微积分 1B:积分

Calculus 1B: Integration

Discover the integral—what it is and how to compute it. See how to use calculus to model real world phenomena. Part 2 of 3.

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麻省理工学院
edX
  • 完成时间大约为 15
  • 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

Some differential equation models for physical phenomena and solutions

The geometric interpretation, and physical meaning of the integral

The connection of the integral to the derivative

Several methods of numerically and symbolically integrating functions

To apply integrals to solve real world problems

课程概况

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.

But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.

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 Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, 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. 

课程大纲

Abridged SyllabusLimits

Limit Laws
Continuity
Intermediate Value Theorem

Differentiation

Introducing the Derivative
Rules for differentiation of all known functions
Approximations

Applications of Differentiation

Curve Sketching
Optimization
Related Rates

预备知识

18.01.1x Calculus 1A - Differentiation

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