Back to Calculus: Single Variable Part 2 - Differentiation

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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 second part--part two of five--we cover derivatives, differentiation rules, linearization, higher derivatives, optimization, differentials, and differentiation operators....

RS

Apr 24, 2024

A truly well-built and detailed course. I already knew a few of the concepts taught in this course, however, I never really understood them. This course was filled with many 'Aha!' moments for me.

JB

Feb 17, 2018

So much fun, and hits all sorts of things I'd always wanted to know. The homework took me a long time, so I didn't get to watch all the bonus lectures, but the ones I did were really interesting.

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By 江祖榮

•Jul 19, 2019

Good in giving though-invoking concept and visualization of differentiation, chain rule, relative rate of change, as well as Newton's linear approximation.

These corresponding demo example are illustrative and help us understand the main idea and underlying metaphor of differential operator "D" and symbol df/dx.

In addition, the technique of domain change in differentiation by using exponent and logarithm and implicit differentiation is really powerful and useful.

By Wolfe G

•Feb 17, 2017

Not a class for someone with no calculus experience. However, if you have some calculus knowledge it will deepen your knowledge more than any other MOOC I have found. Truly a great course.

By Jim B

•Feb 18, 2018

So much fun, and hits all sorts of things I'd always wanted to know. The homework took me a long time, so I didn't get to watch all the bonus lectures, but the ones I did were really interesting.

By Nruparaj S

•Jun 30, 2018

It's really a learning experience. Questions have the practical approach. It provides a wider prospective of knowledge and application. Thank you for being a part this group.

By mrunmoy s

•Jan 31, 2020

After completing part 1, I headed for this second part of the 5 part series. Yes, it is a hard course but if you are persistent and keep at it, things will eventually make sense and you'll have some very good tools at your disposal to solve complex problem. Massive Thanks to Prof G and Team for this course.

By Tom B

•Jun 7, 2022

These calculus courses by Prof Ghrist are absolutely great. I'm a high school math teacher and tutor, and these courses provide a ton of interesting insights that I can pass onto students, even though they are not be studying calculus yet.

By Kamran S

•Jan 10, 2021

Excellent Course

A new look at the concepts of Limits, Taylor and Derivatives that expand your mathematical thinking and Flourishes the math another time. This is however not confusing though but more of a talent bonus.

By Rahul

•Jun 19, 2021

This course is highly interactive. You'll never experience boredom. This is recommendable to learners of standard level. Remember you should have at least studied calculus at high school.

By Mark B

•Jul 6, 2022

Wikipedia, Lang's calculus textbook, and the course notes from the internet archive were my constant companions. The homeworks certainly got me to study!

By Zejd I

•May 3, 2022

Great course. Even if you know differenetiation you will still find some useful information you didn't know about it. Let's go to integration ;)

By CMC

•Jun 28, 2018

This course has an appropriate amount of rigor for an intermediate math course. I was pleasantly surprised at how much I have learned.

By Shraavan S

•Oct 3, 2018

Great for reviewing concepts! Techniques for evaluating complex limits and the Taylor series have been explained very well.

By Jorge E M L V

•May 26, 2019

Excelente curso donde aprendí el cálculo de variable real, lo recomiendo mucho ya que se aprende bastante acerca del tema

By Devarshi P

•Jun 7, 2020

Highly application oriented course. Better to have strong grounding in theory and principles before starting.

By JUNJIE W

•Jul 11, 2019

It is a very informative course!

By Alinaswe C

•Jan 12, 2022

The course is great although deeper explanations and more examples are needed.

By Kevin O

•Aug 22, 2019

This is an extremely useful and informative course into which Dr. Ghrist has poured an enormous amount of energy, work, knowledge, and forethought. He is an exceptionally talented polyglot of both Mathematics and English, but I could have used additional explanations as to how to tackle the problems. I would have preferred it if solutions would have been provided for the quizzes and challenge problems. I believe that one learns calculus best this way, but Dr. Ghrist has become another excellent mentor that I have been fortunate enough to have in my quest to understand calculus.

By Brian N A

•Jul 11, 2018

As with part I, a real benefit of this course is its quality practice problems. They require you to work. I usually spent at least 30 minutes per problem (sometimes hours at the extreme), so you end up accumulating a lot of practice, and it certainly pays. I haven't previously put much effort in math, and as a result I would often make errors in my derivations. Not only does this course expose you to a lot of methods and knowledge, but the sheer amount of practice has made me inherently less prone to errors. Which makes math a LOT more fun.

By Konstantin P

•Feb 13, 2020

Problems are really interesting. These courses helped me to understand basic approaches and methodologies of single-variable calculus. I got a lot of satisfaction passing them and solving the problems especially challenging problems. I think these lectures fit purposes of people who aim to generalize and structure their knowledge of single-variable calculus. Thank you very much! I really hope to find similar courses on other fields of mathematics (multivariable calc, linear and abstract algebra)

By Ayman S

•Jul 26, 2019

Smart way of teaching, giving you the chance to learn new things with a very interactive way, enlarging your brain and synapses fire in it.

The core home work is the best practice to what you have learnt in the lectures and do not be discouraged solving the challenging H.W., keep going and "think outside the box.", you will learn a lot.

Thanks Prof. Ghrist, you are awesome.

By Gregorio A A P

•Jul 8, 2017

Excelente, felicitaciones , solo que es triste no poder disfrutar al 100% un curso de esta calidad al no estar traducido al español, le agradecería que por favor lo traduzca del ingles al idioma español ya que solo esta parcialmente traducido.

nuevamente felicitaciones por la gran didáctica con la que imparte el curso y sobre todo por la calidad con la que enseña.

By Fred V

•Aug 6, 2020

The slides with animation, about a wide range of applications, are close to a masterpiece. One thing that could easily be improved, though, is to make the audio more conversational: the spaces between between words, to slow the rhythm, do not really help. Apart from this minor irritation, this is a great course, in which I re-learnt and learnt a lot.

By Darleen J T S

•May 29, 2020

Charmed!. A course that strengthens the knowledge acquired in Chapter 1; and broadens the horizon with the introduction of a new concept (differentiation) with countless applications.

Congratulations to Professor R. Ghrist and the University of Pennsylvania team; for such a dedicated and powerful course.

By Айнаш С

•May 2, 2024

Good afternoon! A very good and informative course. Each chapter is interesting in its own way. The presentation of the material is excellent. I passed the exam for 70. But the certificate was not given. She completed the course according to the condition. Thank you very much!

By Derek S

•Aug 4, 2019

When I encounter differentials in the future, I will think of the techniques and graphics that I learnt in this lessons as either a mental tool or a reference. The part 2 is as good as the first part 1 and I expect to this level of quality in more advanced chapters.