Integration Basics: Uses & Benefits

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  • Thread starter Thread starter Mayukh Sen
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Discussion Overview

The discussion revolves around the usefulness of integration in various fields, particularly in relation to calculus and its applications in describing changes in quantities over time through differential equations.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • Some participants assert that integration is useful "everywhere calculus is used."
  • One participant highlights the application of integration in solving differential equations, which are used to describe changes in various contexts such as physics, population dynamics, and epidemics.
  • Participants reference educational videos from YouTube channels like Domain of Science and 3Blue1Brown to illustrate concepts related to integration and calculus.

Areas of Agreement / Disagreement

Participants generally agree on the broad applicability of integration in calculus, but specific examples and resources mentioned vary, indicating a lack of consensus on the best illustrative materials.

Contextual Notes

Some assumptions about the audience's familiarity with calculus and differential equations are present, but these are not explicitly stated. The discussion does not delve into the mathematical details of integration or differential equations.

Who May Find This Useful

Readers interested in calculus, its applications in science and mathematics, and educational resources on these topics may find this discussion relevant.

Mayukh Sen
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Where is it useful?
 
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Everywhere Calculus is used.

There are some great concept videos on YouTube namely the Domain of Science channel where he recently posted a video on Calculus and how it’s used.
 
Thank you
 
Mayukh Sen said:
Where is it useful?
We usually describe the world around us with differential equations, from physics, to populations, and epidemics. The reason is, that we want to know how certain quantities change over time, and this is a differential equation. In order to solve them, we have to perform integrations.
 
You might try this 3Blue1Brown video
 
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I was thinking of posting that one too but went with the Domain of Science one first as 3Blue1Brown is a set of ten videos on Calculus.
 
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