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Calculus: Single Variable Part 3 - Integration
Course
en
English
Subtitles available
24 h
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- Self-paced
- Free Access
- Fee-based Certificate
- 4 Sequences
- Introductive Level
- Subtitles in Spanish
Course details
Syllabus
- Week 1 - 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... - Week 2 - 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. - Week 3 - 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 permit... - Week 4 - 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 ...
Prerequisite
None.
Instructors
Robert Ghrist
Professor
Mathematics and Electrical & Systems Engineering
Editor
The University of Pennsylvania (commonly known as Penn), founded in 1740, is a private university located in Philadelphia, Pennsylvania, USA. A member of the Ivy League, Penn is the fourth oldest institution of higher learning in the United States and considers itself the first university in the United States to offer both undergraduate and graduate degrees.
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