Bøger i Texts in Computational Science and Engineering serien

This text teaches finite element methods and basic finite difference methods from a computational point of view. It emphasizes developing flexible computer programs using the numerical library Diffpack, which is detailed for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow.

After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them.

The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions.

To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; This book provides precisely this type of supporting material for the textbook "Numerical Linear Algebra and Matrix Factorizations," published as Vol.

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms.

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language.

This book presents computer programming as a key method for solving mathematical problems. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.

This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods¿ journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing ¿ making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.

This book is open access under a CC BY 4.0 license. This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods.

This book offers an introduction to the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes. Includes numerous complete, ready-to-run programs in Matlab and Maple.

Now in its fourth edition, this volume collates an array of material on using MATLAB and Octave in science computing, offering hundreds of examples, solved exercises, and programs that will greatly extend the range and abilities of the software's users.

There is much additional software including many versions of the case study as it gets built up and progressively refactored using design patterns. There will be a home web-site for this book which will contain up-to-date information about the software and other aspects of the case study.

This book presents in detail the necessary numerical methods, the theoretical background and foundations and the techniques involved in creating particle models, including linked-cell method, SPME-method, tree codes, amd multipol technique.

The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. It is our goal to teach principles and ideas that carry over from field to field.

Introducing the finite element method as a general computational method for solving partial differential equations approximately, this book goes on to cover important applications including diffusion and transport phenomena, solid and fluid mechanics and more.

There are descriptions of the current algorithms in GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students.

This is the second of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses more advanced topics than volume one, and is largely not a prerequisite for volume three.

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

The goal of this book is to demonstrate how to develop tailored, flexible working environments built from small programs (scripts) written in the easy-to-learn, high-level language Python. The focus is on applications relevant to computational scientists.

This book presents computer programming as a key method for solving mathematical problems. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.

This book is intended for students of computational systems biology with only a limited background in mathematics. The result is not a book on systems biology, but on computational methods in systems biology.

This is the first of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses basic principles of computation, and fundamental numerical algorithms that will serve as basic tools for the subsequent two volumes. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 80 examples, 324 exercises, 77 algorithms, 35 interactive JavaScript programs, 391 references to software programs and 4 case studies. Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in LAPACK, GSLIB and MATLAB. This book could be used for an introductory course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as principles of computer languages or numerical linear algebra.

This book explores the most significant computational methods and the history of their development. It begins with the earliest mathematical / numerical achievements made by the Babylonians and the Greeks, followed by the period beginning in the 16th century. For several centuries the main scientific challenge concerned the mechanics of planetary dynamics, and the book describes the basic numerical methods of that time. In turn, at the end of the Second World War scientific computing took a giant step forward with the advent of electronic computers, which greatly accelerated the development of numerical methods. As a result, scientific computing became established as a third scientific method in addition to the two traditional branches: theory and experimentation. The book traces numerical methods' journey back to their origins and to the people who invented them, while also briefly examining the development of electronic computers over the years. Featuring 163 references and more than 100 figures, many of them portraits or photos of key historical figures, the book provides a unique historical perspective on the general field of scientific computing - making it a valuable resource for all students and professionals interested in the history of numerical analysis and computing, and for a broader readership alike.

Linking the differing techniques deployed in describing space-filling curves to their corresponding algorithms, this book introduces SFCs as tools in scientific computing, focusing in particular on the representation of SFCs and on the resulting algorithms.

This overview conveys the fundamentals of mathematical models, numerical methods and algorithms. Readers will find a tutorial on the most important classes of numerical methods and an introduction to the use of spectral methods as central tools.

The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students.

There are descriptions of the current algorithms in GSLIB and MATLAB. This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students.

This is the second of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses more advanced topics than volume one, and is largely not a prerequisite for volume three.

This textbook provides and introduction to numerical computing and its applications in science and engineering. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used.