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所在平台: Udemy |
课程主页: https://www.udemy.com/course/introduction-to-calculus-3-infinite-sequences-and-series/
课程评论：没有评论
**课程名称：** 微积分 III 入门：无穷序列与级数 **课程概述：** 本课程是“微积分 III”完整课程的前三个章节，涵盖无穷序列与级数的核心概念。通过详细的视频讲解、同步的白板笔记和附带解答的练习题，帮助学习者掌握微积分 III 的基础知识。课程特别强调每一步的推导过程，确保学习者能透彻理解概念和解题技巧。 **课程内容：** * **第二章：无穷序列** * 序列的定义与收敛性 * 单调有界序列 * **第三章：无穷级数** * 级数的定义 * 几何级数、裂项级数、调和级数 * 级数敛散性判别法： * 发散判别法 * 积分判别法 * 比较判别法 * 极限比较判别法 * 交错级数判别法 * ratio 判别法 * root 判别法 * 级数求和的估计 * 交错级数求和的估计 * 绝对收敛 * **第四章：幂级数** * 幂级数的定义 * 收敛半径与收敛区间 * 函数表示为幂级数 * 泰勒级数与麦克劳林级数 * 泰勒不等式 * 幂级数计算方法： * 直接计算法 * 逐项微分积分法 * 幂级数求和、乘除法 * 泰勒多项式的应用 **课程特色：** 1. **可下载的视频讲座：** 随时随地学习。 2. **可下载的讲义：** 方便回顾复习，尤其是在无法观看视频时。 3. **完整的练习题及解答：** 每章包含一套练习题（共三套），并提供详细解答，帮助巩固学习。 4. **分步详解：** 提供问题解决的每一步指导，帮助学习者深入理解。 **学习目标：** 掌握无穷序列和无穷级数的核心概念，学会使用各种判别法判断级数的敛散性，并能将函数表示为幂级数，理解泰勒级数及其应用。
HOW THIS COURSE WORK:This course, Introduction to Calculus 3: Infinite Sequences and Series, includes the first three sections of my complete course in Calculus 3, including video, notes from whiteboard during lectures, and practice problems (with solutions!). I also show every single step in examples and theorems. The course is organized into the following topics:Section 2: Infinite SequencesSequencesConvergence of a SequenceMonotonic and/or Bounded SequenceSection 3: Infinite SeriesSeriesGeometric SeriesTelescoping SeriesHarmonic Series1. Test for Divergence2. Integral TestEstimating the Sum of a Series3. Comparison Test4. Limit Comparison Test5. Alternating TestEstimating the Sum of an Alternating SeriesAbsolute Convergence6. Ratio Test7. Root TestSection 4: Power SeriesPower SeriesRadius of Convergence and Interval of ConvergenceRepresentations of Functions as Power SeriesTaylor Series and Maclaurin SeriesTaylor's InequalityMethod 1: Direct ComputationMethod 2: Use Term-by-term Differentiation and IntegrationMethod 3: Use Summation, Multiplication, and Division of Power SeriesApplications of Taylor PolynomialsCONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again.HIGHLIGHTS:#1: Downloadable lectures so you can watch whenever and wherever you are.#2: Downloadable lecture notes and some extra notes so you can review the lectures if you don't have a device to watch or listen to the recordings.#3: Three complete problem sets with solutions (1 at the end of each section) for you to do more practices.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina:)
