How do I find B using the boundary condition ux(0,t) = -Q in Laplace transforms?

In summary, a Laplace transform is a mathematical operation that converts a function of time into a function of complex frequency, commonly used in engineering and physics. It differs from a Fourier transform in that it is more applicable to functions defined for all time. The purpose of using a Laplace transform is to simplify calculations and solve differential equations, as well as represent signals and systems in a more compact form. To calculate a Laplace transform, one can use the formula or table of Laplace transform pairs. Some common applications of Laplace transforms include electrical engineering, control systems, signal processing, and physics.
  • #1
squenshl
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4
I'm deriving the heat equation using Laplace transforms.
I'm up to u(bar) = Aesqrt(s)x + Be-sqrt(s)x.
My boundary conditions are lim(x tends to 0) = 0 & this makes A = 0, so u(bar) = Be-sqrt(s)x
My other BC is ux(0,t) = -Q
My question is how do I get B using this BC?
I tried using the def of Laplace transforms and get -dQ(bar)/dx
 
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  • #2
I got B = Q/sqrt(s) and this implies that U(bar) = Qe-sqrt(s)x/sqrt(s), I hope that's right
 

1. What is a Laplace transform?

A Laplace transform is a mathematical operation that transforms a function of time into a function of complex frequency. It is commonly used in engineering and physics to simplify calculations and solve differential equations.

2. How is a Laplace transform different from a Fourier transform?

While both Laplace and Fourier transforms involve converting a function from one domain to another, Laplace transforms are more applicable to functions that are defined for all time, while Fourier transforms are used for functions that are defined for a finite period of time.

3. What is the purpose of using a Laplace transform?

A Laplace transform is often used to solve differential equations and analyze systems in the frequency domain. It can also be used to represent signals and systems in a more compact form, making it easier to manipulate and analyze them.

4. How do I calculate a Laplace transform?

To calculate a Laplace transform, you can use the Laplace transform formula or table of Laplace transform pairs. This involves taking the integral of the function multiplied by an exponential term and setting the limits of integration from 0 to infinity.

5. What are some common applications of Laplace transforms?

Laplace transforms are commonly used in electrical engineering, control systems, signal processing, and physics. They are also used in the analysis of linear systems, such as in circuit analysis and mechanical systems.

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