返回到 Calculus: Single Variable Part 4 - Applications

4.9

星

192 个评分

•

41 条评论

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 fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability....

VB

Apr 5, 2020

The course material are very well prepared. The focus is on direct application in engineering field. The concepts have been presented very elegantly - it shows deep knowledge of Prof Ghrist.

HY

Mar 9, 2020

Simply awesome!\n\nI would love to learn the digital calculus and the multi-variate calculus online with professor Ghrist.\n\nThank you! Dr. Ghrist

筛选依据：

创建者 Sanchit S

•Aug 21, 2016

Hey guys. So I just completed a Discrete Calculus course, offered by UPenn, through Coursera. I'd like to give a you guys an overview of the course, and my experience through this journey.

This, 5 part course, is designed to be completed within 21 weeks, with a work time of 6-8 hours a week. However, if you're really dedicated and have enough time, you can probably finish it within 8 weeks (like me). Oh, and it is taught by Prof. Robert Ghrist (he's cool, trust me).

First, for the prerequisites, you should have taken at least Calculus AB, to do well in this course. Practice with advanced integration techniques and some prior knowledge of Taylor Series is a plus.

Part 1 of the course begins with a study of Taylor Series. From what I've noticed, part 1 emphasizes the importance of using Taylor Series to develop an intuition about the behavior of a function at limits such as 0 and infinity. After revisiting some familiar topics with the perspective of Taylor, part 1 ends with introducing asymptotic analysis (big O), which took me a while to grasp.

Part 2 is review for the most part. However, it helps to further strengthen the idea of differentials, and their uses. Some bonus lectures introduce topology, and spacial curvature. Also, there is an introduction to the algebra of operators (which is elaborated in part 5) Some BC topics are also reviewed.

Part 3 mostly deals with practicing integration techniques, however emphasizes on Differential Equations (with specific focus on coupled oscillators). Formal definite integrals are introduced. Some more BC topics are reviewed.

Part 4, focuses on applying knowledge from the preceding parts. Although it starts off easy with areas, volumes, and arc length, the focus shifts to statistics and physical applications. There is a weird study of Work. Rotational Inertia and PDFs are taught in tandem. There is a brief study of high dimension spaces and hyper volumes. Centroids are taught through the use of double integrals.

Finally, part 5 introduces discrete calculus. Basically, continuous calculus, retaught with the perspective of series, in a discretized, non continuous setting. It begins with the study of finite differences, and a rather comprehensive practice of discrete integration. Differential equations (aka recursion relations) are taught, through the use of operators. Then, the focus shifts to numerical analysis, by introducing methods to approximate integrals (like Runge Kutta method). Following that, there is a very comprehensive study of convergence of series. And trust me, it is taught super well (way more in-depth than BC). Finally, the focus shifts to the rather obscure Taylor Remainder Theorem. This might be review for some.

This course was pretty challenging for me. I spent a lot of time doing my homework, and taking really good notes (for future reference). After a fee of $50, I earned my course certificate after the final exam (sigh).

This is a super cool course.

创建者 CMC

•Jul 6, 2018

The course taught me about how calculus is used to explain probability and statistics. This is exactly what I need to began studying these areas.

创建者 Alex G

•Jun 23, 2016

this was simply an amazing course, perfect for my skill level and exactly what i needed to learn. Thank you for the opportunity.

创建者 Louis J C J

•Feb 14, 2019

There is lots of material covered but the course hangs together well.

创建者 Michael C

•May 2, 2019

Great course.

创建者 Rafael C

•Jun 17, 2019

I can fully comprehend the purpose of this part, application, but the contradiction is that for students majoring in business, sociology or whatever, we're not bothered about how calculus can be applied in physics or geometry. Only the last part of probability is of interest to me. So I would propose that this part should be redesigned for different fields of application instead of integrating all different disciplines into one part, cuz much of the whole offering will have no connection with my later study. Yet the content of the course itself is good.

创建者 Paul K M

•Sep 6, 2019

This was a tough course. The lectures are very good, but I did have to rely on a lot of other material to really make sense of the concepts. Nonetheless, this course has given me a structure to organize my studies. The homework is tricky but rewarding. I have a much better grasp of calculus than a few months ago. I could recomend this course to anyone who really wants to understand calculus and its applications.

创建者 Behzad K N

•Jul 9, 2020

I have been exposed to so many applications in this course, have been constantly challenged which I have enjoyed even though I feel my head hearts!

I am retired teacher so i am motivated by how Prof/g skillfully conveys his thoughts to a learner such as me. I am grateful:

创建者 Gian M D G

•Feb 3, 2017

Entertaining and well thought, it seamlessly concatenates many calculus ideas into one tight program. The treatment of the infinitesimal elements as being the focus of understanding every concept was brilliant. Professor Ghrist is indeed a fantastic tutor and guide.

