Part of Encyclopedia of Mathematics and its Applications
Publication planned for: February 2016
format: Hardback
isbn: 9781107138384
In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities. Here, the authors take the unique approach of investigating differential inequalities rather than equations, the reason being that the simplest way to study an equation is often to study a corresponding inequality; for example, using sub and superharmonic functions to study harmonic functions. Another unusual feature of the present book is that it is based on integral representation formulae and nonlinear potentials, which have not been widely investigated so far. This approach can also be used to tackle higher order differential equations. The book will appeal to graduate students interested in analysis, researchers in pure and applied mathematics, and engineers who work with partial differential equations. Readers will require only a basic knowledge of functional analysis, measure theory and Sobolev spaces.
Chapman and Hall/CRC 2015 352 pages
Series: Textbooks in Mathematics
Hardback: ￡57.99
978-1-49-875403-3
22nd December 2015
This text for the second course in linear algebra presents a conscise, student-friendly approach to the theory. The author covers vector spaces, linear transformations, The Jordan canonical form, Inner product spaces and applications. This briefer book also offers carefully constructed proofs and answers to selected exercises.
1 Fields and Matrix Algebra 1
2 Vector Spaces 23
3 Linear transformations 47
4 The Jordan canoninal form 59
5 Inner product spaces 83
6 Answers to Exercises 107
CRC Press 2016 560 pages
Hardback: ￡62.99
978-1-48-225722-9
17th February 2016
The second edition of this book contains changes that have been suggested by mathematicians and mathematics professors. A new chapter has been added on classical solutions of ordinary linear differential equations (other methods), and a partial chapter on response of first and second order systems has been expanded into a standalone chapter to stress its importance. Other chapters have been updated, and new problems and examples have been added, including several problems that can be used as projects.
Introduction. Objects in a Gravitational Field. Classical Solutions of Ordinary Linear Differential Equations. Classical Solutions of Ordinary Linear Differential Equations - Other Methods. Laplace Transforms. Response of First and Second Order Systems. Mechanical Systems: Translational. Mechanical Systems: Rotational. Mass Balances. Thermal Systems. Electrical Systems. Numerical Simulation.
EMS Series of Lectures in Mathematics
ISBN print 978-3-03719-154-5,
August 2015, 230 pages, softcover, 17 x 24 cm.
The field of 3-manifold topology has made great strides forward since 1982, when Thurston articulated his influential list of questions. Primary among these is Perelman's proof of the Geometrization Conjecture, but other highlights include the Tameness Theorem of Agol and Calegari?Gabai, the Surface Subgroup Theorem of Kahn?Markovic, the work of Wise and others on special cube complexes, and finally Agol's proof of the Virtual Haken Conjecture. This book summarizes all these developments and provides an exhaustive account of the current state of the art of 3-manifold topology, especially focussing on the consequences for fundamental groups of 3-manifolds.
As the first book on 3-manifold topology that incorporates the exciting progress of the last two decades, it will be an invaluable resource for researchers in the field who need a reference for these developments. It also gives a fast-paced introduction to this material ? although some familiarity with the fundamental group is recommended, little other previous knowledge is assumed, and the book is accessible to graduate students.
The book closes with an extensive list of open questions, which will also be of interest to graduate students and established researchers alike.