My Favourite Applied Math Books
Students often ask me ``What is the best book on . . . <SUBJECT
X>?" I don't always have an answer, but in certain areas
of applied mathematics (especially related to fluid mechanics or scientific
computing) I do have my favourites.
When reading this list, please keep in mind that all choices are biased
toward my own personal mathematical interests, and that the focus here
is more on books suitable for teaching rather than research monographs.
That said, please enjoy perusing this list. Comments, criticisms and
suggestions are welcome!
- What is the best book on . . . fluid mechanics?
- For teaching, I like Acheson's Elementary
Chorin and Marsden's A
Mathematical Introduction to Fluid Mechanics is a more advanced
treatise that is timeless. An honourable mention also goes to
Ockendon and Ockendon's Viscous
Flow, which is an absolute pleasure to read.
- What is the best book on . . . computational fluid dynamics?
- This is a tough call. Most texts have a strong engineering bent,
which I am not keen on. The best I've come across is Pozrikidis'
to Theoretical and Computational Fluid Dynamics, which as the
title indicates covers both the theory and computation. There are
lots of practical examples and algorithms for incompressible flow and
moving boundary problems. It's missing a discussion of hyperbolic
problems (see below).
- What is the best book on . . . special topics in fluid dynamics?
- My hands-down favourite is John Crank's Free
and Moving Boundary Problems which has everything you
need to know about the Stefan problem and related models. A
beautiful little book on suspension flows is A
Physical Introduction to Suspension Dynamics. The clarity and
insight of this text is complemented beautifully by the stunning
- What is the best book on . . . (applied) PDE?
- I really like to teach undergraduates from a book like
Differential Equations: Analytical and Numerical Methods.
This book stresses the mind-numbingly beautiful connection with linear
algebra by developing everything in terms of linear operators on
vector spaces and essentially ignoring the cookbook-style focus on
"separation of variables" of most other books. He
doesn't go as deeply into the theory as some authors, but I think
he strikes just the right balance for an undergraduate level
course. And there is the added bonus that the author provides
Matlab and Maple code to experiment with.
- What is the best book on . . . numerical PDE?
- Without a doubt, Strikwerda's Finite
Difference Schemes and Partial Differential Equations. I am
constantly referring to this book since it's so full of
information. I am also a big fan of Morton and Mayer's Numerical
Solution of Partial Differential Equations. It's short, sweet and
has a collection of very nice exercises.
- What is the best book on . . . hyperbolic PDE?
- My favourite book is LeVeque's Numerical
Methods for Conservation Laws. It's short and very sweet, and its
only drawback is the lack of an index. But I've read it cover to
cover so many times I don't need the index anyways. I prefer the
style of this little book to LeVeque's more
recent and expansive text
on the subject . . . although that is also a very nice text if you're
interested in the details of the algorithms behind his excellent CLAWPACK code.
I cannot neglect to mention Tartar's From Hyperbolic
Systems to Kinetic Theory: A Personalized Quest, which is a
simply beautiful book to read. If only more math texts were
written in this style . . .
- What is the best book on . . . introductory numerical analysis?
- The simple answer here is that there isn't one, at least from a
teaching standpoint. I have yet to find a text that I am happy
teaching an introductory numerical analysis class from. At SFU, we
teach primarily to computer scientists and engineers using Matlab, and
a good compromise is Recktenwald's Numerical
Methods with MATLAB: Implementations and Applications.
- What is the best book on . . . mathematical modelling?
- I am a big fan of Fowler's Mathematical
Models in the Applied Sciences, which betrays the time I have
spent attending Study Groups.
- What is the best book on . . . porous media flow?
- Here again, there isn't one, but the best I've found is Kaviany's
of Heat Transfer in Porous Media.
- What is the best . . . mathematics reference book?
- Abramowitz and Stegun's Handbook
of Mathematical Functions wins in this category, hands down. I
don't think this book will ever lose its place on my shelf. Even the
indexed electronic version doesn't appeal to me as much as paging
through my dusty, yellowed old copy of A&S.
- What is the best book on . . . professional development for academics?
- There are three books that I recommend to my students, as well as
anyone else who asks:
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Last modified: Wed Jan 4 2017