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微积分 1C:坐标系与无穷级数 | MOOC中国 - 慕课改变你,你改变世界

微积分 1C:坐标系与无穷级数

Calculus 1C: Coordinate Systems & Infinite Series

Master the calculus of curves and coordinate systems—approximate functions with polynomials and infinite series. Part 3 of 3.

642 次查看
麻省理工学院
edX
  • 完成时间大约为 10
  • 中级
  • 英语
注:因开课平台的各种因素变化,以上开课日期仅供参考

你将学到什么

To compute arc length

Methods for parameterizing curves

To do calculus in polar coordinates

How to approximate functions with Taylor polynomials

To determine convergence properties of infinite series

课程概况

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.

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

预备知识

18.01.2x Calculus 1B: Integration

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