Informações sobre o curso
4.9
101 classificações
21 avaliações
100% online

100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Horas para completar

Aprox. 25 horas para completar

Sugerido: 6-8 hours/week...
Idiomas disponíveis

Inglês

Legendas: Inglês
100% online

100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Horas para completar

Aprox. 25 horas para completar

Sugerido: 6-8 hours/week...
Idiomas disponíveis

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana
1
Horas para completar
3 horas para concluir

Computing Areas and Volumes

Having seen some calculus before, you may recall some of the motivations for integrals arising from area computations. We will review those classical applications, while introducing the core idea of this module -- a differential element. By computing area and volume elements, we will see how to tackle tough geometry problems in a principled manner. ...
Reading
6 videos (Total 78 min), 2 leituras, 8 testes
Video6 videos
Complex Areas15min
BONUS!8min
Volumes15min
BONUS!6min
Complex Volumes15min
Reading2 leituras
How to Get Started in this Course10min
How Grading Works10min
Quiz8 exercícios práticos
Core Homework: Simple Areas10min
Challenge Homework: Simple Areas4min
Core Homework: Complex Areas10min
Challenge Homework: Complex Areas6min
Core Homework: Simple Volumes10min
Challenge Homework: Simple Volumes6min
Core Homework: Complex Volumes12min
Challenge Homework: Complex Volumes2min
Semana
2
Horas para completar
2 horas para concluir

Other Geometric Applications

There's more to geometry than just area and volume! In this module, we will take things "to the next level", ascending to higher dimensions. Coming back to the 3-d world, we will return to problems of length and area, but this time in the context of curves and surfaces. As always, the emphasis will be on how to construct the appropriate differential element for integrating. ...
Reading
4 videos (Total 66 min), 6 testes
Video4 videos
BONUS13min
Arclength17min
Surface Area16min
Quiz6 exercícios práticos
Core Homework: Volume and Dimension6min
Challenge Homework: Volume and Dimension8min
Core Homework: Arclength10min
Challenge Homework: Arclength4min
Core Homework: Surface Area8min
Challenge Homework: Surface Area4min
Semana
3
Horas para completar
1 hora para concluir

Physical Applications

There is so much more to applications of integrals than geometry! So many subjects, from physics to finance, have, at heart, the need for setting up and computing definite integrals. In this short but intense module, we will cover applications including work, force, torque, mass, and present & future value. ...
Reading
3 videos (Total 36 min), 4 testes
Video3 videos
Work15min
Elements13min
BONUS!6min
Quiz4 exercícios práticos
Core Homework: Work8min
Challenge Homework: Work4min
Core Homework: Elements10min
Challenge Homework: Elements2min
Semana
4
Horas para completar
2 horas para concluir

Averages and Mass

There is a statistical aspect to integrals that has not yet been brought up in this course: integrals are ideal for computing averages. Motivated by physical problems of mass, centroid, and moments of inertia, we will cover applications of integrals to averages. ...
Reading
5 videos (Total 65 min), 6 testes
Video5 videos
Centroids16min
BONUS!8min
Moments and Gyrations16min
BONUS!8min
Quiz6 exercícios práticos
Core Homework: Averages10min
Challenge Homework: Averages4min
Core Homework: Centroids10min
Challenge Homework: Centroids4min
Core Homework: Moments and Gyrations8min
Challenge Homework: Moments and Gyrations6min

Instrutores

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

Sobre 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. ...

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