Articles by "Numerical Mathematics"

Showing posts with label Numerical Mathematics. Show all posts

Eihab B. M. Bashier ... 348 pages - Publisher: CRC Press; (March, 2020) ... Language: English - ISBN-10: 0367076691 - ISBN-13: 978-0367076696.

Practical Numerical and Scientific Computing with MATLAB and Python concentrates on the practical aspects of numerical analysis and linear and non-linear programming. It discusses the methods for solving different types of mathematical problems using MATLAB and Python. Although the book focuses on the approximation problem rather than on error analysis of mathematical problems, it provides practical ways to calculate errors. The book is divided into three parts, covering topics in numerical linear algebra, methods of interpolation, numerical differentiation and integration, solutions of differential equations, linear and non-linear programming problems, and optimal control problems. This book has the following advantages: It adopts the programming languages, MATLAB and Python, which are widely used among academics, scientists, and engineers, for ease of use and contain many libraries covering many scientific and engineering fields. + It contains topics that are rarely found in other numerical analysis books, such as ill-conditioned linear systems and methods of regularization to stabilize their solutions, nonstandard finite differences methods for solutions of ordinary differential equations, and the computations of the optimal controls. It provides a practical explanation of how to apply these topics using MATLAB and Python. + It discusses software libraries to solve mathematical problems, such as software Gekko, pulp, and pyomo. These libraries use Python for solutions to differential equations and static and dynamic optimization problems. + Most programs in the book can be applied in versions prior to MATLAB 2017b and Python 3.7.4 without the need to modify these programs. This book is aimed at newcomers and middle-level students, as well as members of the scientific community who are interested in solving math problems using MATLAB or Python.

B. S. Grewal ... 1597 pages - Publisher: Mercury Learning and Information; (September, 2018) ... Language: English - AmazonSIN: B07HHJ611G.

This book is intended as an introduction to numerical methods for scientists and engineers. Providing an excellent balance of theoretical and applied topics, it shows the numerical methods used with C, C++, and MATLAB.

Brief Table of Contents: 1: Approximations and Errors in Computation. 2: Solution of Algebraic and Transcendental Equations. 3: Solution of Simultaneous Algebraic Equations. 4: Matrix Inversion and the Eigenvalue Problem. 5: Empirical Laws and Curve-Fitting. 6: Finite Differences. 7: Interpolation. 8: Numerical Differentiation and Integration. 9: Difference Equations. 10: Numerical Solution of Ordinary Differential Equations. 11: Numerical Solution of Partial Differential Equations. 12: Linear Programming. 13: A Brief Review of Computers. 14: Numerical Methods Using C. 15: Numerical Methods Using C++. 16: Numerical Methods Using MATLAB. Appendix A: Useful Information. Appendix B: Answers to Exercises. Appendix C: Bibliography. Index.

Daniel Dubin ... 633 pages - Publisher: Wiley-Interscience; (May, 2003) ... Language: English - ISBN-10: 0471266108 - ISBN-13: 978-0471266105.

Utilizing state-of-the-art software to facilitate solutions to real-world problems: Practitioners in the field of physical science are continually faced with a variety of complex, real-world problems, the solution of which requires a working knowledge of both analytical and numerical techniques. An Introduction to Mathematical and Computational Physics Using Mathematica® is designed to help prospective scientists develop a practical, working knowledge of these techniques using the latest, most efficient electronic methodologies. Written from the perspective of a physicist rather than a mathematician, the text focuses on modern practical applications in the physical and engineering sciences, attacking these problems with a range of numerical and analytical methods, both elementary and advanced. Incorporating the widely used and highly praised Mathematica® software package, the author offers solution techniques for the partial differential equations of mathematical physics such as Poisson’s equation, the wave equation, and Schrödinger’s equation, including Fourier series and transforms, Green’s functions, the method of characteristics, grids, Galerkin and simulation methods, elementary probability theory, and statistical methods. The incorporation of Mathematica® offers students a wealth of practical benefits in that it: Requires little or no previous computer experience + Offers maximum flexibility and sophistication + Delivers easy access to the important ideas behind the various numerical methods + Facilitates important but often tedious analytic calculations + Is easily adapted to the application of other related software packages. Designed for both advanced undergraduate and graduate students in the physical and engineering sciences, as well as professionals who want to learn these methods, An Introduction to Mathematical and Computational Physics Using Mathematica® is also provided electronically on an accompanying CD. The electronic version contains the full text of the book, along with animations, user-modifiable source code, and links to related Web material.

