Practical Problems Involving Differentiation/Integration/Limits

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SUMMARY

This discussion centers on the need for real-life applications of differentiation, integration, and limits, particularly for learners who struggle with theoretical concepts. Participants emphasize that while there are countless examples, practical applications are often found in scientific fields, especially physics. Suggestions include searching for geometric examples, such as the volume of rotational objects and path lengths, to bridge the gap between theory and practice. The consensus is that real-world problems can enhance understanding and retention of these mathematical concepts.

PREREQUISITES
  • Understanding of basic calculus concepts: differentiation, integration, and limits.
  • Familiarity with physics principles, particularly those involving motion and forces.
  • Knowledge of geometric shapes and their properties, especially in relation to volume and area.
  • Basic research skills to find examples online using search engines.
NEXT STEPS
  • Research "real-life applications of differentiation in physics" to find relevant examples.
  • Explore "integration in calculating volumes of solids of revolution" for practical geometric problems.
  • Investigate "limits in real-world scenarios" to understand their applications in various fields.
  • Look into "acceleration examples in everyday life" to see how differentiation applies to motion.
USEFUL FOR

Students, educators, and anyone seeking to connect theoretical calculus concepts with practical applications in science and engineering.

Crabman
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Hi guys,

As somebody who likes to learn and understand everyday problems I've really hit a wall...

I learned differentiation, integration and limits in my undergrad course, passed the exams etc but the way it was taught was pretty bad, nobody ever gave us "real life" examples. Personally I find that I learn much better with real life examples and so I thought I'd post here for some advice.

The real question is: Could you point me in the direction of some "real life" (simple, applicable problems) which require differentiation/integration to solve?

I know that there must literally be thousands and thousands but any help is appreciated.

Many thanks...
 
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Crabman said:
I know that there must literally be thousands and thousands but any help is appreciated.
Thousands of examples, yes. Everyday examples, no. You don't need differentiation or integration at the bakery around the corner. In science, however, and especially in physics it is daily business and examples can be found for any quantity which is defined as an integral, which solves a differential equation, or which is a derivative itself. So basically any physical quantity!

As I don't think those examples are meant I refrain from listing them. Google "work + example" or "acceleration + example" for those. Maybe geometric examples like the volume of rotation objects or path lengths is closest as you can get for "everyday" examples.
 

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