About this Course
4.8
194 ratings
30 reviews
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Hours to complete

Approx. 21 hours to complete

Suggested: 6-8 hours/week...
Available languages

English

Subtitles: English, Spanish

Skills you will gain

Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Hours to complete

Approx. 21 hours to complete

Suggested: 6-8 hours/week...
Available languages

English

Subtitles: English, Spanish

Syllabus - What you will learn from this course

Week
1
Hours to complete
3 hours to complete

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 videos (Total 75 min), 2 readings, 8 quizzes
Video5 videos
A Simple O.D.E.16m
More O.D.E.s15m
O.D.E. Linearization16m
BONUS!8m
Reading2 readings
How Grading Works10m
Your Guide to Getting Started in this Course10m
Quiz8 practice exercises
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
2
Hours to complete
2 hours to complete

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 videos (Total 76 min), 8 quizzes
Video6 videos
Integration by Parts16m
Trig Substitution15m
BONUS!7m
Partial Fractions15m
BONUS!6m
Quiz8 practice exercises
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
3
Hours to complete
1 hour to complete

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 videos (Total 46 min), 3 quizzes
Video3 videos
The F.T.I.C.16m
BONUS!12m
Quiz3 practice exercises
Core Homework: Definite Integrals10m
Core Homework: The F.T.I.C.10m
Challenge Homework: The F.T.I.C.8m
Week
4
Hours to complete
2 hours to complete

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 videos (Total 50 min), 1 reading, 6 quizzes
Video4 videos
BONUS!6m
Trigonometric Integrals15m
Tables and Software11m
Reading1 reading
About the Chpater 3 Exam10m
Quiz6 practice exercises
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

Instructor

Avatar

Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering

About 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. ...

Frequently Asked Questions

  • 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.

More questions? Visit the Learner Help Center.