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The Finite Difference Method in Partial Differential Equations
Extensively revised edition of Computational Methods in Partial Differential Equations. A more general approach has been adopted for the splitting of operators for parabolic and hyperbolic equations to include Richtmyer and Strang type splittings in addition to alternating direction implicit and locally one dimensional methods. A description of the now standard factorization and SOR/ADI iterative techniques for solving elliptic difference equations has been supplemented with an account or preconditioned conjugate gradient methods which are currently gaining in popularity. Prominence is also given to the Galerkin method using different test and trial functions as a means of constructing difference approximations to both elliptic and time dependent problems. The applications of finite difference methods have been revised and contain examples involving the treatment of singularities in elliptic equations, free and moving boundary problems, as well as modern developments in computational fluid dynamics. Emphasis throughout is on clear exposition of the construction and solution of difference equations. Material is reinforced with theoretical results when appropriate.
Introduction to Quantum Mechanics
Changes and additions to the new edition of this classic textbook include a new chapter on symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, and consolidated treatment of time-dependent potentials.
Introduction to Electrodynamics
This is a re-issued and affordable printing of the widely used undergraduate electrodynamics textbook.
Numerical Methods for Ordinary Differential Equations
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exerci...
The Finite Element Method
Designed for students without in-depth mathematical training, this text includes a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories. Solution guide available upon request.
Introduction to Quantum Mechanics
This bestselling textbook teaches students how to do quantum mechanics and provides an insightful discussion of what it actually means.
Dynamical Systems and Numerical Analysis
The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined.
Learning LaTeX
Here is a short, well-written book that covers the material essential for learning LaTeX. This manual includes the following crucial features: - numerous examples of widely used mathematical expressions; - complete documents illustrating the creation of articles, reports, presentations, and posters; - troubleshooting tips to help you pinpoint an error; - details of how to set up an index and a bibliography; and - information about online LaTeX resources. This second edition of the well-regarded and highly successful book includes additional material on - the American Mathematical Society packages for typesetting additional mathematical symbols and multi-line displays; - the BiBTeX program for creating bibliographies; - the Beamer package for creating presentations; and - the a0poster class for creating posters.
Proceedings of the Second International Colloquium on Numerical Analysis
The Second International Colloquium on Numerical Analysis was organized by UNESCO and the Plovdiv Technical University, with the help of many international mathematical organizations, and was held in Plovdiv, Bulgaria, 13--17 August 1993. This proceedings volume contains selected invited talks which deal with the following topics: -- numerical methods of algebra -- analysis -- ordinary and partial differential equations
Chaotic Numerics
Much of what is known about specific dynamical systems is obtained from numerical experiments. Although the discretization process usually has no significant effect on the results for simple, well-behaved dynamics, acute sensitivity to changes in initial conditions is a hallmark of chaotic behavior. How confident can one be that the numerical dynamics reflects that of the original system? Do numerically calculated trajectories always shadow a true one? What role does numerical analysis play in the study of dynamical systems? And conversely, can advances in dynamical systems provide new insights into numerical algorithms? These and related issues were the focus of the workshop on Chaotic Numerics, held at Deakin University in Geelong, Australia, in July 1993. The contributions to this book are based on lectures presented during the workshop and provide a broad overview of this area of research.
