geometry and nonlinear partial differential equations

Geometry and Nonlinear Partial Differential Equations

ISBN: , SKU: , AUTHOR: S T Yau Shuxing Chen, PUBLISHER: American Mathematical Society, NA

Handbook of Nonlinear Partial Differential Equations, Second

ISBN: , SKU: , AUTHOR: Polyanin, Andrei D. / Zaitsev, Valentin F. / Pol'ianin, A. D., PUBLISHER: CRC Press, Updated and expanded, this popular handbook provides a catalog of nonlinear PDEs and their solutions. With nearly 400 pages of new and updated material, this edition contains over 500 nonlinear PDEs with solutions and many new nonlinear systems of PDEs with solutions. In the first half of the book, numerous new and nonlinear systems of PDEs are described with a focus on equations containing one or more arbitrary parameters. The authors cover equations that arise in heat transfer, wave theory, nonlinear mechanics, hydrodynamics, gas dynamics, plasticity theory, nonlinear optics, theoretical physics, differential geometry, control theory, biology, and other fields. The second half of the book presents the exact methods used for solving these types of equations. The authors explore classical methods and some recent developments, along with examples that illustrate applications of the methods.

Differential Equations: A Modeling Perspective, Preliminary

ISBN: , SKU: , AUTHOR: Borrelli, Robert / Coleman, Courtney S., PUBLISHER: John Wiley & Sons, Reform Differential Equations book specifically targeted toward engineers and future engineers. It emphasizes modeling, nonlinearity, visualization, and the use of technology.

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis,

ISBN: , SKU: , AUTHOR: Hesthaven, Jan S. / Warburton, Tim, PUBLISHER: Springer, This book offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. It covers all key theoretical results, including an overview of relevant results from approximation theory, convergence theory for numerical PDE's, and orthogonal polynomials. Through embedded Matlab codes, coverage discusses and implements the algorithms for a number of classic systems of PDE's: Maxwell's equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations.

Optimal Control of Differential Equations

ISBN: , SKU: , AUTHOR: Pavel, Nicolae H. / Pavel, Pavel H., PUBLISHER: CRC Press, "Based on the International Conference on Optimal Control of Differential Equations held recently at Ohio University, Athens, this Festschrift to honor the sixty-fifth birthday of Constantin Corduneanu an outstanding researcher in differential and integral equations provides in-depth coverage of recent advances, applications, and open problems relevant to mathematics and physics. Introduces new results as well as novel methods and techniques "

Controllability of Partial Differential Equations Governed

ISBN: , SKU: , AUTHOR: Alexander Y Khapalov, PUBLISHER: Springer, NA

Direct Methods in the Theory of Elliptic Equations

ISBN: , SKU: , AUTHOR: Necas, Jindrich / Tronel, Gerard / Kufner, Alois, PUBLISHER: Springer, Necas's famous book Direct methods in the theory of elliptic equations has become standard reference material on the mathematical theory of linear elliptic equations and systems, and also on the related function spaces framework. It provides a concise and self-contained introduction to the modern theory of partial differential equations, the theory of weak solutions and related topics. It is recommended to scientists working in the field of partial differential equations, postgraduate and graduate students, and applied mathematicians. The first chapter is devoted to directs methods, introduction to the Sobolev spaces, weak solution, Lax-Milgram theorem, Galerkin metods and spectral theory. The second chapter deals with the basic properties of Sobolev spaces (imbeddings, traces, compact imbeddings, fractional spaces).The third chapter contains existence and uniqueness theorems for problems, including the Fredholm alternative and systems of equations with variable coefficients. The next chapter describes regularity properties of weak solutions. Chapter 5 deals with applications of Rellich's inequality and Chapter 6 introduces the Sobolev spaces with weights. Finally the last chapter studies regularity of solutions and their dependence on coefficients and also on irregular domains.

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis,

ISBN: , SKU: , AUTHOR: Hesthaven, Jan S. / Warburton, Tim, PUBLISHER: Springer, The text offers an introduction to the key ideas, basic analysis, and efficient implementation of discontinuous Galerkin finite element methods (DG-FEM) for the solution of partial differential equations. All key theoretical results are either derived or discussed, including an overview of relevant results from approximation theory, convergence theory for numerical PDEa (TM)s, orthogonal polynomials etc. Through embedded Matlab codes, the algorithms are discussed and implemented for a number of classic systems of PDEa (TM)s, e.g., Maxwella (TM)s equations, Euler equations, incompressible Navier-Stokes equations, and Poisson- and Helmholtz equations. These developments are done in detail in one and two dimensions on general unstructured grids with high-order elements and all essential routines for 3D extensions are also included and discussed briefly. The three appendices contain an overview of orthogonal polynomials and associated library routines used throughout, a brief introduction to grid generation, and an overview of the associated software (where to get it, list of variables etc). A variety of exercises are included at the end of most chapters.

