Partial Differential Equations book

In summary, the conversation discusses recommendations for introductory books on partial differential equations, with one suggestion being Boyce and DiPrima for its coverage of ordinary differential equations and another being Haberman for its focus on partial differential equations.
  • #1
Goldbeetle
210
1
Dear all,
I'm interested in partial differential equations. I would like to find an introductory book with solutions methods of known mathematical phisycs equations, rigorous but no high-tech math, and one a more advanced in terms of math.

Do you have any text to recommend?

Thank you for your time and attention.

Goldbeetle
 
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  • #2
https://www.physicsforums.com/showpost.php?p=1874831&postcount=4"

Here is a link to the post, that was given as an answer to my question. Very similar to yours I think but I asked for some more maths as well. Basically Howers recommends
Howers said:
...I strongly suggest you study differential equations from a book like Boyce and DiPrima.

This was though given as a suggestion to a science (Chemistry) oriented student. So you might be more of a mathematician not sure.
 
Last edited by a moderator:
  • #3
It's worth noting that Boyce and DiPrima primarily covers ordinary differential equations, while the parent poster asked for a book on partial differential equations. One of the standard texts for a first course in partial differential equations is Applied Partial Differential Equations by Haberman.
 
  • #4
I second Haberman.
 

1. What are partial differential equations (PDEs) and why are they important?

Partial differential equations are mathematical equations that involve multiple variables and their partial derivatives. They are used to model and study phenomena in fields such as physics, engineering, and economics. PDEs are important because they allow us to describe and understand complex systems and make predictions about their behavior.

2. Is a background in calculus necessary to understand PDEs?

Yes, a solid understanding of calculus is necessary to understand and solve PDEs. PDEs involve derivatives, integrals, and other concepts from calculus. It is also helpful to have a foundational understanding of linear algebra and differential equations.

3. What are some real-world applications of PDEs?

PDEs have a wide range of applications in various fields. They are used to model heat transfer, fluid dynamics, diffusion processes, and electromagnetic fields. They are also used in finance to model stock prices and in biology to model population dynamics.

4. Are there different types of PDEs?

Yes, there are several types of PDEs, including elliptic, parabolic, and hyperbolic equations. These types describe different types of behavior in the solutions to the equations. For example, elliptic equations describe steady-state behavior, while parabolic equations describe diffusion processes.

5. How can I learn more about PDEs and their applications?

There are many resources available for learning about PDEs, including textbooks, online courses, and tutorials. It is also helpful to practice solving PDEs and to explore their applications in different fields. Consulting with a mentor or joining a study group can also be beneficial in understanding PDEs.

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