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 3 - Integration
Université de PennsylvanieÀ propos de ce cours
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Approx. 17 heures pour terminer
Anglais
Sous-titres : Français, Portugais (européen), Russe, Anglais, Espagnol
Compétences que vous acquerrez
- Differential Equations
- Integration By Parts
- Improper Integral
- Integration By Substitution
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Approx. 17 heures pour terminer
Anglais
Sous-titres : Français, Portugais (européen), Russe, Anglais, Espagnol
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 de cours : ce que vous apprendrez dans ce cours
6 heures pour terminer
Integrating Differential Equations
Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions.
6 heures pour terminer
5 vidéos (Total 75 min), 2 lectures, 8 quiz
5 heures pour terminer
Techniques of Integration
Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques.
5 heures pour terminer
6 vidéos (Total 76 min)
2 heures pour terminer
The Fundamental Theorem of Integral Calculus
Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals.
2 heures pour terminer
3 vidéos (Total 46 min)
4 heures pour terminer
Dealing with Difficult Integrals
The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need.
4 heures pour terminer
4 vidéos (Total 50 min), 1 lecture, 6 quiz
Avis
- 5 stars87,32 %
- 4 stars11,03 %
- 3 stars0,93 %
- 2 stars0,23 %
- 1 star0,46 %
Meilleurs avis pour CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION
par ML4 févr. 2016
So far so good, pero el primer tema es confuso o yo soy muy torpe <3
par JP25 avr. 2018
Just superb, not easy, challenging but so well prepared. Thanks for it Dr Ghrist.
par AK25 avr. 2017
I have really enjoyed learning materials from this course. This is a great chapter!
par VV23 juil. 2017
Some sections were too hard with limited information from the videos. I had to study other material to be able to complete them.
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