Intro book on PDE

[const451]

Could someone recommend an introductory book on PDE.

I am taking a PDE prereq course at my local univ. that has required book by Strauss. I need a supplementary book as I usually find it helpful to have a second book to consult with if I do not comprehend some of the concepts from the required one.

THX!

 

[bigbadwolf]

Loads of intro PDE books. What specifically do you want (in terms of content and emphasis)?

Before I forget to mention it, get hold of An Introduction to Linear Analysis, by Kreider, Kuller, Ostberg and Perkins. Long out of print, but used copies floating around. When you get your copy, put it under lock and key, guard it with your life, mention it to no-one.

<iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=B000VXJW5A&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>

 

[const451]

Loads of intro PDE books. What specifically do you want (in terms of content and emphasis)?

No, nothing in particular, just a clear Intro to PDE. This is what covered in the PDE textbook by Strauss required for my course. I am looking for something similar.

First-order equations; classification of second-order equations; Initial-boundary value problems
for heat, wave, and related equations; Separation of variables; eigenvalue
problems; Fourier series; existence and uniqueness questions; Laplace’s equation and
properties of harmonic functions. Green’s functions. Distributions and
Fourier transforms. Eigenvalue problems and generalized Fourier series.

Before I forget to mention it, get hold of An Introduction to Linear Analysis, by Kreider, Kuller, Ostberg and Perkins. Long out of print, but used copies floating around. When you get your copy, put it under lock and key, guard it with your life, mention it to no-one.

:D - I have actually ordered it; but what is it, Linear Algebra?

 

[Sanket Patel]

I'm not too familiar with various textbooks, but my PDE class also used Strauss. I highly recommend supplementing Strauss with another book - I found Strauss to rather dry and vague. I prefer texts that are thorough and develop concepts with several examples. In my opinion, Strauss fell short in that regard.

I ended up supplementing Strauss with the following two books:

• Applied Partial Differential Equations : J. David Logan<iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=0387209530&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>

• Partial Differential Equations : Arthur David Snider <iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=0486453405&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>

 

[Minh Tran]

Is it more sense to do PDEs numerically instead?

 

[chrisd]

Partial Differential Equations for Scientists and Engineers by Stanley Farlow is a decent enough (and cheap enough) book as far as solving PDEs analytically. Doesn't have a lot of exercises, though, and doesn't address some of the more theoretical issues.

Also, the Schaum's Outline of PDE might be useful. I haven't used the PDE one, but they tend to useful supplements, with a lot of exercises and worked examples.

 

[bigbadwolf]

:D - I have actually ordered it; but what is it, Linear Algebra?

No, 'course not. Chapters 9-15 (pp 329-635) provide excellent coverage of orthogonal series of polynomials and boundary-value problems for PDEs (including one chapter on BVPs for ODEs). It's an ideal introduction to Fourier series, special functions, ODEs, and PDEs. I've had the book for the last quarter-century and have examined many books on PDEs in the interim: this has to be one of the best. For anyone reading this post, and with a genuine interest in PDEs (not just a mercenary interest in getting through some MFE program), go and nab one of the used copies floating around. My own two copies have armed guards protecting them.

 

[const451]

Do you have opinion on these books? I need it for an intro course.


Elementary Applied Partial Differential Equations With Fourier Series and Boundary Value Problems by Richard Haberman <iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=013263807X&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>

Partial Differential Equations by Fritz John <iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=0387906096&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>

Basic Partial Differential Equations by Bleeker <iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=0442015216&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>


Partial Differential Equations by Evans -- this seems to be advanced level - not for me right now. <iframe src="http://rcm.amazon.com/e/cm?t=quantfinaneng-20&o=1&p=8&l=as1&asins=0821807722&fc1=000000&IS2=1&lt1=_blank&lc1=0000FF&bc1=FFFFFF&bg1=F7F7F7&f=ifr" style="width:120px;height:240px;" scrolling="no" marginwidth="0" marginheight="0" frameborder="0"></iframe>


Thanks!

 

[bigbadwolf]

Elementary Applied Partial Differential Equations With Fourier Series and Boundary Value Problems by Richard Haberman
Partial Differential Equations by Fritz John
Basic Partial Differential Equations by Bleeker
Partial Differential Equations by Evans -- this seems to be advanced level - not for me right now.

