Good texts for solving PDE's by integral transforms

In summary, the conversation is about a person looking for recommendations on books for solving partial differential equations (PDE's) using integral transforms, specifically Fourier and Laplace transforms. They are looking for a book that focuses on the methods rather than the theory and prefers one with many solved examples. The expert recommends Transform Methods for Solving Partial Differential Equations by Dean G. Duffy, which is clear and thorough with lots of worked problems and references. They also mention that Duffy has written several related books on the topic.
  • #1
I look for good books on solving partial diffrential equations (PDE's) using integral transforms specially Fourier and laplace transforms.

Do you have any recommendations for such books? I don't look for a book concerned with the theory, rather, with the methods itself (a suitable book for a physicist not a mathematician). So , the more solved examples there are, the better it will be!
 
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  • #3
My favorite is Transform Methods for Solving Partial Differential Equations by Dean G. Duffy
Lots of neat worked problems and references

Duffy wrote several related books
Advanced Engineering Mathematics by Dean G. Duffy
Solutions of Partial Differential Equations by Dean G. Duffy
Transform Methods for Solving Partial Differential Equations by Dean G. Duffy
Green's Functions with Applications by Dean G. Duffy
Mixed Boundary Value Problems by Dean G. Duffy
 

1. How do integral transforms help in solving PDE's?

Integral transforms are mathematical tools that allow us to convert a complicated PDE into a simpler form, making it easier to solve. They essentially transform the PDE into an algebraic equation that can be solved using standard techniques.

2. What are some commonly used integral transforms in solving PDE's?

Some commonly used integral transforms include Fourier transform, Laplace transform, and Mellin transform. Each transform has its own advantages and can be used to solve different types of PDE's.

3. Can any PDE be solved using integral transforms?

No, not all PDE's can be solved using integral transforms. The PDE must have certain properties, such as linearity and boundary conditions, for integral transforms to be applicable. Nonlinear PDE's may require different techniques for solving.

4. How do I know which integral transform to use for a specific PDE?

The choice of integral transform depends on the type of PDE and the boundary conditions given. It is important to understand the properties and limitations of each transform to determine the most suitable one for a given problem.

5. Can I use integral transforms for real-world applications?

Yes, integral transforms are commonly used in various fields such as physics, engineering, and finance to solve real-world problems involving PDE's. They provide an efficient and accurate way of obtaining solutions for complex systems.

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