Release Date: 19 Dec 2015
Print Book ISBN :9780128498941
Pages:484
Dimensions:235 X 191
Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry
Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes
Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives
Numerical Methods for Partial Differential Equations: Finite Difference
and Finite Volume Methods focuses on two popular deterministic methods
for solving partial differential equations (PDEs), namely finite difference
and finite volume methods. The solution of PDEs can be very challenging,
depending on the type of equation, the number of independent variables,
the boundary, and initial conditions, and other factors. These two methods
have been traditionally used to solve problems involving fluid flow.
For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful.
The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.
Graduate level Mechanical, Aerospace, Civil, Biomedical, and Chemical Engineering students; engineering professionals involved in areas such as computational mechanics, computational fluid dynamics, and computational electromagnetics.
Part of New Mathematical Monographs
Publication planned for: March 2016
availability: Not yet published - available from March 2016
format: Hardback
isbn: 9781107137431
This book presents a detailed and contemporary account of the classical theory of convergence of semigroups. The author demonstrates the far-reaching applications of this theory using real examples from various branches of pure and applied mathematics, with a particular emphasis on mathematical biology. These examples also serve as short, non-technical introductions to biological concepts. The book may serve as a useful reference, containing a significant number of new results ranging from the analysis of fish populations to signalling pathways in living cells. It comprises many short chapters, which allows readers to pick and choose those topics most relevant to them, and contains 160 end-of-chapter exercises, so that the reader can test their understanding of the material as they go along.
Publication planned for: May 2016
availability: Not yet published - available from May 2016
format: Hardback
isbn: 9781107086586
Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang?Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.
Acknowledgements
1. Introduction
2. Introduction to on-shell functions and diagrams
3. Permutations and scattering amplitudes
4. From on-shell diagrams to the Grassmannian
5. Configurations of vectors and the positive Grassmannian
6. Body configurations, graphs, and permutations
7. The invariant top-form and the positroid stratification
8. (Super) conformal and dual conformal invariance
9. Positive diffeomorphisms and Yangian invariance
10. The kinematical support of physical on-shell forms
11. Homological identities among Yangian-invariants
12. (Relatively) orienting canonical coordinate charts on positroids
13. Classification of Yangian-invariants and their relations
14. The Yang?Braxter relation and ABJM theories
15. On-shell diagrams for theories with N<4 supersymmetries
16. Dual graphs and cluster algebras
17. On-shell representations of scattering amplitudes
18. Outlook
References.
availability: Not yet published - available from May 2016
format: Hardback
isbn: 9781107017085
format: Paperback
isbn: 9781107602724
This book can form the basis of a second course in algebraic geometry.
As motivation, it takes concrete questions from enumerative geometry and
intersection theory, and provides intuition and technique, so that the
student develops the ability to solve geometric problems. The authors explain
key ideas, including rational equivalence, Chow rings, Schubert calculus
and Chern classes, and readers will appreciate the abundant examples, many
provided as exercises with solutions available online. Intersection is
concerned with the enumeration of solutions of systems of polynomial equations
in several variables. It has been an active area of mathematics since the
work of Leibniz. Chasles' nineteenth-century calculation that there are
3264 smooth conic plane curves tangent to five given general conics was
an important landmark, and was the inspiration behind the title of this
book. Such computations were motivation for Poincare's development of topology,
and for many subsequent theories, so that intersection theory is now a
central topic of modern
mathematics.
Introduction
1. Introducing the Chow ring
2. First examples
3. Introduction to Grassmannians and lines in P3
4. Grassmannians in general
5. Chern classes
6. Lines on hypersurfaces
7. Singular elements of linear series
8. Compactifying parameter spaces
9. Projective bundles and their Chow rings
10. Segre classes and varieties of linear spaces
11. Contact problems
12. Porteous' formula
13. Excess intersections and the Chow ring of a blow-up
14. The Grothendieck Riemann-Roch theorem
Appendix A. The moving lemma
Appendix B. Direct images, cohomology and base change
Appendix C. Topology of algebraic varieties
Appendix D. Maps from curves to projective space
References
Index.
Part of Cambridge Studies in Advanced Mathematics
availability: Not yet published - available from August 2016
format: Hardback
isbn: 9781107153523
Exploring the full scope of differential topology, this comprehensive account of geometric techniques for studying the topology of smooth manifolds offers a wide perspective on the field. Building up from first principles, concepts of manifolds are introduced, supplemented by thorough appendices giving background on topology and homotopy theory. Deep results are then developed from these foundations through in-depth treatments of the notions of general position and transversality, proper actions of Lie groups, handles (up to the h-cobordism theorem), immersions and embeddings, concluding with the surgery procedure and cobordism theory. Fully illustrated and rigorous in its approach, little prior knowledge is assumed, and yet growing complexity is instilled throughout. This structure gives advanced students and researchers an accessible route into the wide-ranging field of differential topology.
Introduction
1. Foundations
2. Geometrical tools
3. Differentiable group actions
4. General position and transversality
5. Theory of handle decompositions
6. Immersions and embeddings
7. Surgery
8. Cobordism
Appendix A. Topology
Appendix B. Homotopy theory
References
Index of notation
Index.