创建者 Jose D

•Jan 28, 2017

This is a very educational MOOC. It summarizes major topics very efficiently while making the presentation agile and interesting. It includes a number of really good and challenging quizzes and homeworks.

I really like it so far!!.

创建者 Mukund M

•Apr 10, 2020

I am neither a student nor a teacher. I am retired engineer age 73. I had a very little chance to use my

knowledge in my carrier . I just joined the course for refreshing my past study.

I enjoyed the course very much. Thank you .

创建者 Vishu B

•Apr 6, 2020

The course material are very well prepared. The focus is on direct application in engineering field. The concepts have been presented very elegantly - it shows deep knowledge of Prof Ghrist.

创建者 Herve Y

•Mar 10, 2020

Simply awesome!

I would love to learn the digital calculus and the multi-variate calculus online with professor Ghrist.

Thank you! Dr. Ghrist

创建者 Sachin M V

•Dec 10, 2016

Really its hard to complete as many questions are tricky, but now i feel very nice after completion.

创建者 Rafer

•Sep 15, 2019

the reading‘s math symbol is little complex for me.And it’s a good experience for me.Thanks Prof G.

创建者 Ricardo S L

•Apr 29, 2018

Great that prof does not feed you with a spoon, but makes you work to understand the content.

创建者 Radoslaw J

•Mar 17, 2017

The best math course I've ever seen, and also the best MOOC. The presentation is stellar.

创建者 杨佳熙

•Jun 21, 2016

the first four session is free which is econmic friendly. show u my respect :)

_{
}^{
}~~
~~

创建者 Nafis F

•Aug 8, 2020

AWESOME. Professor Ghrist, I can never thank you enough. So I won't even try.

创建者 江祖榮

•Aug 30, 2019

Great with fruitful and vivid illustration with math and physic example.

创建者 Zamir M

•May 27, 2016

Excellent examples and surprising relationship between the concepts!

创建者 HyoungJin J

•Jan 5, 2018

great...awesome lecture....his voice is little bit funny though...

创建者 Paul D

•Feb 13, 2017

Great course as always --- took me a while this time

创建者 Vitaliy D

•Oct 18, 2019

A great course for engineers who want to learn math

创建者 Carlos T B

•Apr 13, 2020

Excellent Calculus course.

- Finding Purpose & Meaning in Life
- Understanding Medical Research
- Japanese for Beginners
- Introduction to Cloud Computing
- Foundations of Mindfulness
- Fundamentals of Finance
- 机器学习
- 使用 SAS Viya 进行机器学习
- 幸福科学
- Covid-19 Contact Tracing
- 适用于所有人的人工智能课程
- 金融市场
- 心理学导论
- Getting Started with AWS
- International Marketing
- C++
- Predictive Analytics & Data Mining
- UCSD Learning How to Learn
- Michigan Programming for Everybody
- JHU R Programming
- Google CBRS CPI Training

- Natural Language Processing (NLP)
- AI for Medicine
- Good with Words: Writing & Editing
- Infections Disease Modeling
- The Pronounciation of American English
- Software Testing Automation
- 深度学习
- 零基础 Python 入门
- 数据科学
- 商务基础
- Excel 办公技能
- Data Science with Python
- Finance for Everyone
- Communication Skills for Engineers
- Sales Training
- 职业品牌管理职业生涯品牌管理
- Wharton Business Analytics
- Penn Positive Psychology
- Washington Machine Learning
- CalArts Graphic Design

- 专业证书
- MasterTrack 证书
- Google IT 支持
- IBM 数据科学
- Google Cloud Data Engineering
- IBM Applied AI
- Google Cloud Architecture
- IBM Cybersecurity Analyst
- Google IT Automation with Python
- IBM z/OS Mainframe Practitioner
- UCI Applied Project Management
- Instructional Design Certificate
- Construction Engineering and Management Certificate
- Big Data Certificate
- Machine Learning for Analytics Certificate
- Innovation Management & Entrepreneurship Certificate
- Sustainabaility and Development Certificate
- Social Work Certificate
- AI and Machine Learning Certificate
- Spatial Data Analysis and Visualization Certificate

- Computer Science Degrees
- Business Degrees
- 公共卫生学位
- Data Science Degrees
- 学士学位
- 计算机科学学士
- MS Electrical Engineering
- Bachelor Completion Degree
- MS Management
- MS Computer Science
- MPH
- Accounting Master's Degree
- MCIT
- MBA Online
- 数据科学应用硕士
- Global MBA
- Master's of Innovation & Entrepreneurship
- MCS Data Science
- Master's in Computer Science
- 公共健康硕士