## 关键信息

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**免费进入**

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**收费证书**

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**总共30个小时**

## 关于内容

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences. Distinguishing features of the course include: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this fifth part--part five of five--we cover a calculus for sequences, numerical methods, series and convergence tests, power and Taylor series, and conclude the course with a final exam. Learners in this course can earn a certificate in the series by signing up for Coursera's verified certificate program and passing the series' final exam.

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## 课程大纲

- Week 1 -
**A Calculus for Sequences**

It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a*discrete*input. These are*sequences*, and... - Week 2 -
**Introduction to Numerical Methods**

That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of**numerical analysis**, answering such questions as*"how do we ...* *Week 3 -***Series and Convergence Tests**

In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or**series**. The determination of convergence for such will occupy ...*Week 4 -***Power and Taylor Series**

This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make se...*Week 5 -***Concluding Single Variable Calculus**

Are we at the end? Yes, yes, we are. Standing on top of a high peak, looking back down on all that we have climbed together. Let's take one last look down and prepare for what lies above.

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The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.
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## 教师

**Robert Ghrist**

Professor

Mathematics and Electrical & Systems Engineering

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## 内容设计师

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## 平台

Coursera是一家数字公司，提供由位于加利福尼亚州山景城的计算机教师Andrew Ng和达芙妮科勒斯坦福大学创建的大型开放式在线课程。

Coursera与顶尖大学和组织合作，在线提供一些课程，并提供许多科目的课程，包括：物理，工程，人文，医学，生物学，社会科学，数学，商业，计算机科学，数字营销，数据科学 和其他科目。

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