John W. Bull ... 464 pages - Publisher: CRC Press; (March, 2009) ... Language: English - ISBN-10: 0415420504 - ISBN-13: 978-0415420501

Correctly understanding, designing and analyzing the foundations that support structures is fundamental to their safety. This book by a range of academic, design and contracting world experts provides a review of the state-of-the-art techniques for modelling foundations using both linear and non linear numerical analysis. It applies to a range of infrastructure, civil engineering and structural engineering projects and allows designers, engineers, architects, researchers and clients to understand some of the advanced numerical techniques used in the analysis and design of foundations. Topics include: Ground vibrations caused by trains +Pile-group effects +Bearing capacity of shallow foundations under static and seismic conditions + Bucket foundation technology for offshore oilfields  + Seismically induced liquefaction in earth embankment foundations and in pile foundations  + Free vibrations of industrial chimneys and TV towers with flexibility of the soil  + Settlements of high rise structures + Seepage, stress fields and dynamic responses in dams + Site investigation.

Abdelwahab Kharab, Ronald B. Guenther ... 631 pages - Publisher: CRC Press; 4th edition (September, 2018) ... Language: English - ASIN: B07G423TJM by Amazon

Previous editions of this popular textbook offered an accessible and practical introduction to numerical analysis. An Introduction to Numerical Methods: A MATLAB® Approach, Fourth Edition continues to present a wide range of useful and important algorithms for scientific and engineering applications. The authors use MATLAB to illustrate each numerical method, providing full details of the computed results so that the main steps are easily visualized and interpreted. This edition also includes a new chapter on Dynamical Systems and Chaos

James F. Epperson ... 614 pages - Publisher: Wiley; 2nd edition (October, 2013) ... Language: English - ISBN-10: 1118367596 - ISBN-13: 978-1118367599 ...

The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material + Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises + Widespread exposure and utilization of MATLAB  + An appendix that contains proofs of various theorems and other material. The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Luis Ribeiro e Sousa, Eurípedes Vargas Jr., M.M. Fernandes, Roberto Azevedo ... 474 pages - Publisher: CRC Press; 1st edition (May, 2012) ... Language: English - ASIN: B00BEKEZVA by Amazon ...

Since the 1990s five books on ‘Applications of Computational Mechanics in Geotechnical Engineering’ have been published. Innovative Numerical Modelling in Geomechanics is the 6th and final book in this series, and contains papers written by leading experts on computational mechanics. The book treats highly relevant topics in the field of geotechnics, such as environmental geotechnics, open and underground excavations, foundations, embankments and rockfill dams, computational systems and oil geomechanics. Special attention is paid to risk in geotechnical engineering, and to recent developments in applying Bayesian networks and Data Mining techniques. Innovative Numerical Modelling in Geomechanics will be of interest to civil, mining and environmental engineers, as well as to engineering geologists. The book will also be useful for academics and researchers involved in geotechnics.

Amos Gilat, Vish Subramaniam ... 480 pages - Publisher: Wiley; 1st edition (April, 2007) ... Language: English - ISBN-10: 0471734403 - ISBN-13: 978-0471734406 ...

Following a unique approach, this innovative book integrates the learning of numerical methods with practicing computer programming and using software tools in applications. It covers the fundamentals while emphasizing the most essential methods throughout the pages. Readers are also given the opportunity to enhance their programming skills using MATLAB to implement algorithms. They'll discover how to use this tool to solve problems in science and engineering. A clear and concise guide to numerical methods and their application: Mastering numerical methods has never been easier than with Gilat/Subramaniam’s Numerical Methods For Engineers and Scientists: An Introduction with Applications Using MATLAB. Uniquely accessible and concise, this book takes an innovative approach that integrates the study of numerical methods with hands-on programming practice using the popular MATLAB environment to solve realistic problems in engineering and science. Ideal for both students and professionals who would like to become more adept at numerical methods, Numerical Methods For Engineers and Scientists familiarizes you with: The mathematical background and fundamentals of numerical methods + Solving  nonlinear equations + Solving a system of linear equations + Eigenvalues and Eigenvectors + Function approximation, curve fitting, and interpolation + Differentiation + Integration + First-order and higher-order ODEs + Initial and boundary value problems. Using MATLAB’s built-in functions as tools for solving problems, you will practice applying numerical methods for analysis of real-world problems. All the information is presented in manageable, step-by-step fashion, supported by a large number of annotated examples and end-of-chapter problems. Lucid, carefully structured, and flexibly designed to fulfill a wide range of academic and practical needs, this book will help you develop the skills in numerical methods that will serve you well as a practicing engineer.

