Advanced Topics in Computational Partial Differential Equations

Advanced Topics in Computational Partial Differential Equations
Numerical Methods and Diffpack Programming

by Hans Petter Langtangen,Aslak Tveito

  • Publisher : Springer Science & Business Media
  • Release : 2003-10-29
  • Pages : 663
  • ISBN : 9783540014386
  • Language : En, Es, Fr & De
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A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Numerical Analysis Using MATLAB and Excel

Numerical Analysis Using MATLAB and Excel
A Book

by Steven T. Karris

  • Publisher : Orchard Publications
  • Release : 2007
  • Pages : 632
  • ISBN : 1934404039
  • Language : En, Es, Fr & De
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This text is written primarily for students/readers who have a good background of high-school algebra, geometry, trigonometry, and the fundamentals of differential and integral calculus.

Introduction to Numerical Analysis

Introduction to Numerical Analysis
A Book

by Francis Begnaud Hildebrand

  • Publisher : Courier Corporation
  • Release : 1987
  • Pages : 669
  • ISBN : 0486653633
  • Language : En, Es, Fr & De
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The ultimate aim of the field of numerical analysis is to provide convenient methods for obtaining useful solutions to mathematical problems and for extracting useful information from available solutions which are not expressed in tractable forms. This well-known, highly respected volume provides an introduction to the fundamental processes of numerical analysis, including substantial grounding in the basic operations of computation, approximation, interpolation, numerical differentiation and integration, and the numerical solution of equations, as well as in applications to such processes as the smoothing of data, the numerical summation of series, and the numerical solution of ordinary differential equations. Chapter headings include: l. Introduction 2. Interpolation with Divided Differences 3. Lagrangian Methods 4. Finite-Difference Interpolation 5. Operations with Finite Differences 6. Numerical Solution of Differential Equations 7. Least-Squares Polynomial Approximation In this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. This new material includes discussions of machine errors and recursive calculation, increased emphasis on the midpoint rule and the consideration of Romberg integration and the classical Filon integration; a modified treatment of prediction-correction methods and the addition of Hamming's method, and numerous other important topics. In addition, reference lists have been expanded and updated, and more than 150 new problems have been added. Widely considered the classic book in the field, Hildebrand's Introduction to Numerical Analysis is aimed at advanced undergraduate and graduate students, or the general reader in search of a strong, clear introduction to the theory and analysis of numbers.

Advanced Calculus

Advanced Calculus
An Introduction to Modern Analysis

by Voxman

  • Publisher : CRC Press
  • Release : 1981-03-01
  • Pages : 696
  • ISBN : 9780824769499
  • Language : En, Es, Fr & De
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Advanced Calculus: An Introduction to Modem Analysis, an advanced undergraduate textbook,provides mathematics majors, as well as students who need mathematics in their field of study,with an introduction to the theory and applications of elementary analysis. The text presents, inan accessible form, a carefully maintained balance between abstract concepts and applied results ofsignificance that serves to bridge the gap between the two- or three-cemester calculus sequence andsenior/graduate level courses in the theory and appplications of ordinary and partial differentialequations, complex variables, numerical methods, and measure and integration theory.The book focuses on topological concepts, such as compactness, connectedness, and metric spaces,and topics from analysis including Fourier series, numerical analysis, complex integration, generalizedfunctions, and Fourier and Laplace transforms. Applications from genetics, spring systems,enzyme transfer, and a thorough introduction to the classical vibrating string, heat transfer, andbrachistochrone problems illustrate this book's usefulness to the non-mathematics major. Extensiveproblem sets found throughout the book test the student's understanding of the topics andhelp develop the student's ability to handle more abstract mathematical ideas.Advanced Calculus: An Introduction to Modem Analysis is intended for junior- and senior-levelundergraduate students in mathematics, biology, engineering, physics, and other related disciplines.An excellent textbook for a one-year course in advanced calculus, the methods employed in thistext will increase students' mathematical maturity and prepare them solidly for senior/graduatelevel topics. The wealth of materials in the text allows the instructor to select topics that are ofspecial interest to the student. A two- or three ll?lester calculus sequence is required for successfuluse of this book.

