Partial Differential EQs for Engineers

In summary, The speaker is an engineer looking for a PDEs self-study book that has both applications and rigor. They have considered Farlow's text but feel it is too focused on applications. They ask for recommendations and are suggested Pinchover and Rubinstein's book as a good introduction with some rigor. Other suggestions can be found in the Amazon reviews.
  • #1
Saladsamurai
3,020
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Hello all! :smile: I have searched this, but I am still looking for additional input. I am an engineer and I want to self-study PDEs. I looked at Farlow's text and though it is nice from an applications standpoint, I think that it is not 'mathy' enough for me. Don't get me wrong, I am not the best math student by any stretch; all of my background has been in 'engineering maths' not 'math major maths'. But again, I think Farlow is too applications oriented for me, I like a "little rigor."

Any thoughts on an intro PDE text that has a 'little bit' of rigor yet is still accessible to the Engineer?

Thanks! :smile:
 
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  • #2
How about Pinchover and Rubinstein? From what I have seen, it is a fairly rigorous book and a good introduction, but it is not a thorough treatment. If you read the Amazon reviews of the book, you'll get some other suggestions as well.
 

What are partial differential equations (PDEs)?

Partial differential equations are mathematical equations that involve multiple independent variables and their partial derivatives. They are commonly used to model physical phenomena that vary continuously in space and time, such as heat transfer, fluid flow, and electromagnetic fields.

Why are PDEs important for engineers?

PDEs are important for engineers because they provide a powerful tool for analyzing and solving complex physical problems. Many real-world engineering problems, such as designing heat exchangers or predicting weather patterns, can be described using PDEs. Solving these equations allows engineers to understand and optimize the behavior of systems in various fields.

What are the types of PDEs commonly encountered by engineers?

The two main types of PDEs encountered by engineers are elliptic and hyperbolic equations. Elliptic equations are used to describe steady-state phenomena, such as heat conduction, while hyperbolic equations are used to describe wave-like phenomena, such as sound or electromagnetic waves. There are also parabolic equations, which are used to describe transient phenomena, such as diffusion and heat transfer.

What methods are used to solve PDEs?

There are several methods for solving PDEs, including analytical, numerical, and graphical methods. Analytical solutions involve finding exact closed-form solutions using mathematical techniques such as separation of variables or Fourier transforms. Numerical methods involve approximating the solution using algorithms and computers. Graphical methods involve visually representing the solution using contour plots or other graphical techniques.

What are some real-world applications of PDEs in engineering?

PDEs have numerous real-world applications in engineering, including designing airplane wings, predicting weather patterns, modeling traffic flow, and designing heat exchangers. They are also used in computer graphics and animation, as well as in finance and economics to model stock prices and interest rates.

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