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Calculus: Single Variable Part 2 - Differentiation

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Created by: Robert Ghrist

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Course Description

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.

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Instructor Details

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Robert Ghrist is the Andrea Mitchell University Professor of Mathematics and Electrical & Systems Engineering at the University of Pennsylvania. Prof. Ghrist is an applied mathematician whose expertise consists of finding novel applications for previously un-applied branches of Mathematics to Engineering Systems. Examples include applications of algebraic topology to sensor networks, sheaf theory to optimization and network data, CAT(0) geometry to robot motion planning, and braid theory to dynamical systems. His work has been honored by Scientific American as a "SciAm50 Top for Research Innovation" in 2007 and a Presidential Early Career Award for Scientists and Engineers (PECASE) in 2004. The S. Reid Warren, Jr. Award was granted to Prof. Ghrist by Penn students in 2009 for exceptional teaching. Prof. Ghrist is the 2013 recipient of the Chauvenet prize, the highest award for mathematical expository writing.

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Reviews

4.8

79 reviews in total

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By Rocky S on 17-Oct-19

Very explanative!

By Mubashir-Ul-Hassan on 7-Oct-19

That course is much harder than function part 1

By Sameen N on 2-Oct-19

Thnk you for clearing the concepts of differentiation

By Pavel K on 7-Sep-19

Gives a new perspective on derivatives and the clear insight into how a simple calculator works

By Kevin O on 22-Aug-19

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 Bendeguz S on 10-Aug-19

Presentations are great, albeit some topics were neglected or were too short. Overall 8,5/10

By OMAR A D L S R on 7-Aug-19

interesting

By Derek S on 4-Aug-19

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.

By ELJAYI A on 1-Aug-19

excellent

By Charlene R on 1-Aug-19

Thanks for offering this course!

By Ayman I F S on 26-Jul-19

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 江祖榮 on 19-Jul-19

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.

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Overall Score : 96 / 100