date_range Inicia em 6 de novembro de 2019
event_note Termina em 26 de fevereiro de 2020
list 15 sequencias
assignment Nível: Intermediário
chat_bubble_outline Idioma: Inglês
card_giftcard 900 pontos
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Informações principais

credit_card Free accesso
verified_user Certificado pago
timer 90 total de horas

Sobre o conteúdo

How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.

But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.

The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.

This course, in combination with Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.

Learn more about our High School and AP* Exam Preparation Courses

This course was funded in part by the Wertheimer Fund.

 

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings. 

  • Some differential equation models for physical phenomena and solutions
  • The geometric interpretation, and physical meaning of the integral
  • The connection of the integral to the derivative
  • Several methods of numerically and symbolically integrating functions
  • To apply integrals to solve real world problems

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Programa de estudos

Abridged Syllabus

Limits
  1. Limit Laws
  2. Continuity
  3. Intermediate Value Theorem
Differentiation
  1. Introducing the Derivative
  2. Rules for differentiation of all known functions
  3. Approximations
Applications of Differentiation
  1. Curve Sketching
  2. Optimization
  3. Related Rates
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Instrutores

David Jerison
Professor of Mathematics
Massachusetts Institute of Technology

Gigliola Staffilani
Abby Rockefeller Mauzé Professor of Mathematics
Massachusetts Institute of Technology

Jennifer French
Lecturer & Digital Learning Scientist
Massachusetts Institute of Technology

Karene Chu
Lecturer and Research Scientist
Massachusetts Institute of Technology

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Criador do conteúdo

MIT

Le Massachusetts Institute of Technology (MIT), en français Institut de technologie du Massachusetts, est un institut de recherche américain et une université, spécialisé dans les domaines de la science et de la technologie. Situé à Cambridge, dans l'État du Massachusetts, à proximité immédiate de Boston, au nord-est des États-Unis, le MIT est souvent considéré comme une des meilleures universités mondiales.

Il édite la Technology Review, une revue scientifique consacrée aux sciences de l'ingénieur et à l'innovation.

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Plataforma

Edx

EdX est une plateforme d'apprentissage en ligne (dite FLOT ou MOOC). Elle héberge et met gratuitement à disposition des cours en ligne de niveau universitaire à travers le monde entier. Elle mène également des recherches sur l'apprentissage en ligne et la façon dont les utilisateurs utilisent celle-ci. Elle est à but non lucratif et la plateforme utilise un logiciel open source.

EdX a été fondée par le Massachusetts Institute of Technology et par l'université Harvard en mai 2012. En 2014, environ 50 écoles, associations et organisations internationales offrent ou projettent d'offrir des cours sur EdX. En juillet 2014, elle avait plus de 2,5 millions d'utilisateurs suivant plus de 200 cours en ligne.

Les deux universités américaines qui financent la plateforme ont investi 60 millions USD dans son développement. La plateforme France Université Numérique utilise la technologie openedX, supportée par Google.

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