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.
ofrecido por
Single Variable Calculus
Universidad de PensilvaniaAcerca de este Curso
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Aprox. 14 horas para completar
Inglés (English)
SubtÃtulos: Francés (French), Portugués (europeo), Ruso (Russian), Inglés (English), Español (Spanish)
Fechas lÃmite flexibles
Restablece las fechas lÃmite en función de tus horarios.
Certificado para compartir
Obtén un certificado al finalizar
100Â % en lÃnea
Comienza de inmediato y aprende a tu propio ritmo.
Aprox. 14 horas para completar
Inglés (English)
SubtÃtulos: Francés (French), Portugués (europeo), Ruso (Russian), Inglés (English), Español (Spanish)
ofrecido por
Universidad de Pensilvania
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.
Programa - Qué aprenderás en este curso
4 horas para completar
A Calculus for Sequences
It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>.
4 horas para completar
4 videos (Total 53 minutos), 2 lecturas, 5 cuestionarios
1 hora para completar
Introduction to Numerical Methods
That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations.
1 hora para completar
2 videos (Total 34 minutos)
4 horas para completar
Series and Convergence Tests
In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or <b>series</b>. The determination of convergence for such will occupy our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!
4 horas para completar
4 videos (Total 65 minutos)
3 horas para completar
Power and Taylor Series
This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series.
3 horas para completar
4 videos (Total 59 minutos)
Reseñas
- 5 stars78,59Â %
- 4 stars12,63Â %
- 3 stars3,15Â %
- 2 stars1,05Â %
- 1 star4,56Â %
Principales reseñas sobre SINGLE VARIABLE CALCULUS
por JA12 de sep. de 2020
je voudrais un certificat de ce cours , Donnez-moi l'accès pour que je puisse payer le cours?
por XL3 de dic. de 2017
Again and again and again ... love the bonus lectures! Really enlightening! Please release the Multi-variable Calculus ASAP! Can't wait to take it!
por DK10 de abr. de 2021
This provides a new outlook on calculus! I thoroughly enjoyed it
por MJ10 de jun. de 2019
This fifth unit is highly original! I loved the "digital calculus" part.
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