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.
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Calculus: Single Variable Part 2 - Differentiation
Université de PennsylvanieÀ propos de ce cours
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Approx. 6 heures pour terminer
Anglais
Sous-titres : Anglais, Espagnol, Chinois (simplifié)
Compétences que vous acquerrez
Differential (Mathematics)Newton'S MethodLinear ApproximationDifferential CalculusDerivative
Résultats de carrière des étudiants
50%
ont commencé une nouvelle carrière après avoir terminé ce cours
33%
ont bénéficié d'un avantage concret dans leur carrières grâce à ce cours
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Approx. 6 heures pour terminer
Anglais
Sous-titres : Anglais, Espagnol, Chinois (simplifié)
Offert par
Université de Pennsylvanie
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.
Programme du cours : ce que vous apprendrez dans ce cours
2 heures pour terminer
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.
2 heures pour terminer
3 vidéos (Total 45 min), 2 lectures, 4 quiz
2 lectures
How Grading Works10 min
Your Guide to Getting Started in this Course10 min
4 exercices pour s'entraîner
Core Homework: Derivatives16 min
Challenge Homework: Derivatives4 min
Core Homework: Differentiation Rules18 min
Challenge Homework: Differentiation Rules6 min
2 heures pour terminer
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.
2 heures pour terminer
5 vidéos (Total 66 min)
6 exercices pour s'entraîner
Core Homework: Linearization12 min
Challenge Homework: Linearization4 min
Core Homework: Higher Derivatives12 min
Challenge Homework: Higher Derivatives2 min
Core Homework: Optimization10 min
Challenge Homework: Optimization8 min
2 heures pour terminer
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.
2 heures pour terminer
3 vidéos (Total 38 min), 1 lecture, 5 quiz
1 lecture
About the Chapter 2 Exam10 min
5 exercices pour s'entraîner
Core Homework: Differentials12 min
Challenge Homework: Differentials8 min
Core Homework: Differentiation Operator12 min
Challenge Homework: Differentiation Operator10 min
Chapter 2: Differentiation - Exam20 min
Avis
Meilleurs avis pour CALCULUS: SINGLE VARIABLE PART 2 - DIFFERENTIATION
par JB17 févr. 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.
par WG16 févr. 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.
par U16 janv. 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.
par NS29 juin 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.
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