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.
Calculus: Single Variable Part 3 - Integration
Calculus: Single Variable Part 3 - Integration
Instructor: Robert Ghrist
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Gain insight into a topic and learn the fundamentals.
4.8
(539 reviews)
1 week to complete
at 10 hours a week
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Assessments
26 assignments
Taught in English
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There are 4 modules in this course
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.
What's included
5 videos2 readings9 assignments
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.
What's included
6 videos8 assignments
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.
What's included
3 videos3 assignments
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.
What's included
4 videos1 reading6 assignments
Instructor
Instructor ratings
4.8 (71 ratings)Offered by
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4.8
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Showing 3 of 539
MZ
5
Reviewed on Aug 14, 2023
It is not an ordinary course in integration rather than a course that should be taught in universities! Wonderful ideas by Prof. Ghrist.
RB
4
Reviewed on Mar 20, 2025
I am unable get my certificate. IF POSSIBLE PROVIDE MY CERTIFICATE SOON.
JM
4
Reviewed on Mar 4, 2021
Students should be able to use trig and calculus cheat sheets while working problems. I would suggest they be provided and approved by the instructor.
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