Introduction To Numerical Computation, An (Second Edition)

Introduction To Numerical Computation, An (Second Edition)
A Book

by Wen Shen

  • Publisher : World Scientific
  • Release : 2019-08-28
  • Pages : 340
  • ISBN : 9811204438
  • Language : En, Es, Fr & De
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This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.The book covers many of the introductory topics for a first course in numerical computation, which fits in the short time frame of a semester course. Topics range from polynomial approximations and interpolation, to numerical methods for ODEs and PDEs. Emphasis was made more on algorithm development, basic mathematical ideas behind the algorithms, and the implementation in Matlab.The book is supplemented by two sets of videos, available through the author's YouTube channel. Homework problem sets are provided for each chapter, and complete answer sets are available for instructors upon request.The second edition contains a set of selected advanced topics, written in a self-contained manner, suitable for self-learning or as additional material for an honored version of the course. Videos are also available for these added topics.

Numerical Analysis

Numerical Analysis
Mathematics of Scientific Computing

by David Ronald Kincaid,Elliott Ward Cheney

  • Publisher : American Mathematical Soc.
  • Release : 2002
  • Pages : 788
  • ISBN : 0821847880
  • Language : En, Es, Fr & De
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This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.

Numerical Analysis: Pearson New International Edition

Numerical Analysis: Pearson New International Edition
A Book

by Timothy Sauer

  • Publisher : Pearson Higher Ed
  • Release : 2013-08-28
  • Pages : 612
  • ISBN : 1292036745
  • Language : En, Es, Fr & De
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Numerical Analysis, Second Edition, is a modern and readable text for the undergraduate audience. This book covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers—topics such as compression, forward and backward error analysis, and iterative methods of solving equations—all while maintaining a level of discussion appropriate for undergraduates. Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB® is used throughout to demonstrate and implement numerical methods. The Second Edition features many noteworthy improvements based on feedback from users, such as new coverage of Cholesky factorization, GMRES methods, and nonlinear PDEs.

Numerical Analysis for Statisticians

Numerical Analysis for Statisticians
A Book

by Kenneth Lange

  • Publisher : Springer Science & Business Media
  • Release : 2010-06-15
  • Pages : 600
  • ISBN : 1441959440
  • Language : En, Es, Fr & De
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Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Numerical Methods for Energy Applications

Numerical Methods for Energy Applications
A Book

by Naser Mahdavi Tabatabaei,Nicu Bizon

  • Publisher : Springer Nature
  • Release : 2021-07-03
  • Pages : 1028
  • ISBN : 303062191X
  • Language : En, Es, Fr & De
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This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including: • a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption. This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.

Numerical Analysis

Numerical Analysis
A Book

by Timothy Sauer

  • Publisher : Unknown Publisher
  • Release : 2013-07-26
  • Pages : 608
  • ISBN : 9781292023588
  • Language : En, Es, Fr & De
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Numerical Analysis, Second Edition, is a modern and readable text for the undergraduate audience. This book covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers-topics such as compression, forward and backward error analysis, and iterative methods of solving equations-all while maintaining a level of discussion appropriate for undergraduates. Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB(r) is used throughout to demonstrate and implement numerical methods. The Second Edition features many noteworthy improvements based on feedback from users, such as new coverage of Cholesky factorization, GMRES methods, and nonlinear PDEs.

Analysis for Computer Scientists

Analysis for Computer Scientists
Foundations, Methods, and Algorithms

by Michael Oberguggenberger,Alexander Ostermann

  • Publisher : Springer
  • Release : 2018-11-06
  • Pages : 378
  • ISBN : 9783319911540
  • Language : En, Es, Fr & De
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This easy-to-follow textbook/reference presents a concise introduction to mathematical analysis from an algorithmic point of view, with a particular focus on applications of analysis and aspects of mathematical modelling. The text describes the mathematical theory alongside the basic concepts and methods of numerical analysis, enriched by computer experiments using MATLAB, Python, Maple, and Java applets. This fully updated and expanded new edition also features an even greater number of programming exercises. Topics and features: describes the fundamental concepts in analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives, integrals, and curves; discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes added material on hyperbolic functions, curves and surfaces in space, second-order differential equations, and the pendulum equation (NEW); contains experiments, exercises, definitions, and propositions throughout the text; supplies programming examples in Python, in addition to MATLAB (NEW); provides supplementary resources at an associated website, including Java applets, code source files, and links to interactive online learning material. Addressing the core needs of computer science students and researchers, this clearly written textbook is an essential resource for undergraduate-level courses on numerical analysis, and an ideal self-study tool for professionals seeking to enhance their analysis skills.

