Single Variable Calculus

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Single Variable Calculus

University of Pennsylvania

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....

100% 在線課程

立即開始，按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

建議：6-8 hours/week

完成時間大約為18 小時

English

字幕：English

100% 在線課程

立即開始，按照自己的計劃學習。

可靈活調整截止日期

根據您的日程表重置截止日期。

建議：6-8 hours/week

完成時間大約為18 小時

English

字幕：English

教學大綱 - 您將從這門課程中學到什麼

1

章節

完成時間為 2 小時

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 they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for discrete calculus....

4 個視頻（共 53 分鐘）, 2 個閱讀材料, 5 個測驗

4 個視頻

Sequences14分鐘

BONUS!5分鐘

Differences17分鐘

Discrete Calculus16分鐘

2 個閱讀材料

Your Guide to Getting Started in this Course10分鐘

How Grading Works10分鐘

5 個練習

Core Homework: Sequences14分鐘

Core Homework: Differences12分鐘

Challenge Homework: Differences8分鐘

Core Homework: Discrete Calculus10分鐘

Challenge Homework: Discrete Calculus4分鐘

2

章節

完成時間為 1 小時

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 approximate solutions to differential equations?" and "how do we approximate definite integals?" Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations....

2 個視頻（共 34 分鐘）, 1 個測驗

2 個視頻

Numerical O.D.E.s17分鐘

Numerical Integration16分鐘

1 個練習

Core Homework: Numerical O.D.E.s4分鐘

3

章節

完成時間為 2 小時

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 our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!...

4 個視頻（共 65 分鐘）, 6 個測驗

4 個視頻

Infinite Series16分鐘

Convergence Tests I16分鐘

Convergence Tests II16分鐘

Absolute & Conditional14分鐘

6 個練習

Core Homework: Infinite Series10分鐘

Challenge Homework: Infinite Series4分鐘

Core Homework: Convergence Tests I16分鐘

Challenge Homework: Convergence Tests I4分鐘

Core Homework: Convergence Tests II6分鐘

Core Homework: Absolute & Conditional4分鐘

4

章節

完成時間為 2 小時

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 sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series. ...

4 個視頻（共 59 分鐘）, 5 個測驗

4 個視頻

Power Series16分鐘

Taylor Series Redux15分鐘

Approximation and Error17分鐘

BONUS!9分鐘

5 個練習

Core Homework: Power Series12分鐘

Challenge Homework: Power Series8分鐘

Core Homework: Taylor Series Redux8分鐘

Challenge Homework: Taylor Series Redux4分鐘

Core Homework: Approximation and Error10分鐘

講師

Robert Ghrist

Professor

Mathematics and Electrical & Systems Engineering

關於 University of Pennsylvania

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. ...

常見問題

When will I have access to the lectures and assignments?
Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
What is the refund policy?
Is financial aid available?

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Single Variable Calculus

Single Variable Calculus

100% 在線課程

可靈活調整截止日期

建議：6-8 hours/week

English

100% 在線課程

可靈活調整截止日期

建議：6-8 hours/week

English

教學大綱 - 您將從這門課程中學到什麼

1

A Calculus for Sequences

2

Introduction to Numerical Methods

3

Series and Convergence Tests

4

Power and Taylor Series

熱門審閱

講師

Robert Ghrist

關於 University of Pennsylvania

常見問題