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所在平台: Udemy |
课程主页: https://www.udemy.com/course/visual-real-analysis/
课程评论：没有评论
课程简介：视觉实分析：实数与实序列 如果您是一名在STEM领域的大学生，并且正在学习有关实序列的课程，那么这个课程正适合您。该课程包含视觉化和易于理解的视频，帮助您更好地掌握实数和实序列相关的概念。课程采用实践方式，您将在观看视频的过程中需要多次暂停，并回答一些问题，以帮助您进步。希望在课程结束时，您发现作业和考试变得更容易。 课程分为两个部分：第一部分探讨实数。它定义了实数，并介绍了与实数集ℝ相关的概念，包括实数的下限和上限、绝对值、子集的稠密性、上确界、上界和最大元素。 第二部分聚焦于实序列。课程从实序列的定义及其不同可视化方式开始，接着明确几个与实序列相关的概念：数学归纳法、收敛性、发散性、单调性和子序列。此外，还介绍了与实序列相关的工具和定理，如相邻序列、夹逼定理和不动点定理等。最后，课程讨论了在您学术旅程中将频繁遇到的特定序列：算术序列、几何序列、一阶和二阶递归序列，以及一般递归序列。 通过这个课程，您将更深入地理解实数和实序列，为今后的学习打下坚实的基础。
If you're a college/university student in a STEM field and you're taking a course on real sequences, this is for you. This course contains visual and brain-friendly videos that will help you better understand concepts related to real numbers and real sequences.This course is hands-on. You will have to pause several times during the videos and answer some questions that will help you make progress. Hopefully, at the end of this course, assignments and exams will look a lot easier for you.The first section of this course deals with real numbers. It defines real numbers and presents concepts related to the set ℝ of real numbers. These concepts are the floor and ceiling of a real number, the absolute value, the density of a subset of ℝ, the supremum, the upper bound, and the greatest element.The second section of this course is about real sequences. It starts with the definition and the different ways to visualize a real sequence. Then it clarifies several concepts related to real sequences: mathematical induction, convergence, divergence, monotonicity, and subsequences. Further, it presents tools and theorems related to real sequences: adjacent sequences, squeeze theorem, fixed point theorem, etc. And finally, it discusses particular sequences you will see a lot during your academic journey: arithmetic and geometric sequences, first- and second-order recursive sequences, and general recursive sequences.
