課程信息
4.9
104 ratings
21 reviews
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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立即開始,按照自己的計劃學習。
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建議:6-8 hours/week

完成時間大約為18 小時
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English

字幕:English
Globe

100% 在線課程

立即開始,按照自己的計劃學習。
Calendar

可靈活調整截止日期

根據您的日程表重置截止日期。
Clock

建議:6-8 hours/week

完成時間大約為18 小時
Comment Dots

English

字幕:English

教學大綱 - 您將從這門課程中學到什麼

1

章節
Clock
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 <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>....
Reading
4 個視頻(共 53 分鐘), 2 個閱讀材料, 5 個測驗
Video4 個視頻
Sequences14分鐘
BONUS!5分鐘
Differences17分鐘
Discrete Calculus16分鐘
Reading2 個閱讀材料
Your Guide to Getting Started in this Course10分鐘
How Grading Works10分鐘
Quiz5 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
Clock
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 <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations....
Reading
2 個視頻(共 34 分鐘), 1 個測驗
Video2 個視頻
Numerical Integration16分鐘
Quiz1 個練習
Core Homework: Numerical O.D.E.s4分鐘

3

章節
Clock
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 <b>series</b>. 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!...
Reading
4 個視頻(共 65 分鐘), 6 個測驗
Video4 個視頻
Convergence Tests I16分鐘
Convergence Tests II16分鐘
Absolute & Conditional14分鐘
Quiz6 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
Clock
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. ...
Reading
4 個視頻(共 59 分鐘), 5 個測驗
Video4 個視頻
Power Series16分鐘
Taylor Series Redux15分鐘
Approximation and Error17分鐘
BONUS!9分鐘
Quiz5 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
4.9

熱門審閱

創建者 MMJan 11th 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

創建者 RBFeb 11th 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.\n\nLooking forward to Multi Variable Calculus.

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

  • 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.

  • 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.

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