Numerical Analysis and Its Applications

Numerical Analysis and Its Applications
6th International Conference, NAA 2016, Lozenetz, Bulgaria, June 15-22, 2016, Revised Selected Papers

by Ivan Dimov,István Faragó,Lubin Vulkov

  • Publisher : Springer
  • Release : 2017-04-12
  • Pages : 785
  • ISBN : 9783319570983
  • Language : En, Es, Fr & De
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This book constitutes thoroughly revised selected papers of the 6th International Conference on Numerical Analysis and Its Applications, NAA 2016, held in Lozenetz, Bulgaria, in June 2016. The 90 revised papers presented were carefully reviewed and selected from 98 submissions. The conference offers a wide range of the following topics: Numerical Modeling; Numerical Stochastics; Numerical Approx-imation and Computational Geometry; Numerical Linear Algebra and Numer-ical Solution of Transcendental Equations; Numerical Methods for Differential Equations; High Performance Scientific Computing; and also special topics such as Novel methods in computational finance based on the FP7 Marie Curie Action,Project Multi-ITN STRIKE - Novel Methods in Compu-tational Finance, Grant Agreement Number 304617; Advanced numerical and applied studies of fractional differential equations.

Numerical Analysis

Numerical Analysis
A Book

by Walter Gautschi

  • Publisher : Birkhäuser
  • Release : 2011-12-08
  • Pages : 588
  • ISBN : 9780817682583
  • Language : En, Es, Fr & De
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Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

Fundamentals of Structural Dynamics

Fundamentals of Structural Dynamics
A Book

by Roy R. Craig,Andrew J. Kurdila

  • Publisher : John Wiley & Sons
  • Release : 2011-08-24
  • Pages : 744
  • ISBN : 1118174445
  • Language : En, Es, Fr & De
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From theory and fundamentals to the latest advances in computational and experimental modal analysis, this is the definitive, updated reference on structural dynamics. This edition updates Professor Craig's classic introduction to structural dynamics, which has been an invaluable resource for practicing engineers and a textbook for undergraduate and graduate courses in vibrations and/or structural dynamics. Along with comprehensive coverage of structural dynamics fundamentals, finite-element-based computational methods, and dynamic testing methods, this Second Edition includes new and expanded coverage of computational methods, as well as introductions to more advanced topics, including experimental modal analysis and "active structures." With a systematic approach, it presents solution techniques that apply to various engineering disciplines. It discusses single degree-of-freedom (SDOF) systems, multiple degrees-of-freedom (MDOF) systems, and continuous systems in depth; and includes numeric evaluation of modes and frequency of MDOF systems; direct integration methods for dynamic response of SDOF systems and MDOF systems; and component mode synthesis. Numerous illustrative examples help engineers apply the techniques and methods to challenges they face in the real world. MATLAB(r) is extensively used throughout the book, and many of the .m-files are made available on the book's Web site. Fundamentals of Structural Dynamics, Second Edition is an indispensable reference and "refresher course" for engineering professionals; and a textbook for seniors or graduate students in mechanical engineering, civil engineering, engineering mechanics, or aerospace engineering.

Advanced Numerical Applications and Plasticity in Geomechanics

Advanced Numerical Applications and Plasticity in Geomechanics
A Book

by Vaughan D. Griffiths,Giancarlo Gioda

  • Publisher : Springer Science & Business Media
  • Release : 2001-07-19
  • Pages : 333
  • ISBN : 9783211833377
  • Language : En, Es, Fr & De
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Numerical application of Plasticity to Geomechanics is an area of research that has grown rapidly since its origins in the late 1960s. This growth led to new methodologies and analysis approaches that are nowadays commonly employed in Geotechnical Engineering practice. Through the contribution of well-known scholars this book intends to provide an updated overview of some relevant developments and applications in this field. The topics covered in the various chapters of the volume can be summarised as follows: constitutive models for geomaterials, "damage soil mechanics, non-linear consolidation, swelling soils, influence of the statistical variability of soil properties on the stability of slopes and foundations, numerical analysis of ground improvement techniques, tunneling problems.

