Tao Tang

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.

Unique and authoritative reference combining concepts, theories, and hands-on analysis in the ArcGIS Pro software environment Fundamentals of Geographic Information Systems (GIS) Analysis bridges the gap between academic discussions and research with public and private professional practices in the field. The book discusses and illustrates essential concepts and theories, with tutorials showing students how to conduct hands-on analysis in the ArcGIS Pro software environment. Supplementary material for this text includes data files for the tutorials and students exercises. All datasets are sourced from public domains, including the US Census Bureau data, the New York State ITS Geospatial Services (https://data.gis.ny.gov/), the New York State Department of Environmental Conservation (NYSDEC), the GIS Services of Erie County New York, and others. Written by a highly qualified academic, the book covers topics such as: Digital data models representing geographic information, including vector, raster, and 3D modelsMethods of spatial data input in vector and raster data formats to incorporate geographic features and events with their attribute dataGeographic data collections in natural sciences, engineering, and social sciences, and relational, spatial, and structural querying of a databaseCoordinate systems, map projection, geo-referencing, geographic analyses, and internet-enabled geographic information sharingSpatial interpolation and spatial statistical analysis, network analysis, digital mapping, and map presentations Uniquely combining academic research and discussions with professional practices in the software and data analysis environments, Fundamentals of Geographic Information Systems (GIS) Analysis is an essential reference for GIS analysts and technicians, urban planners, civil engineers, and computer scientists, along with students in related programs of study.

This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB® codes, all available online.

This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB® codes, all available online.