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. In this fourth part--part four of five--we cover computing areas and volumes, other geometric applications, physical applications, and averages and mass. We also introduce probability.
Calculus: Single Variable Part 4 - Applications
от партнера
- Security Engineers
- Pharmacists
- Machine Learning Engineers
- Economists
- Technical Solutions Engineers
Программа курса: что вы изучите
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.
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.
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.
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.
Лучшие отзывы о курсе Calculus: Single Variable Part 4 - Applications
The course taught me about how calculus is used to explain probability and statistics. This is exactly what I need to began studying these areas.
this was simply an amazing course, perfect for my skill level and exactly what i needed to learn. Thank you for the opportunity.
Преподаватели
Robert Ghrist
ProfessorО Пенсильванский университет
Часто задаваемые вопросы
Когда я получу доступ к лекциям и заданиям?
Зарегистрировавшись на сертификацию, вы получите доступ ко всем видео, тестам и заданиям по программированию (если они предусмотрены). Задания по взаимной оценке сокурсниками можно сдавать и проверять только после начала сессии. Если вы проходите курс без оплаты, некоторые задания могут быть недоступны.
Остались вопросы? Посетите Центр поддержки учащихся.
