Informações sobre o curso
4.8
120 classificações
25 avaliações

100% online

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Aprox. 18 horas para completar

Sugerido: 6-8 hours/week...

Inglês

Legendas: Inglês

100% online

Comece imediatamente e aprenda em seu próprio cronograma.

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.

Aprox. 18 horas para completar

Sugerido: 6-8 hours/week...

Inglês

Legendas: Inglês

Programa - O que você aprenderá com este curso

Semana
1
2 horas para concluir

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 vídeos (total de (Total 53 mín.) min), 2 leituras, 5 testes
4 videos
BONUS!5min
Differences17min
Discrete Calculus16min
2 leituras
Your Guide to Getting Started in this Course10min
How Grading Works10min
5 exercícios práticos
Core Homework: Sequences14min
Core Homework: Differences12min
Challenge Homework: Differences8min
Core Homework: Discrete Calculus10min
Challenge Homework: Discrete Calculus4min
Semana
2
1 horas para concluir

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....
2 vídeos (total de (Total 34 mín.) min), 1 teste
2 videos
Numerical Integration16min
1 exercícios práticos
Core Homework: Numerical O.D.E.s4min
Semana
3
2 horas para concluir

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 vídeos (total de (Total 65 mín.) min), 6 testes
4 videos
Convergence Tests I16min
Convergence Tests II16min
Absolute & Conditional14min
6 exercícios práticos
Core Homework: Infinite Series10min
Challenge Homework: Infinite Series4min
Core Homework: Convergence Tests I16min
Challenge Homework: Convergence Tests I4min
Core Homework: Convergence Tests II6min
Core Homework: Absolute & Conditional4min
Semana
4
2 horas para concluir

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. ...
4 vídeos (total de (Total 59 mín.) min), 5 testes
4 videos
Taylor Series Redux15min
Approximation and Error17min
BONUS!9min
5 exercícios práticos
Core Homework: Power Series12min
Challenge Homework: Power Series8min
Core Homework: Taylor Series Redux8min
Challenge Homework: Taylor Series Redux4min
Core Homework: Approximation and Error10min
4.8
25 avaliaçõesChevron Right

Melhores avaliações

por MMJan 11th 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

por RBFeb 11th 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.\n\nLooking forward to Multi Variable Calculus.

Instrutores

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

Sobre Universidade da Pensilvânia

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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