The provided text is the preface and table of contents for the book "Numerical Partial Differential Equations: Finite Difference Methods" by J.W. Thomas, published by Springer Science+Business Media, LLC. The book is part of the "Texts in Applied Mathematics" series, edited by J.E. Marsden, L. Sirovich, M. Golubitsky, W. Jäger, and F. John (deceased), with G. Iooss as the advisor. The book is divided into two parts: the first part covers finite difference methods for time-dependent equations, including parabolic and hyperbolic problems, multi-dimensional problems, systems, and dissipation and dispersion. The second part focuses on conservation laws and elliptic equations, including stability theory for initial-boundary value problems, numerical schemes for conservation laws, numerical solution of elliptic problems, and irregular regions and grids. Key features of the book include: - Emphasis on both theoretical and computational aspects of numerical methods. - Implementation of schemes through homework problems and computational interludes. - Discussion of convergence, consistency, and stability in computational space. - Use of symbolic computing and graphics for analysis. - Historical context and background on the development of numerical methods. The book aims to prepare graduate students in applied mathematics and engineering to solve a wide range of problems, evaluate numerical results, and understand the limitations of numerical methods. It also serves as a reference for students and researchers in the field.The provided text is the preface and table of contents for the book "Numerical Partial Differential Equations: Finite Difference Methods" by J.W. Thomas, published by Springer Science+Business Media, LLC. The book is part of the "Texts in Applied Mathematics" series, edited by J.E. Marsden, L. Sirovich, M. Golubitsky, W. Jäger, and F. John (deceased), with G. Iooss as the advisor. The book is divided into two parts: the first part covers finite difference methods for time-dependent equations, including parabolic and hyperbolic problems, multi-dimensional problems, systems, and dissipation and dispersion. The second part focuses on conservation laws and elliptic equations, including stability theory for initial-boundary value problems, numerical schemes for conservation laws, numerical solution of elliptic problems, and irregular regions and grids. Key features of the book include: - Emphasis on both theoretical and computational aspects of numerical methods. - Implementation of schemes through homework problems and computational interludes. - Discussion of convergence, consistency, and stability in computational space. - Use of symbolic computing and graphics for analysis. - Historical context and background on the development of numerical methods. The book aims to prepare graduate students in applied mathematics and engineering to solve a wide range of problems, evaluate numerical results, and understand the limitations of numerical methods. It also serves as a reference for students and researchers in the field.