Mathematical Foundations Of Computational Engineering
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Author | : Peter J. Pahl |
Publisher | : Springer Science & Business Media |
Total Pages | : 1022 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 3642568939 |
Computational engineering is the treatment of engineering tasks with computers. It is based on computational mathematics, which is presented here in a comprehensive handbook. From the existing rich repertoire of mathematical theories and methods, the fundamentals of engineering computation are here presented in a coherent fashion. They are brought into a suitable order for specific engineering purposes, and their significance for typical applications shown. The relevant definitions, notations and theories are presented in a durable form which is independent of the fast development of information and communication technology.
Author | : Franck Assous |
Publisher | : Springer |
Total Pages | : 460 |
Release | : 2018-06-09 |
Genre | : Mathematics |
ISBN | : 3319708422 |
This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
Author | : Xin-she Yang |
Publisher | : World Scientific Publishing Company |
Total Pages | : 342 |
Release | : 2014-11-26 |
Genre | : Mathematics |
ISBN | : 9814635804 |
This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of contemporary numerical algorithms, scientific computing and optimization. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. This edition covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithm, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, nonlinear curve-fitting to data modelling, bio-inspired algorithms and swarm intelligence. This book is especially suitable for both undergraduates and graduates in computational mathematics, numerical algorithms, scientific computing, mathematical programming, artificial intelligence and engineering optimization. Thus, it can be used as a textbook and/or reference book.
Author | : Ronald A. DeVore |
Publisher | : Cambridge University Press |
Total Pages | : 418 |
Release | : 2001-05-17 |
Genre | : Mathematics |
ISBN | : 9780521003490 |
Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Author | : Dietmar Hildenbrand |
Publisher | : Springer Science & Business Media |
Total Pages | : 217 |
Release | : 2012-12-31 |
Genre | : Computers |
ISBN | : 3642317944 |
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technology is driven by the invention of conformal geometric algebra as a 5D extension of the 4D projective geometric algebra and by the recent progress in parallel processing, and with the specific conformal geometric algebra there is a growing community in recent years applying geometric algebra to applications in computer vision, computer graphics, and robotics. This book is organized into three parts: in Part I the author focuses on the mathematical foundations; in Part II he explains the interactive handling of geometric algebra; and in Part III he deals with computing technology for high-performance implementations based on geometric algebra as a domain-specific language in standard programming languages such as C++ and OpenCL. The book is written in a tutorial style and readers should gain experience with the associated freely available software packages and applications. The book is suitable for students, engineers, and researchers in computer science, computational engineering, and mathematics.
Author | : Jerrold E. Marsden |
Publisher | : Courier Corporation |
Total Pages | : 578 |
Release | : 2012-10-25 |
Genre | : Technology & Engineering |
ISBN | : 0486142272 |
Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.
Author | : Carol Critchlow |
Publisher | : |
Total Pages | : 256 |
Release | : 2011 |
Genre | : Computers |
ISBN | : |
Foundations of Computation is a free textbook for a one-semester course in theoretical computer science. It has been used for several years in a course at Hobart and William Smith Colleges. The course has no prerequisites other than introductory computer programming. The first half of the course covers material on logic, sets, and functions that would often be taught in a course in discrete mathematics. The second part covers material on automata, formal languages and grammar that would ordinarily be encountered in an upper level course in theoretical computer science.
Author | : Einar Smith |
Publisher | : Springer Nature |
Total Pages | : 344 |
Release | : 2020-12-02 |
Genre | : Mathematics |
ISBN | : 3030608085 |
The book provides an introduction to common programming tools and methods in numerical mathematics and scientific computing. Unlike widely used standard approaches, it does not focus on any particular language but aims to explain the key underlying concepts. In general, new concepts are first introduced in the particularly user-friendly Python language and then transferred and expanded in various scientific programming environments from C / C ++, Julia and MATLAB to Maple. This includes different approaches to distributed computing. The fact that different languages are studied and compared also makes the book useful for mathematicians and practitioners trying to decide which programming language to use for which purposes.
Author | : Robert M. Stark |
Publisher | : Courier Corporation |
Total Pages | : 609 |
Release | : 2005-01-05 |
Genre | : Mathematics |
ISBN | : 0486438988 |
Text develops typical mathematical techniques of operations research and systems engineering and applies them to design and operation of civil engineering systems. Solutions to selected problems; solution guide available upon request. 1972 edition.
Author | : Y. N. Singh |
Publisher | : New Age International |
Total Pages | : 24 |
Release | : 2005 |
Genre | : Mathematics |
ISBN | : 8122416675 |
The Interesting Feature Of This Book Is Its Organization And Structure. That Consists Of Systematizing Of The Definitions, Methods, And Results That Something Resembling A Theory. Simplicity, Clarity, And Precision Of Mathematical Language Makes Theoretical Topics More Appealing To The Readers Who Are Of Mathematical Or Non-Mathematical Background. For Quick References And Immediate Attentions3⁄4Concepts And Definitions, Methods And Theorems, And Key Notes Are Presented Through Highlighted Points From Beginning To End. Whenever, Necessary And Probable A Visual Approach Of Presentation Is Used. The Amalgamation Of Text And Figures Make Mathematical Rigors Easier To Understand. Each Chapter Begins With The Detailed Contents, Which Are Discussed Inside The Chapter And Conclude With A Summary Of The Material Covered In The Chapter. Summary Provides A Brief Overview Of All The Topics Covered In The Chapter. To Demonstrate The Principles Better, The Applicability Of The Concepts Discussed In Each Topic Are Illustrated By Several Examples Followed By The Practice Sets Or Exercises.