Partial differential problem in introductory tensor analysis

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SUMMARY

The discussion centers on the interpretation of the differential operator ∂/(∂y) in the context of introductory tensor analysis. The participant references a specific equality from course literature, y = ∂/(∂y), and questions its validity and implications. They conclude that while the expression \frac{\partial \psi}{\partial y} = y\psi is correct, it does not provide new insights without the established equality. The participant expresses confidence in their understanding and appreciation for the community's input.

PREREQUISITES
  • Understanding of differential operators in calculus
  • Familiarity with tensor analysis concepts
  • Knowledge of partial differential equations
  • Basic grasp of mathematical notation and expressions
NEXT STEPS
  • Research the properties of differential operators in tensor analysis
  • Study the implications of the equality y = ∂/(∂y) in various contexts
  • Explore applications of partial differential equations in physics
  • Learn about the role of differentials in mathematical modeling
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Students and educators in mathematics, particularly those studying tensor analysis and partial differential equations, as well as researchers interested in the application of differential operators.

freddyfish
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So far I have only seen ∂/(∂y) as being interpreted as an operator being of no use unless it is applied to some vector etc.

Now, however, my course literature asserts the following equality:

y=∂/(∂y)

What is the interpretation of the differentials in this case?
 
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I suppose is a short way to express [itex]\frac{\partial \psi}{\partial y}=y\psi[/itex].
 
Yes, that is a correct statement, but it relies on the asserted equality, so unfortunately it brings nothing new to the party. Luckily I have it all figured out by now, so I thank you for your answer and continue my studies. :)
 

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