Fritz John is a classic, but too concise and difficult. Evans is meant for grad math students. I don't know the other two, so I looked them up on Amazon. I'd stick with Bleecker. One recommendation, in passing, is Al-Gwaiz's Sturm-Liouville Theory and its Applications.

Postscript: There's a discussion here that may be helpful.

 

[chrisd]

Partial Differential Equations by Evans -- this seems to be advanced level - not for me right now.
Thanks!

Evans is hardcore analysis... definitely not what you're looking for

 

[justlooking]

I just ordered Basic Partial Differential Equations by Bleecker myself, it seems well written and easy-going.

edit: bleecker not bleeker

 

[const451]

I have ordered these two books so far:

"Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics)"
Stanley J. Farlow; Paperback; $11.53

"Introduction to Partial Differential Equations with Applications"
E. C. Zachmanoglou; Paperback; $10.85

Shaums is not good on PDE, I have it on ODE.


I found another book: Partial differential equations by Michael E. Taylor, could you comment on it?

The good thing it is in three volumes from basic to advanced so you can study progressively from the same author. I am afraid though the first volume - Basic Theory - is not that basic. He talks about Manifolds.

 

[chrisd]

I found another book: Partial differential equations by Michael E. Taylor, could you comment on it?

The good thing it is in three volumes from basic to advanced so you can study progressively from the same author. I am afraid though the first volume - Basic Theory - is not that basic. He talks about Manifolds.

The blurb on Amazon says its aimed at graduate students and professional mathematicians. Looking at the table of contents, it's definitely not aimed at people who don't know a lot of analysis.

 

[bigbadwolf]

I found another book: Partial differential equations by Michael E. Taylor, could you comment on it?

You're groping in the dark. Books like Evans and Taylor are not written for the quant student; they assume a background in Hilbert spaces, distribution theory, Sobelov Spaces, and maybe even manifolds and differential forms. They are written for research students interested in theoretical problems. This is not you. You want a "PDE for engineers/scientists/dummies" sort of book, which explains some practical methods of solving the three basic kinds of linear PDEs (particularly the heat equation), including material on Fourier series and other orthogonal series of functions/polynomials, and also has some material on numerical methods (e.g. finite-difference schemes). This is all intensely relevant to the aspiring quant.

Farlow is good. Bleecker is (probably) good. Kreider, et al (Linear Analysis) is good. Al-Gwaiz is good. This is all you need right now. (I personally don't like Zachmanoglou.) With time, you may want to pick up a book devoted to numerical methods for PDEs.

 

[const451]

I see now - BBW thanks a lot. I am getting Bleecker and Al-Gwaiz.

I also need some other books for my Adv. Calculus class... I'll post another thread.

Thank you!

 

[waterborne]

A First Course In Partial Differential Equations with Complex Variables and Transform Methods by Weinberger is what I used in my PDE class. It is pretty good and pretty cheap.

 

[const451]

Weinberger skips on explanations, but I am looking for the opposite. Thanks.

 

[parisjohn]

It's a PDE Book for financial intrument : Pricing Financial Instruments: The Finite Difference Method by Domingo Tavella

 

[bigbadwolf]

I am getting Bleecker and Al-Gwaiz.

The book by Bleecker and Csordas is excellent: it presupposes only a year of calculus, and covers the necessary material about ODEs in the first chapter (though it would be helpful if one already had prior exposure to ODEs). The explanations are not terse and there are worked examples for everything they discuss. It's an ideal text -- arguably the single best text -- for prospective quants who are trying to learn about PDEs by themselves. Much better than Farlow (which is also good).

 

[muriuki]

The book by Bleecker and Csordas is excellent: it presupposes only a year of calculus, and covers the necessary material about ODEs in the first chapter (though it would be helpful if one already had prior exposure to ODEs). The explanations are not terse and there are worked examples for everything they discuss. It's an ideal text -- arguably the single best text -- for prospective quants who are trying to learn about PDEs by themselves. Much better than Farlow (which is also good).

thanks .. a decade later to save a life