Introduction to Optimum Design

Introduction to Optimum Design
A Book

by Jasbir S. Arora

  • Publisher : Academic Press
  • Release : 2011
  • Pages : 880
  • ISBN : 0123813751
  • Language : En, Es, Fr & De
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Introduction to Optimum Design is the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level within engineering departments of all disciplines, but primarily within mechanical, aerospace and civil engineering. The basic approach of the text is to describe an organized approach to engineering design optimization in a rigorous yet simplified manner, illustrate various concepts and procedures with simple examples, and demonstrate their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB are featured throughout as learning and teaching aids. The 3rd edition has been reorganized and enhanced with new material, making the book even more appealing to instructors regardless of the level they teach the course. Examples include moving the introductory chapter on Excel and MATLAB closer to the front of the book and adding an early chapter on practical design examples for the more introductory course, and including a final chapter on advanced topics for the purely graduate level course. Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable. Applications of the methods for structural, mechanical, aerospace and industrial engineering problems. Introduction to MATLAB Optimization Toolbox. Optimum design with Excel Solver has been expanded into a full chapter. Practical design examples introduce students to usage of optimization methods early in the book. New material on several advanced optimum design topics serves the needs of instructors teaching more advanced courses.

An Introduction to Computational Physics

An Introduction to Computational Physics
A Book

by Tao Pang

  • Publisher : Cambridge University Press
  • Release : 1997-09-28
  • Pages : 392
  • ISBN : 9780521481434
  • Language : En, Es, Fr & De
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This advanced textbook provides an introduction to the basic methods of computational physics, as well as an overview of recent progress in several areas of scientific computing. The author presents many step-by-step examples of practical numerical methods, often with the relevant program listing. The first half of the book deals with basic computational tools and routines, covering differential equations, spectral analysis and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as Monte Carlo simulations, lattice gas methods, molecular dynamics and symbolic computing. The book includes many exercises, and it can be used as a textbook for senior undergraduate or first-year graduate courses on scientific computation. It will also be a useful reference for anyone involved in computational physics or related disciplines.

Applied Statistical Inference

Applied Statistical Inference
Likelihood and Bayes

by Leonhard Held,Daniel Sabanés Bové

  • Publisher : Springer Science & Business Media
  • Release : 2013-11-12
  • Pages : 376
  • ISBN : 3642378870
  • Language : En, Es, Fr & De
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This book covers modern statistical inference based on likelihood with applications in medicine, epidemiology and biology. Two introductory chapters discuss the importance of statistical models in applied quantitative research and the central role of the likelihood function. The rest of the book is divided into three parts. The first describes likelihood-based inference from a frequentist viewpoint. Properties of the maximum likelihood estimate, the score function, the likelihood ratio and the Wald statistic are discussed in detail. In the second part, likelihood is combined with prior information to perform Bayesian inference. Topics include Bayesian updating, conjugate and reference priors, Bayesian point and interval estimates, Bayesian asymptotics and empirical Bayes methods. Modern numerical techniques for Bayesian inference are described in a separate chapter. Finally two more advanced topics, model choice and prediction, are discussed both from a frequentist and a Bayesian perspective. A comprehensive appendix covers the necessary prerequisites in probability theory, matrix algebra, mathematical calculus, and numerical analysis.

Mathematical Reviews

Mathematical Reviews
A Book

by Anonim

  • Publisher : Unknown Publisher
  • Release : 2007
  • Pages : 329
  • ISBN : 9876543210XXX
  • Language : En, Es, Fr & De
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Numerical Methods for Engineers

Numerical Methods for Engineers
A Book

by Santosh K Gupta

  • Publisher : New Age International
  • Release : 1995
  • Pages : 407
  • ISBN : 9788122406511
  • Language : En, Es, Fr & De
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This Book Is Intended To Be A Text For Either A First Or A Second Course In Numerical Methods For Students In All Engineering Disciplines. Difficult Concepts, Which Usually Pose Problems To Students Are Explained In Detail And Illustrated With Solved Examples. Enough Elementary Material That Could Be Covered In The First-Level Course Is Included, For Example, Methods For Solving Linear And Nonlinear Algebraic Equations, Interpolation, Differentiation, Integration, And Simple Techniques For Integrating Odes And Pdes (Ordinary And Partial Differential Equations).Advanced Techniques And Concepts That Could Form Part Of A Second-Level Course Includegears Method For Solving Ode-Ivps (Initial Value Problems), Stiffness Of Ode- Ivps, Multiplicity Of Solutions, Convergence Characteristics, The Orthogonal Collocation Method For Solving Ode-Bvps (Boundary Value Problems) And Finite Element Techniques. An Extensive Set Of Graded Problems, Often With Hints, Has Been Included.Some Involve Simple Applications Of The Concepts And Can Be Solved Using A Calculator, While Several Are From Real-Life Situations And Require Writing Computer Programs Or Use Of Library Subroutines. Practice On These Is Expected To Build Up The Reader'S Confidence In Developing Large Computer Codes.