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Applied Mathematics, by J. David Logan
PDF Download Applied Mathematics, by J. David Logan
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This updated edition of its popular predecessor strikes a balance between the mathematical aspects of the subject and its origin in empirics. It offers, at an elementary level, some of the current topics in applied mathematics such as singular perturbation, nonlinear waves, bifurcation, and the numerical solution of partial differential equations. Features additional sections on the WKB Approximation and asymptotic expansion of integrals along with expanded chapters on Green's Functions and integral equations. Includes Maple programs and examples from biology, chemistry, physics, and engineering.
- Sales Rank: #1892313 in Books
- Published on: 1996-12-18
- Original language: English
- Number of items: 1
- Dimensions: 9.37" h x 1.13" w x 6.32" l, .0 pounds
- Binding: Hardcover
- 496 pages
Review
“…can be thoroughly recommended to all who want an up-to-date approach to their subject.” (Zentralblatt MATH, 2007)
"Future mathematicians, scientists and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." (MAA Reviews, October 12, 2006)
From the Publisher
This updated edition of its popular predecessor strikes a balance between the mathematical aspects of the subject and its origin in empirics. It offers, at an elementary level, some of the current topics in applied mathematics such as singular perturbation, nonlinear waves, bifurcation, and the numerical solution of partial differential equations. Features additional sections on the WKB Approximation and asymptotic expansion of integrals along with expanded chapters on Green's Functions and integral equations. Includes Maple programs and examples from biology, chemistry, physics, and engineering.
From the Back Cover
The outstanding Second Edition -- skillfully revised and thoroughly updated
Since its initial publication over ten years ago, J. David Logan's Applied Mathematics has established itself as an ideal modern introduction to the principles of this important subject. Now, energized with fresh material and refined to achieve optimum clarity, this Second Edition brings Logan's highly acclaimed text fully up to date for the '90s and beyond.
Like the original, this revised volume covers not only such standard topics as fluid mechanics and calculus of variations, but also more contemporary methods, including dimensional analysis and scaling, nonlinear wave propagation, bifurcation, and singular perturbation. New sections have been added on the WKB approximation, the asymptotic expansion of integrals, and numerical methods. The treatment of partial differential equations, integral equations, and Green's functions has also been expanded, and there are many new exercises throughout to help readers develop and improve problem-solving skills with the support of the Maple programs provided.
Classical in approach and broad in scope, Applied Mathematics, Second Edition is firmly rooted in the interdependence of mathematics and the physical sciences, making it an accessible and truly relevant resource for students and practitioners across a wide range of scientific and engineering fields.
Most helpful customer reviews
31 of 32 people found the following review helpful.
Deep and philosophical; happily application-oriented. Possibly misnamed.
By Alexander C. Zorach
This book stands out among applied mathematics books. I like it very much, although it is certainly not easy to read. The equations and mathematics in the book are not particularly intimidating; the book is challenging because it gets you to think about difficult concepts at a sort of "meta" level. One of the best things about this book is that it is really an "applied mathematics" book in the sense that it prepares the reader to use the mathematics in applications.
The book assumes a lot of background, and starts from the rather odd point of dimensional analysis. I like this, because I feel dimensional analysis is an immensely powerful and often under-appreciated tool. The rest of the book covers various methods in partial differential equations, the calculus of variations, perturbation theory, and a lot of other material that I haven't even looked at. Most of the later material in the book assumes background which is not reviewed at all in the text, so this book requires prior coursework and is not self-contained. The result is a hodge-podge that most students will find has an inconsistent difficulty level, but I don't have a problem with this given the book's strengths. Also, the book is arranged so that it's easy to skip around in--and it makes a good reference text.
My main complaint about this book is its name: this book takes a somewhat narrow view of what constitutes "Applied Mathematics", and I think there is more than a little arrogance in the choice of title. When I think of "Applied Mathematics", I include areas such as statistics and combinatorics, which are not touched in this book. With the exception of two small sections on probabilistic discrete models, the focus of this book is almost exclusively on deterministic modeling, and I think that it would be more accurately named: "Applied Mathematics for Modeling" or something more specific.
I still don't know how I feel about this book. I've certainly learned a lot from it, although I don't understand all the subtleties of many chapters. This book was used as a recommended supplement in a graduate course, and I found it indispensable for this purpose. I keep picking it up and I find it provokes a lot of philosophical thought, much more than I'm used to getting out of texts of this type. I would recommend this book to anyone interested in applied mathematics, in particular, people interested in deterministic modeling.
0 of 0 people found the following review helpful.
Perfect for school
By SirWestofAsh
Great book and a wonderful seller to boot!
1 of 1 people found the following review helpful.
Excellent Value on the Eve of a New Edition
By Let's Compare Options Preptorial
This book has lasting value far beyond the "latest edition" craze of many publishers. The fourth is eagerly expected Summer/Fall of 2013. Peek copies we've seen show algorithmic updates and slightly better pedagogy (ie: more worked problems instead of this 3rd edition's fully worked example or two, then answers for the rest you've got to work out yourself).
This series in unique in the history of math books. I read and review hundreds of texts for our library procurement folks, including college libraries, and I've never found another book that balances deep math as tools with deep math as practical insights the way Logan does.
An example. Eigenvalues as "tools" can be seen as efficient ways to generalize induction, change problematic equations into easier to solve matrix forms (linearization), make a system orthogonal, set to 0 or 1 to simplify an equation set, treat as perpendicular vectors, etc. These are all "tools" of both applied and pure math. However, Logan goes beyond both applications and pure math to a "gist" level so you "grok" the meaning at a RARE intuitive level-- He shows, for example, where "this" eigenvalue is a stability indicator in this context, "that" eigenvalue is a growth rate in that context, this other eigenvalue here is a sensitivity to change parameter...
IOW, the craving for wonder you've always had for the WHY or GIST of BOTH applications and pure math are given here like you've never seen it anywhere before. Another example: Some reviews around the web dinged Logan for starting with dimensions, indices and scales (unlike any other general applied text let alone specifically applied texts in physics or engineering). What those reviewers missed is that by showing reduction and generalization of dimensions (like feet per second squared, air density of mass per length cubed etc.) in a way that shows WHERE and WHY, in a 20,000 foot, meta sense, why we USE exponents in general cases!
He does this very subtly and on purpose, stating that indices, scales, etc. are ubiquitous in all of math because they come from and compare "quantities to intrinsic references that appear naturally in physical situations." WOW! In other words, we see WHY and WHERE general equations use certain parameters, indices, constants, variable types, etc. in their most "basic" formula form-- whether applied or pure! Many professional mathematicians (I know, I'm an engineer who hires them) NEVER get to this level of understanding in their career! They simply CANNOT tell you that the reason this eigenvalue is important, and in fact appears here, is because it "acts" as a scalar index or parameter for growth, or proxy for change!!
Pick it up for a deal since 4 is immanent, and I'll let you know in more detail how it compares to 4 when Amazon allows us to review it!!
Library Picks reviews only for the benefit of Amazon shoppers and has nothing to do with Amazon, the authors, manufacturers or publishers of the items we review. We always buy the items we review for the sake of objectivity, and although we search for gems, are not shy about trashing an item if it's a waste of time or money for Amazon shoppers. If the reviewer identifies herself, her job or her field, it is only as a point of reference to help you gauge the background and any biases.
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