Informações sobre o curso
4.8
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29 avaliações
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 third part--part three of five--we cover integrating differential equations, techniques of integration, the fundamental theorem of integral calculus, and difficult integrals....
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cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Calendar

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Clock

Approx. 20 hours to complete

Sugerido: 6-8 hours/week...
Comment Dots

English

Legendas: English, Spanish...

Habilidades que você terá

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
Globe

cursos 100% online

Comece imediatamente e aprenda em seu próprio cronograma.
Calendar

Prazos flexíveis

Redefinir os prazos de acordo com sua programação.
Clock

Approx. 20 hours to complete

Sugerido: 6-8 hours/week...
Comment Dots

English

Legendas: English, Spanish...

Programa - O que você aprenderá com este curso

Week
1
Clock
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....
Reading
5 vídeos (Total de 75 min), 2 leituras, 8 testes
Video5 videos
A Simple O.D.E.16min
More O.D.E.s15min
O.D.E. Linearization16min
BONUS!8min
Reading2 leituras
How Grading Works10min
Your Guide to Getting Started in this Course10min
Quiz8 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
Week
2
Clock
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. ...
Reading
6 vídeos (Total de 76 min), 8 testes
Video6 videos
Integration by Parts16min
Trig Substitution15min
BONUS!7min
Partial Fractions15min
BONUS!6min
Quiz8 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
Week
3
Clock
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. ...
Reading
3 vídeos (Total de 46 min), 3 testes
Video3 videos
The F.T.I.C.16min
BONUS!12min
Quiz3 exercícios práticos
Core Homework: Definite Integrals10min
Core Homework: The F.T.I.C.10min
Challenge Homework: The F.T.I.C.8min
Week
4
Clock
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. ...
Reading
4 vídeos (Total de 50 min), 1 leitura, 6 testes
Video4 videos
BONUS!6min
Trigonometric Integrals15min
Tables and Software11min
Reading1 leituras
About the Chpater 3 Exam10min
Quiz6 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

Instrutores

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. ...

Perguntas Frequentes – FAQ

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  • When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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