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微积分1C：坐标系和无限级数
Calculus 1C: Coordinate Systems & Infinite Series |
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| 课程网址: |
https://openlearninglibrary.mit.edu/courses/course-v1:MITx+18.01....
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| 主讲教师: |
David Jerison; Gigliola Staffilani; Jennifer French; Karene Chu
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| 开课单位: |
麻省理工学院
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| 开课时间: |
2020-06-16
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| 课程语种: |
英语
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| 中文简介: |
牛顿如何描述行星的轨道？为此，他创建了微积分。但他使用了更适合行星运动的不同坐标系。我们将学习改变我们的观点，用参数化曲线和极坐标进行微积分。然后我们将深入探索无限，以获得更深入的理解和强大的功能描述。
计算机如何进行准确的计算？现实世界中不存在绝对精度，计算机无法处理无穷小或无穷大。幸运的是，正如我们使用十进制系统近似数字一样，我们可以使用一系列更简单的函数来近似函数。这些近似值为科学计算提供了强大的框架，并且仍然提供高度准确的结果。它们使我们能够基于以微积分语言表示的世界模型来解决各种工程问题。
改变观点
参数方程
极坐标
级数和多项式近似
系列与融合
泰勒级数和幂级数
本系列中的三个模块在edX上作为XSeries提供。请访问单变量微积分XSeries程序页面了解更多信息并注册模块。
本课程与第1部分和第2部分相结合，涵盖AP*Calculus BC课程。
了解更多关于我们的高中和AP*考试准备课程
本课程部分由Wertheimer基金资助。
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| 课程简介: |
How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.
How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.
Changing Perspectives
Parametric Equations
Polar Coordinates
Series and Polynomial Approximations
Series and Convergence
Taylor Series and Power Series
The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.
This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.
Learn more about our High School and AP* Exam Preparation Courses
This course was funded in part by the Wertheimer Fund.
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| 关 键 词: |
泰勒级数; 幂级数; 极坐标; 泰勒多项式; 无穷级数的收敛性质
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| 课程来源: |
麻省理工学院公开课
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| 数据采集: |
2022-04-08：cyh
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| 最后编审: |
2022-04-08：cyh
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| 阅读次数: |
44
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