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Old 12-28-2007, 02:30 AM
Mike Dubbeld Mike Dubbeld is offline
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Differential Equations good books

Hi, I just finished Cliff's Quick Review Differential Equations by Steven A. Leduc and it was the best I have seen so far being an easy to read and understand book on elementary differential equations. You don't even need much calculus for it. You just need your college Calculus text close by and if you recently finished Calculus you can read it in a short time. Its only 188 pages. 10$ US. I particularly like his applications at the end of the book putting DE's to use analogizing simple harmonic motion with resonance found in an electric circuit with a resistor, inductor, capacitor and voltage source.

Another good one is differential equations DeMystified by Steven G. Krantz. I haven't read it cover to cover but I can easily tell it is another one that is easy to read and is also on elementary differential equations. He goes a little further because he coverse Fourier Series, Partial Differential Equations with Boundary Value problems, Systems of DE's and Numerical methods which Leduc does not cover. Its a bigger book and is 240 pages without the Final Exam and Solutions to the Exercises but is only 20$ US.

A couple of days ago I picked up another DE book at Borders Books in Tampa Florida - Partial Differential Equations for Scientists and Engineers by Stanley J. Farrow and it appears to be one of the best I have ever seen. I already have about 10 books on DE's so I am in a position to compare them. I also picked up Introduction to Vector and Tensor Analysis by Robert C. Wrede and Vector and Tensor Analysis with Applications by A.I. Borisenko and I.E. Tarapov. While I can't say these look to be easy, books like these that are only around 20$ US are hard to come by in non-University book stores where the prices can easily be 100$ or more. There were no books in Borders Tampa on QFT (Quantum Field Theory) that did not appear to be anything but very difficult. I have easier books on QFT than they had.

I think I am going to have to visit a University bookstore to get books on Differential Geometry. I will probably get the Michael Spivak collection if I can.

I was thinking about posting a second order ordinary differential equation example on comparing simple harmonic motion of a block attached to a spring which oscillates to the oscillatory motion of current in an electric circuit in resonance. By building up from ordinary elementary DE's I figure I could then go on to talk about more advanced DE like Partial Differential Equations including the Schrodinger Wave Equation and the use of PDE's in General Relativity. Below are some references to DE's on the web.

'Mathematically, General Relativity is built upon ten so-called "coupled hyperbolic-elliptic nonlinear partial differential equations"'
http://archive.ncsa.uiuc.edu/Cyberia...Equations.html

Schrodinger Wave Equation --
'--the Schrödinger equation may be conveniently reformulated as a partial differential equation for a wavefunction--'
http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation

In any case if anyone wants to talk about DE's let me know. Beats treky space philsophy......

Mike Dubbeld
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Old 12-28-2007, 03:20 AM
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Vector and Tensor Analysis with Applications by A.I. Borisenko

Watch out of the errors.
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Old 12-29-2007, 12:10 AM
Mike Dubbeld Mike Dubbeld is offline
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Yeah errors by these authors drive me nuts because I always presume it is me that is not understanding something or doing something wrong so I try to solve it over and over again refering to other books.

You know it is a crazy idea posting something explaining 2'nd order DE's on FC because they require a lot of background to understand but I figured people could just ask a ton of questions and it would show at least why DE's are important and the get the general idea on how to go about solving the easy ones. If you start at the top with something that can be recognized as having value I figure it is more interesting but I have a feeling that no one here even knows why DE's are important to begin with so they certainly don't recognize things like the Schrodinger wave equation and Metric equations etc. What do people make of it when Brian Green talks about 'Perturbation Theory' and the like in the amature science book? We live in a soccer-mom school teacher/physics for poets school system society. I may just post it anyway just for shits and giggles......
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Old 12-29-2007, 01:58 AM
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The problem with the tensor book is that errors are everywhere. The good thing is that the author explains what he is saying well enough that you can spot the errors rather quickly if you think about what you read.

Anyway, I think you focus way to much on DE. There is more to physics and math than simple analysis.
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Old 12-29-2007, 04:09 AM
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You can probably find these books on eMule.
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Old 12-29-2007, 04:13 AM
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I can't read books online. I need to have them in my hands.
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Old 12-30-2007, 01:50 AM
Mike Dubbeld Mike Dubbeld is offline
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As Ross Kelly puts it 'Partial and non-linear differential equations are the bane of graduate students' - I am sure he is not refering to students getting a degree in mathematics. The entire universe is in a state of change. Differential equations describe change. Since wave superposition is linear, DE are a natural way to understand waves. It may be that as I learn more I will emphasize other things but for most students in engineering DE's are right up there as stumbling blocks. My whole emphasis is on understanding waves and QFT. State Space has a lot to do with solving complex DE's in the time domain and that also fits right in with my interest in comparing neural networks to feedback control systems. Don't forget; to be able to solve a lot of these equations means you need a lot of other math like linear algebra and complex analysis. I believe for me it is best to center my attention on DE's. I am aware of other things like Calculus of Variations and Lie Groups etc but I will be picking them up later (as in sometime in 2008!). I don't think you realize how many people are interested in DE's because they go so far in both classical and modern physics (not to mention engineering). The more advanced you get the less people that know what you are talking about. The more specialized you get the less the knowledge can be applied elsewhere and to me if you can't apply it it is useless. I am not so over-impressed with math that I think any less of say organic chemistry or systems analysis.

You know it is very annoying not having the ability to write equation symbols on FC.

Hope everyone had a nice Christmas.

Mike Dubbeld
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