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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.

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.

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.

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 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 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 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.

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.

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.

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 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.

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.

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.

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.