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.
Offered By
Calculus: Single Variable Part 3 - Integration
University of PennsylvaniaAbout this Course
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Approx. 17 hours to complete
English
Subtitles: French, Portuguese (European), Russian, English, Spanish
Skills you will gain
Differential EquationsIntegration By PartsImproper IntegralIntegration By Substitution
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Approx. 17 hours to complete
English
Subtitles: French, Portuguese (European), Russian, English, Spanish
Offered by
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.
Syllabus - What you will learn from this course
6 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.
6 hours to complete
5 videos (Total 75 min), 2 readings, 8 quizzes
2 readings
How Grading Works10m
Your Guide to Getting Started in this Course10m
8 practice exercises
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 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.
5 hours to complete
6 videos (Total 76 min)
6 videos
Integration by Parts16m
Trig Substitution15m
BONUS!7m
Partial Fractions15m
BONUS!6m
8 practice exercises
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 hours 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.
2 hours to complete
3 videos (Total 46 min)
3 practice exercises
Core Homework: Definite Integrals30m
Core Homework: The F.T.I.C.30m
Challenge Homework: The F.T.I.C.30m
4 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.
4 hours to complete
4 videos (Total 50 min), 1 reading, 6 quizzes
1 reading
About the Chpater 3 Exam10m
6 practice exercises
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
Reviews
TOP REVIEWS FROM CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION
by CCJul 1, 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 XLNov 21, 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.
by ABJun 17, 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.
by VBFeb 17, 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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