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 Equations
- Integration By Parts
- Improper Integral
- Integration By Substitution
Flexible deadlines
Reset deadlines in accordance to your schedule.
100% online
Start instantly and learn at your own 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
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)
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)
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
Reviews
- 5 stars86.86%
- 4 stars11.05%
- 3 stars1.38%
- 2 stars0.23%
- 1 star0.46%
TOP REVIEWS FROM CALCULUS: SINGLE VARIABLE PART 3 - INTEGRATION
by JPApr 25, 2018
Just superb, not easy, challenging but so well prepared. Thanks for it Dr Ghrist.
by JKJul 18, 2021
The best calculus courses I've ever had... let alone it being free!!!
by AKApr 25, 2017
I have really enjoyed learning materials from this course. This is a great chapter!
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.
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