、微积分基本定理、积分替换法、分部积分法、不适积分。 * **积分的应用:** 积分在几何中的应用(面积、体积)、微分方程(可分离方程、斜率场、欧拉法、Logistic增长)。 * **数列与级数:** 数列、收敛性测试(n项测试、比值测试、根值测试、n阶p-级数测试、交错级数测试、直接比较测试、极限比较测试)、收敛区间、泰勒级数、麦克劳林级数、级数的导数与积分、误差界。 * **参数、向量与极坐标:** 参数方程、向量、极坐标函数(斜率、面积)。 **无指定教学大纲。**
Mr. Sutton Presents.AP Calculus BCLet's cut out the fluffy description and get right to the point. You are looking for a convenient, self-paced way to learn some quality mathematics. You want a teacher who speaks, writes and explains clearly and without rambling in his videos. You want lots of practice problems with answers you can look up. You want to pay as little as possible for all this!Here is what all of my courses offer:Clear, concise videos that get to the point quickly with just enough "back story" to provide context, just enough "application" to spice it up, and carefully chosen examples to model the process.PDF versions of each lesson if you get sick of my voice or want to look back without hunting through the video. All lessons were recorded with PowerPoint slides, so you don't have to decipher my handwriting.A printable guided notes handout allowing you to fill-in-the-blanks while you watch each lesson. Very helpful if you learn better by writing things down but want to avoid needless rewriting or a disorganized jumble!2-4 practice problem sets per lesson, including printable handouts AND both PDF and video solutions of every single practice problem - an extra 20-30 hours of video content!End-of-chapter practice quizzes (with handouts and PDF/video solutions) to review multiple concepts at once. Here is what this course covers:Limits and ContinuityIntuitive Limits - FiniteIntuitive Limits - InfiniteAlgebraic Limits - Polynomials and Rational FunctionsAlgebraic Limits - Piecewise FunctionsLimits at InfinityContinuityIntermediate Value Theorem (IVT)Rate of ChangeDerivativesThe Power RuleDifferentiabilityGraphing DerivativesProduct and Quotient RulesDerivatives of Trigonometric FunctionsChain RuleImplicit DifferentiationTangent Lines and Higher Order DerivativesDerivatives of Exponential FunctionsDerivatives of Logarithmic FunctionsDerivatives of Inverse Trigonometric FunctionsApplications of DerivativesExtreme Values of FunctionsIncreasing and Decreasing IntervalsLocal ExtremaConcavityPoints of InflectionGraphical AnalysisMean Value TheoremLinearizationDerivatives of InversesL'Hospital's RuleMotionRelated RatesIntegralsAntiderivativesDefinite Integrals - Geometric ApproachRectangular Approximation Method (RAM)Trapezoidal RuleProperties of Definite IntegralsFTC - Derivative of an IntegralFTC - Graphical AnalysisFTC - Integral Evaluation (Polynomials)FTC - Integral Evaluation (Non-Polynomials and Function Values)Average ValueIntegration by SubstitutionIntegration by Partial Fractions (BC only)Integration by Parts (BC only)Improper Integrals (BC only)Applications of IntegralsDifferential Equations in One VariableSeparable Differential EquationsSlope FieldsExponential Growth and DecayMotion and PositionTotal DistanceAccumulation ProblemsRate In Rate OutArea Between CurvesVolume - Solids of RevolutionVolume - Cross-SectionsIntegration With Respect to the Y-AxisEuler's Method (BC only)Logistic Growth (BC only)Sequences and Series (BC only)Derivatives and Integrals of SeriesMaclaurin SeriesTransforming Maclaurin SeriesTaylor SeriesAlternating Series Error BoundLagrange Error BoundGeometric, Nth Term and Ratio TestsInterval of ConvergenceIntegral and P-Series TestsAlternating Series TestDirect Comparison TestLimit Comparison TestParametric, Vector and Polar Functions (BC only)Parametric FunctionsArc LengthVectorsPolar Functions - Slope and Basic AreaPolar Functions - Advanced Area