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.
oferecido por
Calculus: Single Variable Part 3 - Integration
Universidade da Pensilvânia
Informações sobre o curso
36,270 visualizações recentes
Habilidades que você terá
Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
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Comece imediatamente e aprenda em seu próprio cronograma.
Prazos flexíveis
Redefinir os prazos de acordo com sua programação.
Aprox. 24 horas para completar
Sugerido: 6-8 hours/week
Inglês
Legendas: Inglês, Espanhol
Programa - O que você aprenderá com este curso
3 horas para concluir
Integrating Differential Equations
Our first look at integrals will be motivated by differential equations. Describing how things evolve over time leads naturally to anti-differentiation, and we'll see a new application for derivatives in the form of stability criteria for equilibrium solutions.
3 horas para concluir
5 vídeos (Total 75 mín.), 2 leituras, 8 testes
5 videos
Indefinite Integrals17min
A Simple O.D.E.16min
More O.D.E.s15min
O.D.E. Linearization16min
BONUS!8min
2 leituras
How Grading Works10min
Your Guide to Getting Started in this Course10min
8 exercícios práticos
Core Homework: Indefinite Integrals10min
Challenge Homework: Indefinite Integrals2min
Core Homework: A Simple O.D.E.10min
Challenge Homework: A Simple O.D.E.4min
Core Homework: More O.D.E.s10min
Challenge Homework: More O.D.E.s8min
Core Homework: O.D.E. Linearization14min
Challenge Homework: O.D.E. Linearization6min
2 horas para concluir
Techniques of Integration
Since indefinite integrals are really anti-derivatives, it makes sense that the rules for integration are inverses of the rules for differentiation. Using this perspective, we will learn the most basic and important integration techniques.
2 horas para concluir
6 vídeos (Total 76 mín.)
6 videos
Integration by Parts16min
Trig Substitution15min
BONUS!7min
Partial Fractions15min
BONUS!6min
8 exercícios práticos
Core Homework: Integration by Substitution12min
Challenge Homework: Integration by Substitution4min
Core Homework: Integration by Parts14min
Challenge Homework: Integration by Parts6min
Core Homework: Trig Substitution12min
Challenge Homework: Trig Substitution6min
Core Homework: Partial Fractions12min
Challenge Homework: Partial Fractions6min
1 hora para concluir
The Fundamental Theorem of Integral Calculus
Indefinite integrals are just half the story: the other half concerns definite integrals, thought of as limits of sums. The all-important *FTIC* [Fundamental Theorem of Integral Calculus] provides a bridge between the definite and indefinite worlds, and permits the power of integration techniques to bear on applications of definite integrals.
1 hora para concluir
3 vídeos (Total 46 mín.)
3 exercícios práticos
Core Homework: Definite Integrals10min
Core Homework: The F.T.I.C.10min
Challenge Homework: The F.T.I.C.8min
2 horas para concluir
Dealing with Difficult Integrals
The simple story we have presented is, well, simple. In the real world, integrals are not always so well-behaved. This last module will survey what things can go wrong and how to overcome these complications. Once again, we find the language of big-O to be an ever-present help in time of need.
2 horas para concluir
4 vídeos (Total 50 mín.), 1 leitura, 6 testes
1 leituras
About the Chpater 3 Exam10min
6 exercícios práticos
Core Homework: Improper Integrals16min
Challenge Homework: Improper Integrals10min
Core Homework: Trigonometric Integrals12min
Challenge Homework: Trigonometric Integrals4min
Challenge Homework: Tables and Software8min
Chapter 3: Integration - Exam20min
Avaliações
Principais avaliações do CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION
por CCJul 1, 2018
I like it because it though me differential equations. This topics was previously missing from my education. It can be daunting to learn DE without proper guidance. This course provided just that.
por XLNov 21, 2017
The Bonus lectures are just great! I majored in Mathematics in university, and they're even enlightening to me. BTW, thanks for the introduction to Wolfram Alpha. It's really fun.
por ABJun 17, 2016
A bit difficult, but not truly when a good effort is made. No doubt interesting. Even a post graduate student will truly benefit from this course.
por VBFeb 17, 2020
The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.
oferecido por
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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