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.
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Calculus: Single Variable Part 3 - Integration
Université de PennsylvanieÀ propos de ce cours
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Approx. 17 heures pour terminer
Anglais
Sous-titres : Français, Portugais (européen), Russe, Anglais, Espagnol
Compétences que vous acquerrez
Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Approx. 17 heures pour terminer
Anglais
Sous-titres : Français, Portugais (européen), Russe, Anglais, Espagnol
Offert par
Université de Pennsylvanie
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.
Programme du cours : ce que vous apprendrez dans ce cours
6 heures pour terminer
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 heures pour terminer
5 vidéos (Total 75 min), 2 lectures, 8 quiz
5 vidéos
Indefinite Integrals17 min
A Simple O.D.E.16 min
More O.D.E.s15 min
O.D.E. Linearization16 min
BONUS!8 min
2 lectures
How Grading Works10 min
Your Guide to Getting Started in this Course10 min
8 exercices pour s'entraîner
Core Homework: Indefinite Integrals30 min
Challenge Homework: Indefinite Integrals30 min
Core Homework: A Simple O.D.E.30 min
Challenge Homework: A Simple O.D.E.30 min
Core Homework: More O.D.E.s30 min
Challenge Homework: More O.D.E.s30 min
Core Homework: O.D.E. Linearization30 min
Challenge Homework: O.D.E. Linearization30 min
5 heures pour terminer
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 heures pour terminer
6 vidéos (Total 76 min)
6 vidéos
Integration by Parts16 min
Trig Substitution15 min
BONUS!7 min
Partial Fractions15 min
BONUS!6 min
8 exercices pour s'entraîner
Core Homework: Integration by Substitution30 min
Challenge Homework: Integration by Substitution30 min
Core Homework: Integration by Parts30 min
Challenge Homework: Integration by Parts30 min
Core Homework: Trig Substitution30 min
Challenge Homework: Trig Substitution30 min
Core Homework: Partial Fractions30 min
Challenge Homework: Partial Fractions30 min
2 heures pour terminer
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 heures pour terminer
3 vidéos (Total 46 min)
3 exercices pour s'entraîner
Core Homework: Definite Integrals30 min
Core Homework: The F.T.I.C.30 min
Challenge Homework: The F.T.I.C.30 min
4 heures pour terminer
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 heures pour terminer
4 vidéos (Total 50 min), 1 lecture, 6 quiz
1 lecture
About the Chpater 3 Exam10 min
6 exercices pour s'entraîner
Core Homework: Improper Integrals30 min
Challenge Homework: Improper Integrals30 min
Core Homework: Trigonometric Integrals30 min
Challenge Homework: Trigonometric Integrals30 min
Challenge Homework: Tables and Software30 min
Chapter 3: Integration - Exam30 min
Avis
Meilleurs avis pour CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION
par CC1 juil. 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.
par XL21 nov. 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.
par AB17 juin 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.
par VB17 févr. 2020
The examples and the problems chosen are very thought provoking - the knowledge gained is fully tested by solving these problems.
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