Linear Partial Differential Equations

In summary, we have a conversation about recommendations for books or resources on Linear Partial Differential Equations. One person highly recommends a specific book that they used throughout their undergraduate years and even wrote a review on Amazon. Another person suggests a different book that focuses on more applied PDE's. They also mention another book by Michael Taylor that is considered an instant classic.
  • #1
kuahji
394
2
Just curious if anyone has any good recommendations for books or resources on Linear Partial Differential Equations. Thanks.
 
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  • #2
This book gets my highest recommendations - I used it throughout my entire undergraduate years. I even wrote a review of it on Amazon!
 
  • #3
Thanks for the feedback! This is the one the professor is assigning for the class and was just hoping for one or two supplemental resources.
 
  • #5
In that case another one of my favorites is Boundary Value Problems by David Powers. This is more applied and only deals with PDE's that are separable, but I found this book invaluable.
 
  • #6
apparently michael taylor's was an instant classic when it came out. i haven't used it or even seen it but it's on my bucket list :tongue2: the first two volumes cover linear equations
 

1. What are linear partial differential equations (PDEs)?

Linear partial differential equations are mathematical equations that describe the relationship between multiple variables and their partial derivatives. They are used to model various physical phenomena and are widely used in fields such as physics, engineering, and economics.

2. How are linear PDEs different from nonlinear PDEs?

The main difference between linear and nonlinear PDEs is that linear PDEs have the property of superposition, meaning that the sum of two solutions is also a solution. Nonlinear PDEs do not have this property and are generally more complex and difficult to solve.

3. What are some common methods for solving linear PDEs?

Some common methods for solving linear PDEs include separation of variables, Fourier series, and Laplace transforms. These techniques involve breaking down the PDE into simpler equations that can be solved analytically or numerically.

4. What are boundary conditions in the context of linear PDEs?

Boundary conditions are additional constraints that are applied to the PDE to determine a unique solution. They specify the behavior of the solution at the boundaries of the domain and are essential for solving PDEs.

5. What are some real-world applications of linear PDEs?

Linear PDEs are used to model a wide range of physical phenomena, including heat transfer, fluid dynamics, electromagnetic fields, and quantum mechanics. They are also used in financial modeling and image processing.

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