Plane and Solid Geometry - Wentworth-Smith Mathematical

ISBN: , SKU: , AUTHOR: George Wentworth / David Eugene Smith, PUBLISHER: Merchant Books, An Unabridged Printing, With Text And All Figures Digitally Enlarged. Chapters Include: PLANE GEOMETRY - Rectilinear Figures - The Circle - Proportion - Similar Polygons - Areas Of Polygons - Regular Polygons And Circles - Appendix To Plane Geometry (Symmetry, Maxima And Minima) - SOLID GEOMETRY - Lines And Planes In Space - Polyhedrons, Cylinders, And Cones - The Sphere - Appendix To Solid Geometry - Recreations Of Geometry - Suggestions As To Beginning Demonstrative Geometry - Applications Of Geometry - The History Of Geometry - Table Of Formulas - Comprehensive Index

Advances in Differential Equations and Mathematical Physics

ISBN: , SKU: , AUTHOR: Gunter Stolz Rudi Weikard Yanni Zeng Yulia Karpeshina, PUBLISHER: American Mathematical Society, NA

Geometry

ISBN: , SKU: , AUTHOR: Leff, Lawrence S., PUBLISHER: Barron's Educational Series, Starting in June , the New York State Board of Regents is reinstituting the high school geometry exam. This brand-new "Regents Exams and Answers: Geometry " joins Barronas famous series of Regents aRedbooks, a presenting an in-depth subject review, plus hundreds of practice problems with answers. Topics reviewed include the language of geometry; parallel lines and quadrilaterals and coordinates; similarity; right triangles and trigonometry; circles and angle measurement; transformation geometry; locus and coordinates; and an introduction to solid geometry. Also presented is a full-length practice geometry exam that accurately reflects New York State Regents standards in subject matter and degree of difficulty.

Equations and Inequalities

ISBN: , SKU: , AUTHOR: Herman, Jiri / Herman, J. / Kucera, R., PUBLISHER: Springer, This book presents methods of solving problems in three areas of classical elementary mathematics: Equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are immediately followed by carefully worked out examples of increasing degrees of difficulty, and by exercises which range from routine to rather challenging problems. While this book emphasizes some methods that are not usually covered in beginning university courses, it nevertheless teaches techniques and skills which are useful not only in the specific topics covered here. There are approximately 330 examples and 760 exercises.

Ideals, Varieties, and Algorithms: An Introduction to

ISBN: , SKU: , AUTHOR: Cox, David / Little, John / O'Shea, Donal, PUBLISHER: Springer, Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The algorithms to answer questions such as those posed above are an important part of algebraic geometry. Although the algorithmic roots of algebraic geometry are old, it is only in the last forty years that computational methods have regained their earlier prominence. New algorithms, coupled with the power of fast computers, have led to both theoretical advances and interesting applications, for example in robotics and in geometric theorem proving. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and correctness, this third edition of Ideals, Varieties and Algorithms includes: A significantly updated section on Maple in Appendix C; Updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; A shorter proof of the Extension Theorem presented in Section 6 of Chapter 3. From the 2nd Edition: "I consider the book to be wonderful.... The exposition is very clear, there are many helpful pictures, and there are a great many instructive exercises, some quite challenging... offers the heart and soul of modern commutative and algebraic geometry." -The American Mathematical Monthly

Nonlinear Hyperbolic Problems: Proceedings of an Advanced

ISBN: , SKU: , AUTHOR: Carasso, Claude / Charrier, Pierre / Hanouzet, Bernard, PUBLISHER: Springer, The papers included in this proceedings volume are mostly original research papers, dealing with life-span of waves, nonlinear interaction of waves, and various applications to fluid mechanics.

Riemannian Geometry

ISBN: , SKU: , AUTHOR: Gallot, S., PUBLISHER: Springer, This book covers the topics of differential manifolds, Riemannian metrics, connections, geodesics and curvature, with special emphasis on the intrinsic features of the subject. It treats in detail classical results on the relations between curvature and topology. The book features numerous exercises with full solutions and a series of detailed examples are picked up repeatedly to illustrate each new definition or property introduced.

