Textbook for learning PDE's applied to physics?

In summary, the speaker took a graduate level mathematical methods for physics course but felt lacking in solving equations such as the heat equation, wave equation, and Laplace's equation. They are still unsure about the Green's Function method and using Fourier series. They recommend the textbook Goldbart and Stone, but mention that Lokenath Debnath's books are also good resources, although they can be expensive. They also suggest Duffy's book for learning about Green's functions.
  • #1
Vannay
25
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Took a graduate level mathematical methods for physics course and came out the other side feeling a bit lacking in solving stuff like the heat equation, wave equation, laplaces equation and so on. I'm still unsure of the Green's Function method for them, how to look at them with Fourier series, and so on.

The textbook we used was Goldbart and Stone which often would introduce the Green Function method for a given PDE by saying "So here's the solution" and then showing it is. That doesn't help when I'm taking a test that says solve this diffusion PDE given these certain boundary conditions.
 
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1. What is the purpose of a textbook for learning PDE's applied to physics?

A textbook for learning PDE's applied to physics serves as a comprehensive guide for understanding the mathematical concepts and techniques used to solve partial differential equations in the context of physics. It provides a foundation for further studies in areas such as fluid mechanics, electromagnetism, and quantum mechanics.

2. How is the content of a textbook for learning PDE's applied to physics organized?

The content of a textbook for learning PDE's applied to physics is typically organized into chapters that cover different types of partial differential equations, such as hyperbolic, parabolic, and elliptic equations. Within each chapter, the material is further divided into sections that focus on specific applications and methods for solving PDE's.

3. Are there any prerequisites for using a textbook for learning PDE's applied to physics?

Some familiarity with calculus, linear algebra, and ordinary differential equations is typically required to understand the material presented in a textbook for learning PDE's applied to physics. However, many textbooks also include a review of these topics to help students refresh their knowledge.

4. How can a textbook for learning PDE's applied to physics be used effectively?

A textbook for learning PDE's applied to physics can be used as a supplement to a course or as a self-study tool. It is important to read and understand each section thoroughly, and to work through the provided examples and practice problems to reinforce the concepts learned.

5. Are there any online resources that can enhance the learning experience with a textbook for learning PDE's applied to physics?

Yes, there are many online resources available such as video lectures, interactive simulations, and practice quizzes that can supplement the material covered in a textbook for learning PDE's applied to physics. These resources can provide additional visual and hands-on learning opportunities to help reinforce the concepts and techniques presented in the textbook.

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