A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells´s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths´s period mapping, quadratic transformations, and Kodaira´s vanishing and embedding theorems. Oscar Garcia-Prada´s appendix gives an overview of the developments in the field during the decades since the book appeared.
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.
Addressed to 2nd- and 3rd-year students, this work by a world-famous teacher skillfully spans the pure and applied branches, so that applied aspects gain in rigor while pure mathematics loses none of its dignity. Equally essential as a text, a reference, or simply as a brilliant mathematical exercise. 1971 edition.
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: ´´There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang´s books.´´ --EMS NEWSLETTER
Power your way through ordinary and singular points Understand differential equations through practical tips and examples Do differential equations cause you distress? No worries! This friendly guide explains this intimidating subject in plain English, walking you step by step through all the key concepts -- from linear and separable first order differential equations to higher order equations, power series, and Laplace transforms. You´ll find plenty of examples to increase your problem-solving skills and a variety of helpful definitions and explanations to conquer even the toughest differential equations. Discover how to: * Classify differential equations * Solve with integrating factors * Work with coefficients * Use handy theorems * Have fun with advanced techniques * Apply differential equations in real life
Making Everything Easier! Differential Equations Workbook for Dummies Make sense of these difficult equations Improve your problem-solving skills Practice with clear, concise examples Score higher on standardized tests and exams Steven Holzner, PhD Author, Differential Equations For Dummies Get the confidence and the skills you need to master differential equations! Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you´ll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You´ll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more! The Dummies Workbook Way Quick refresher explanations Step-by-step procedures Hands-on practice exercises Ample workspace to work out problems Tear-out Cheat Sheet A dash of humor and fun Go to Dummies.com(r)for videos, step-by-step photos, how-to articles, or to shop the store! More than 100 problems! Detailed, fully worked-out solutions to problems The inside scoop on first, second, and higher order differential equations A wealth of advanced techniques, including power series
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.