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
Calculus: Single Variable Part 3 - Integration
Universidad de PensilvaniaAcerca de este Curso
21,395 vistas recientes
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Aprox. 17 horas para completar
Inglés (English)
Subtítulos: Francés (French), Portugués (de Brasil), Ruso (Russian), Inglés (English), Español (Spanish)
Habilidades que obtendrás
Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
100 % en línea
Comienza de inmediato y aprende a tu propio ritmo.
Fechas límite flexibles
Restablece las fechas límite en función de tus horarios.
Aprox. 17 horas para completar
Inglés (English)
Subtítulos: Francés (French), Portugués (de Brasil), 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
6 horas para completar
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.
6 horas para completar
5 videos (Total 75 minutos), 2 lecturas, 8 cuestionarios
2 lecturas
How Grading Works10m
Your Guide to Getting Started in this Course10m
8 ejercicios de práctica
Core Homework: Indefinite Integrals30m
Challenge Homework: Indefinite Integrals30m
Core Homework: A Simple O.D.E.30m
Challenge Homework: A Simple O.D.E.30m
Core Homework: More O.D.E.s30m
Challenge Homework: More O.D.E.s30m
Core Homework: O.D.E. Linearization30m
Challenge Homework: O.D.E. Linearization30m
5 horas para completar
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.
5 horas para completar
6 videos (Total 76 minutos)
6 videos
Integration by Parts16m
Trig Substitution15m
BONUS!7m
Partial Fractions15m
BONUS!6m
8 ejercicios de práctica
Core Homework: Integration by Substitution30m
Challenge Homework: Integration by Substitution30m
Core Homework: Integration by Parts30m
Challenge Homework: Integration by Parts30m
Core Homework: Trig Substitution30m
Challenge Homework: Trig Substitution30m
Core Homework: Partial Fractions30m
Challenge Homework: Partial Fractions30m
2 horas para completar
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.
2 horas para completar
3 videos (Total 46 minutos)
3 ejercicios de práctica
Core Homework: Definite Integrals30m
Core Homework: The F.T.I.C.30m
Challenge Homework: The F.T.I.C.30m
4 horas para completar
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.
4 horas para completar
4 videos (Total 50 minutos), 1 lectura, 6 cuestionarios
1 lectura
About the Chpater 3 Exam10m
6 ejercicios de práctica
Core Homework: Improper Integrals30m
Challenge Homework: Improper Integrals30m
Core Homework: Trigonometric Integrals30m
Challenge Homework: Trigonometric Integrals30m
Challenge Homework: Tables and Software30m
Chapter 3: Integration - Exam30m
Reseñas
Principales reseñas sobre CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION
por CC1 de jul. de 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 XL21 de nov. de 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 AB17 de jun. de 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 VB17 de feb. de 2020
The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.
Preguntas Frecuentes
¿Cuándo podré acceder a las lecciones y tareas?
El acceso a las clases y las asignaciones depende del tipo de inscripción que tengas. Si tomas un curso en modo de oyente, verás la mayoría de los materiales del curso en forma gratuita. Para acceder a asignaciones calificadas y obtener un certificado, deberás comprar la experiencia de Certificado, ya sea durante o después de participar como oyente. Si no ves la opción de oyente:
- es posible que el curso no ofrezca la opción de participar como oyente. En cambio, puedes intentar con una Prueba gratis o postularte para recibir ayuda económica.
- Es posible que el curso ofrezca la opción 'Curso completo, sin certificado'. Esta opción te permite ver todos los materiales del curso, enviar las evaluaciones requeridas y obtener una calificación final. También significa que no podrás comprar una experiencia de Certificado.
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