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.
Offered By
Calculus: Single Variable Part 2 - Differentiation
University of PennsylvaniaAbout this Course
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Learner Career Outcomes
50%
started a new career after completing these courses
33%
got a tangible career benefit from this course
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Start instantly and learn at your own schedule.
Flexible deadlines
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Approx. 10 hours to complete
English
Subtitles: French, Portuguese (Brazilian), Chinese (Simplified), Russian, English, Spanish
Skills you will gain
Differential (Mathematics)Newton'S MethodLinear ApproximationDifferential CalculusDerivative
Learner Career Outcomes
50%
started a new career after completing these courses
33%
got a tangible career benefit from this course
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Approx. 10 hours to complete
English
Subtitles: French, Portuguese (Brazilian), Chinese (Simplified), Russian, English, Spanish
Offered by
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.
Syllabus - What you will learn from this course
3 hours to complete
A New Look at Differentiation
Think derivatives mean "slopes"? Not anymore... In this module, we will reconsider what a derivative is and means in terms of the asymptotic (or big-O) notation from the previous chapter. This will give us a new language for describing and understanding rates of change and the rules that govern them.
3 hours to complete
3 videos (Total 45 min), 2 readings, 4 quizzes
2 readings
How Grading Works10m
Your Guide to Getting Started in this Course10m
4 practice exercises
Core Homework: Derivatives30m
Challenge Homework: Derivatives30m
Core Homework: Differentiation Rules30m
Challenge Homework: Differentiation Rules30m
4 hours to complete
Putting Derivatives to Work
Why exactly are derivatives so central to calculus? In part, it is because they are so ubiquitously useful! In this module, we will recall a few core applications of derivatives. In so doing, we'll see exactly how having an understanding of the asymptotics assists in building applications of the derivative.
4 hours to complete
5 videos (Total 66 min)
6 practice exercises
Core Homework: Linearization30m
Challenge Homework: Linearization30m
Core Homework: Higher Derivatives30m
Challenge Homework: Higher Derivatives30m
Core Homework: Optimization30m
Challenge Homework: Optimization30m
3 hours to complete
Differentials and Operators
There is much more to derivatives than simply their computation and applications. So much of how they arise is calculus is in the mysterious guise of *differentials*. These arise from implicit differentiation, which in turn reveals a deeper level of understanding of what differentiation means.
3 hours to complete
3 videos (Total 38 min), 1 reading, 5 quizzes
1 reading
About the Chapter 2 Exam10m
5 practice exercises
Core Homework: Differentials30m
Challenge Homework: Differentials30m
Core Homework: Differentiation Operator30m
Challenge Homework: Differentiation Operator30m
Chapter 2: Differentiation - Exam30m
Reviews
TOP REVIEWS FROM CALCULUS: SINGLE VARIABLE PART 2 - DIFFERENTIATION
by JBFeb 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.
by WGFeb 16, 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 SXSep 1, 2020
I learned a lot from this course.With animation to explain the formula,makes it easily to be understood.The learning of calculus laid the foundation for my future study.Thanks,professor.
by UJan 16, 2016
This module is great. The thing I like most is how professor implements the theory into Physics and other realistic models. Ive also begun liking statistics a little bit. Now, part 3.
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