This excellent text for advanced undergraduate and graduate students covers norms, numerical solutions of linear systems and matrix factoring, eigenvalues and eigenvectors, polynomial approximation, and more. Many examples and problems. 1966 edition.
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.
In its expanded new edition, this book covers boundary layers, multiple scales, homogenisation, slender body theory, symbolic computing, discrete equations and more. Includes exercises derived from current research, drawn from a range of application areas.
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. It formalizes basic tools that are commonly used by researchers in the field but not previously published. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests. For example, courses can emphasize physical applications, or algorithmic efficiency and code development issues, or the more difficult convergence theorems of the subject. This new edition is substantially updated with additional exercises throughout and new chapters on Additive Schwarz Preconditioners and Adaptive Meshes. Review of earlier edition: This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference. Mathematical Reviews, 1995
This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively. Many standard results are proved, including the classical theorems of van der Waerden, Hindman, and Szemerédi. More importantly, the presentation strives to reflect the extent to which the field has been streamlined since breaking onto the scene around twenty years ago. Potential readers who were previously intrigued by the subject matter but found it daunting may want to give a second look.
This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 comput er-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Dieses Lehrbuch erleichtert den Einstieg in die Hochschulmathematik. Mit dem prägnanten Stil, dem klaren, systematischen Aufbau und mit Verständnis für die Schwierigkeiten des Anfängers wird eine solide Grundlage für das Studium geschaffen. Zunächst werden die grundlegenden Inhalte und Methoden der Analysis mit maßvoller Abstraktion dargestellt und an Hand von vielen sorgfältig durchgerechneten Beispielen illustriert. Ausführlich wird auf Reihenentwicklungen eingegangen, da sie eine entscheidende Rolle für das Verständnis der Analysis spielen. Wichtige Themen, die ebenfalls zum Verständnis nötig sind, die aber nicht zur reellen Analysis einer Variablen gehören, werden in Steilkursen im Anhang behandelt: Dazu gehören die Mengenlehre, der konstruktive Aufbau des Zahlensystems und die komplexen Zahlen. So dient das Buch durch seinen Blick für das Wesentliche den Studierenden auch als ständiger Begleiter während des ganzen weiteren Studiums.