Differential Equation Problem. HELP

In summary, the conversation is about solving a problem involving the 2-dimensional transient heat conduction equation. The speaker is trying to find a solution in the frequency space but is having trouble using Laplace and separation of variables. The other party suggests using Fourier transform to convert to the frequency domain.
  • #1
chanda0218
2
0
Differential Equation Problem. HELP!

Ok I have the problem with the 2 Dimensions transient heat conduction equation.
[tex]\frac{du}{dt}= k\left(\frac{d^2u}{dx^2}+ \frac{d^2u}{dy}^2\right)[/tex]
. I can solve it in the temporal space but actually I need to know how it beheave in the frequency space... any suggestions? i tried laplace combine with a separation of variable but i didnt reach to anywhere...

Thank you in advance
 
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  • #2


It is generally the Fourier transform that is used to convert to "frequency space".
 
  • #3


Mmmm indeed to solve that one in a time space one must use Furier Series, so how can I use the Furier transform to pass it to the frequency domain? i need to find how it beheave in term of the frequency w (omega)
Thank you though
 

What is a differential equation?

A differential equation is a mathematical equation that involves derivatives of an unknown function. It represents the relationship between a function and its rate of change.

Why are differential equations important?

Differential equations are used to model and analyze complex systems in various fields such as physics, engineering, economics, and biology. They provide a powerful tool to understand and predict the behavior of these systems.

What are the different types of differential equations?

There are various types of differential equations, such as ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). ODEs involve a single independent variable, PDEs involve multiple independent variables, and SDEs take into account random variables or uncertainty.

How do I solve a differential equation problem?

The method for solving a differential equation depends on the type of equation and its complexity. Some common techniques include separation of variables, substitution, and using integrating factors. It is important to understand the properties of the equation and choose the appropriate method for solving it.

What are some real-life applications of differential equations?

Differential equations have many practical applications, such as predicting population growth, describing the motion of objects in physics, analyzing circuits in electrical engineering, and modeling chemical reactions. They are also used in fields such as finance, medicine, and ecology to understand and make predictions about complex systems.

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