Ebook: Computational Methods for Physicists: Compendium for Students

This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.

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This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.

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This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.
Content:
Front Matter....Pages I-XX
Basics of Numerical Analysis....Pages 1-55
Solving Non-linear Equations....Pages 57-108
Matrix Methods....Pages 109-157
Transformations of Functions and Signals....Pages 159-205
Statistical Analysis and Modeling of Data....Pages 207-275
Modeling and Analysis of Time Series....Pages 277-333
Initial-Value Problems for ODE....Pages 335-400
Boundary-Value Problems for ODE....Pages 401-465
Difference Methods for One-Dimensional PDE....Pages 467-517
Difference Methods for PDE in Several Dimensions....Pages 519-573
Spectral Methods for PDE....Pages 575-620
Back Matter....Pages 621-715

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This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.
Content:
Front Matter....Pages I-XX
Basics of Numerical Analysis....Pages 1-55
Solving Non-linear Equations....Pages 57-108
Matrix Methods....Pages 109-157
Transformations of Functions and Signals....Pages 159-205
Statistical Analysis and Modeling of Data....Pages 207-275
Modeling and Analysis of Time Series....Pages 277-333
Initial-Value Problems for ODE....Pages 335-400
Boundary-Value Problems for ODE....Pages 401-465
Difference Methods for One-Dimensional PDE....Pages 467-517
Difference Methods for PDE in Several Dimensions....Pages 519-573
Spectral Methods for PDE....Pages 575-620
Back Matter....Pages 621-715
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