Offered By

University of Pennsylvania

About this Course

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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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Suggested: 6-8 hours/week...

Subtitles: English, Spanish

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 6-8 hours/week...

Subtitles: English, Spanish

Week

1Our 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....

5 videos (Total 75 min), 2 readings, 8 quizzes

How Grading Works10m

Your Guide to Getting Started in this Course10m

Core Homework: Indefinite Integrals10m

Challenge Homework: Indefinite Integrals2m

Core Homework: A Simple O.D.E.10m

Challenge Homework: A Simple O.D.E.4m

Core Homework: More O.D.E.s10m

Challenge Homework: More O.D.E.s8m

Core Homework: O.D.E. Linearization14m

Challenge Homework: O.D.E. Linearization6m

Week

2Since 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. ...

6 videos (Total 76 min), 8 quizzes

Integration by Parts16m

Trig Substitution15m

BONUS!7m

Partial Fractions15m

BONUS!6m

Core Homework: Integration by Substitution12m

Challenge Homework: Integration by Substitution4m

Core Homework: Integration by Parts14m

Challenge Homework: Integration by Parts6m

Core Homework: Trig Substitution12m

Challenge Homework: Trig Substitution6m

Core Homework: Partial Fractions12m

Challenge Homework: Partial Fractions6m

Week

3Indefinite 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. ...

3 videos (Total 46 min), 3 quizzes

Core Homework: Definite Integrals10m

Core Homework: The F.T.I.C.10m

Challenge Homework: The F.T.I.C.8m

Week

4The 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 videos (Total 50 min), 1 reading, 6 quizzes

About the Chpater 3 Exam10m

Core Homework: Improper Integrals16m

Challenge Homework: Improper Integrals10m

Core Homework: Trigonometric Integrals12m

Challenge Homework: Trigonometric Integrals4m

Challenge Homework: Tables and Software8m

Chapter 3: Integration - Exam20m

4.9

31 ReviewsBy CC•Jul 2nd 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.

By AB•Jun 18th 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.

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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Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

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