Ken P. Chong, Arthur P. Boresi, Sunil Saigal, James D. Lee ... 332 pages - Publisher: CRC Press; 3rd edition (December, 2017) ... Language: English - ISBN-10: 1138719161 - ISBN-13: 978-1138719163 ...

In the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physical model of the problem and a proper understanding of the assumptions employed. With computers and appropriate software we can model and analyze complex physical systems and problems. However, efficient and accurate use of numerical results obtained from computer programs requires considerable background and advanced working knowledge to avoid blunders and the blind acceptance of computer results. This book provides the background and knowledge necessary to avoid these pitfalls, especially the most commonly used numerical methods employed in the solution of physical problems. It offers an in-depth presentation of the numerical methods for scales from nano to macro in nine self-contained chapters with extensive problems and up-to-date references, covering: Trends and new developments in simulation and computation * Weighted residuals methods * Finite difference methods * Finite element methods * Finite strip/layer/prism methods * Boundary element methods * Meshless methods * Molecular dynamics * Multiphysics problems * Multiscale methods.

Ga Zhang, Pengcheng Fu, Fayun Liang ... Journal of Applied Mathematics - 318 pages (October, 2013) ...

Mathematical and numerical modeling is a mature yet vibrant research area in geotechnical engineering. Its advancement has been accelerated in recent years by many emerging computational techniques as well as the increasing availability of computational power. A wide spectrum of approaches, on the basis of continuously advancing understanding of soil behavior, has been developed and applied to solve various problems in geotechnical engineering. These methods are increasingly playing important roles not only in achieving better understanding of fundamental behavior of geomaterials and geostructures but also in ensuring the safety and sustainability of large-scale complex geoengineering projects. The aim of this special issue is to present original research articles on mathematical and numerical modeling in geotechnical engineering. A total of 26 high-quality peer-reviewed papers were selected to be published in this special issue. The topics cover various aspects as follows: (1) Development and discussion of constitutive models of geomaterials including unsaturated soil, granular, rockfill, joint rock mass, and soil-structure interface. (2) Proposal of analytical solutions to soil-structure interaction systems. (3) Development of numerical methods to evaluate response of retaining wall, pile foundation. (4) Novel applications of mathematical and numerical modeling to practical geotechnical projects such as pile foundations, soil nails, mining, joint rock mass, rock grouting, rockfill dams, and arc dams. These papers are expected to be helpful references for all those in the field of mathematical and numerical modeling in geotechnical engineering.

Steven Chapra, R. Canale ... 992 pages - Publisher: McGraw-Hill; 7th edition (May, 2014) ...
Language: English - ISBN-10: 1259170543 - ISBN-13: 978-1259170546 ...

The seventh edition of Chapra and Canale's Numerical Methods for Engineers retains the instructional techniques that have made the text so successful. Chapra and Canale's unique approach opens each part of the text with sections called "Motivation," "Mathematical Background," and "Orientation." Each part closes with an "Epilogue" containing "Trade-Offs," "Important Relationships and Formulas," and "Advanced Methods and Additional References." Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. Helpful separate Appendices. "Getting Started with MATLAB" and "Getting Started with Mathcad" which make excellent references. Numerous new or revised problems are drawn from actual engineering practice. The expanded breadth of engineering disciplines covered is especially evident in these exercises, which now cover such areas as biotechnology and biomedical engineering. Excellent new examples and case studies span all areas of engineering giving students a broad exposure to various fields in engineering. Users will find use of files for many popular software packages, specifically MATLAB®, Excel® with VBA, and Mathcad®. There is also material on developing MATLAB® m-files and VBA macros.