Approximation and Optimization of Discrete and Differential

ISBN: , SKU: , AUTHOR: Elimhan N Mahmudov, PUBLISHER: Elsevier, NA

Nonlinear Optimization with Engineering Applications

ISBN: , SKU: , AUTHOR: Bartholomew-Biggs, Michael, PUBLISHER: Springer, This textbook examines a broad range of problems in science and engineering, describing key numerical methods applied to real life. The case studies presented are in such areas as data fitting, vehicle route planning and optimal control, scheduling and resource allocation, sensitivity calculations and worst-case analysis. Chapters are self-contained with exercises provided at the end of most sections. Nonlinear Optimization with Engineering Applications is ideal for self-study and classroom use in engineering courses at the senior undergraduate or graduate level. The book will also appeal to postdocs and advanced researchers interested in the development and use of optimization algorithms.

Monte Carlo Methods, Basics

ISBN: , SKU: , AUTHOR: Kalos, Malvin H. / Whitlock, Paula A., PUBLISHER: Wiley-VCH Verlag GmbH, This introduction to Monte Carlo Methods seeks to identify and study the unifying elements that underlie their effective application. It focuses on two basic themes. The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modelling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on that example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrodinger equation by random walks. The detailed discussion of variance reduction includes Monte Carlo evaluation of finite-dimensional integrals. Special attention is given to importance sampling, partly because of its intrinsic interest in quadrature, partly because of its general usefulness in the solution of integral equations. One significant feature is that Monte Carlo Methods treats the "Metropolis algorithm" in the context of sampling methods, clearly distinguishing it from importance sampling. Physicists, chemists, statisticians, mathematicians, and computer scientists will find Monte Carlo Methods a complete and stimulating introduction.

61 Cooperative Learning Activities for Geometry Classes

ISBN: , SKU: , AUTHOR: Jenkins, Bob, PUBLISHER: Walch Education, Explores key concepts including angles, perimeter, 3-dimensional geometry, triangles, and more. Demonstrates how each activity correlates with the NCTM Standards.

Optimization and Dynamical Systems

ISBN: , SKU: , AUTHOR: Moore, John B. / Brockett, R. / Helmke, Uwe, PUBLISHER: Springer, This study addresses both classical and previously unsolved optimization tasks in linear algebra, linear systems theory, control theory and signal processing. Exploiting developments in Computation such as Parallel Computing and Neural Networks, it gives a dynamical systems approach for tackling a wide class of constrained optimization tasks. Optimization and Dynamical Systems will be of interest to engineers and mathematicians. Engineers will learn the mathematics and the technical approach necessary to solve a wide class of constrained optimization tasks. Mathematicians will see how techniques from global analysis and differential geometry can be developed to achieve useful construction procedures for optimization on manifolds.

The Pullback Equation for Differential Forms

ISBN: , SKU: , AUTHOR: Csat, Gyula / Dacorogna, Bernard / Kneuss, Olivier, PUBLISHER: Birkhauser Boston, An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map so that it satisfies the pullback equation: *(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 k n 1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge Morrey decomposition and to give several versions of the Poincar lemma. The core of the book discusses the case k = n, and then the case 1 k n 1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses H lder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on H lder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.

Stable Adaptive Control and Estimation for Nonlinear

ISBN: , SKU: , AUTHOR: Spooner, Jeffrey T. / Maggiore, Manfredi / Ordó Ñ EZ, Raú L., PUBLISHER: Wiley-Interscience, Includes a solution manual for problems. Provides MATLAB code for examples and solutions. Deals with robust systems in both theory and practice.

Multidimensional Integral Equations and Inequalities

ISBN: , SKU: , AUTHOR: Pachpatte, B. G., PUBLISHER: Atlantis Press, Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.

Brain Benders, Intermediate: Challenging Puzzles and Games

ISBN: , SKU: , AUTHOR: Publishing, Carson Dellosa / Rainbow Bridge Publishing, PUBLISHER: Rainbow Bridge Publishing (UT), Math and language arts skills are covered through critical thinking, creative problem solving, and deductive reasoning. Perfect at home or in school, these puzzles will tease and boggle puzzle-loving brains Activities include logic problems, analogies, word equations, number games, and more

Quantum-Classical Correspondence: Dynamical Quantization and

ISBN: , SKU: , AUTHOR: Bolitschek, Josef, PUBLISHER: Springer, At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entree to an intriguing and thorny issue at the core of modern physics.

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