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所在平台: Udemy |
课程主页: https://www.udemy.com/course/limits-infinite-wisdom/
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《微积分1：极限与导数》课程概述 这门由Infinite Wisdom提供的Coursera课程，旨在深入讲解微积分中的基础概念——极限与导数。课程强调概念理解的重要性，为学生在微积分1及后续课程中取得成功奠定坚实基础。 课程内容涵盖： * **极限的探索：** 从图形、数值（表格）、代数和几何（图形）等多个角度解析极限。 * **导数的定义与应用：** 介绍平均变化率、导数的定义（瞬时变化率）、函数在一点的导数及其在切线和法线中的应用。 * **导数规则：** 系统讲解幂法则、可导性与连续性、基本导数规则、乘法法则、除法法则以及三角函数导数。 * **特殊类型函数：** 涵盖分段函数极限、三角函数极限、无穷极限、连续性等。 * **重要定理：** 解释极限性质和介值定理。 * **全面复习：** 提供详细的复习材料和答案解析，以巩固学习成果。 **课程特色：** * **多维度学习：** 结合讲座、表格、实践题（附视频和书面解答）、公式表和课程复习题，全方位学习。 * **目标受众广泛：** 适合已完成预备微积分的高中生和大学生，为正在学习微积分1、AP微积分AB/BC的学生提供补充学习和巩固；也适合需要重温基础知识的学生。 本课程是微积分1系列的第一部分，后续单元将很快发布。
Limits and Derivatives are a fundamental concept in Calculus. In order to thrive in the study of Calculus 1 and beyond, it is crucial to have a conceptual understanding of this topic. In this course, we will explore limits and derivatives graphically, numerically, algebraically and analytically. Every lesson contains a lecture with an accompanying follow along sheet, practice problems with solutions given in video and written format, formula sheets, and an extensive set of review problems at the end of the course along with an answer key.List of lessons:Finding Limits from GraphsNumerical Limits from TablesKnow Your Graphs Limits of Piecewise FunctionsAlgebraic Limits Trigonometric Limits Infinite Limits ContinuityLimit PropertiesIntermediate Value Theorem Unit 1 Review Average Rates of ChangeThe Definition of the Derivative and Instantaneous Rates of ChangeThe Derivative of a Function at a Point plus Tangent and Normal LinesThe Power RuleDifferentiability and ContinuityBasic Derivative RulesMore Derivative RulesThe Product and Quotient RulesTrigonometric DerivativesThis course is intended for a variety of high school and college students who have already taken Precalculus. It is perfect for students who want to get a jump start and preview the first two units of Calculus before they begin then course. It is equally ideal for students who are currently taking Calculus 1 or AP Calculus AB or BC and feel that they are not totally understanding the material being taught by their teacher. The course may be used as a refresher for students who took Calculus a while ago and need to re-master the early concepts.The other units in Calculus 1 will be posted very shortly!