Joe D. Hoffman ... 840 pages - Publisher: CRC Press; 2nd edition (May, 2001) ...
Language: English - ISBN-10: 0824704436 - ISBN-13: 978-0824704438 ...

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "…a good, solid instructional text on the basic tools of numerical analysis."

Ian M. Smith, V. Griffiths ... 492 pages - Publisher: Chapman and Hall/CRC; 2nd edition (June, 2006) ... Language: English - ISBN-10: 1584884010 - ISBN-13: 978-1584884019 ...

Although pseudocodes, Mathematica®, and MATLAB® illustrate how algorithms work, designers of engineering systems write the vast majority of large computer programs in the Fortran language. Using Fortran 95 to solve a range of practical engineering problems, Numerical Methods for Engineers, Second Edition provides an introduction to numerical methods, incorporating theory with concrete computing exercises and programmed examples of the techniques presented. Covering a wide range of numerical applications that have immediate relevancy for engineers, the book describes forty-nine programs in Fortran 95. Many of the programs discussed use a sub-program library called nm_lib that holds twenty-three subroutines and functions. In addition, there is a precision module that controls the precision of calculations. Well-respected in their field, the authors discuss a variety of numerical topics related to engineering. Some of the chapter features include… The numerical solution of sets of linear algebraic equations - Roots of single nonlinear equations and sets of nonlinear equations - Numerical quadrature, or numerical evaluation of integrals - An introduction to the solution of partial differential equations using finite difference and finite element approaches. Describing concise programs that are constructed using sub-programs wherever possible, this book presents many different contexts of numerical analysis, forming an excellent introduction to more comprehensive subroutine libraries such as the numerical algorithm group (NAG)..

Steven C. Chapra ... 720 pages - Publisher: McGraw-Hill Education; 4th edition (February, 2017) ... Language: English - ISBN-10: 0073397962 - ISBN-13: 978-0073397962 ... 

Applied Numerical Methods with MATLAB is written for students who want to learn and apply numerical methods in order to solve problems in engineering and science. As such, the methods are motivated by problems rather than by mathematics. That said, sufficient theory is provided so that students come away with insight into the techniques and their shortcomings. McGraw-Hill Education's Connect, is also available as an optional, add on item. Connect is the only integrated learning system that empowers students by continuously adapting to deliver precisely what they need, when they need it, how they need it, so that class time is more effective. Connect allows the professor to assign homework, quizzes, and tests easily and automatically grades and records the scores of the student's work. Problems are randomized to prevent sharing of answers an may also have a "multi-step solution" which helps move the students' learning along if they experience difficulty.

Paul Blanchard, Robert L. Devaney, Glen R. Hall ...
864 pages - Publisher: Cengage Learning; 4th edition (April, 2011) ...
Language: English - ISBN-10: 1133109039 - ISBN-13: 978-1133109037 ...

Incorporating an innovative modeling approach, this book for a one-semester differential equations course emphasizes conceptual understanding to help users relate information taught in the classroom to real-world experiences. Certain models reappear throughout the book as running themes to synthesize different concepts from multiple angles, and a dynamical systems focus emphasizes predicting the long-term behavior of these recurring models. Users will discover how to identify and harness the mathematics they will use in their careers, and apply it effectively outside the classroom.

Ward Cheney, David Kincaid ... 784 pages - Publisher: Brooks Cole; 6th edition (August, 2007) ...
Language: English - ISBN-10: 0495114758 - ISBN-13: 978-0495114758 ...

The authors show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded Numerical Analysis: Mathematics of Scientific Computing-3rd Edition.

William Bober, Chi-Tay Tsai, Oren Masory ... 472 pages - Publisher: CRC Press; 1st edition (August, 2009) ... Language: English - ISBN-10: 1420093568 - ISBN-13: 978-1420093568 ...

Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated. This classroom-tested text first reviews the essentials involved in writing computer programs as well as fundamental aspects of MATLAB. It next explains how matrices can solve problems of linear equations, how to obtain the roots of algebraic and transcendental equations, how to evaluate integrals, and how to solve various ODEs. After exploring the features of Simulink, the book discusses curve fitting, optimization problems, and PDE problems, such as the vibrating string, unsteady heat conduction, and sound waves. The focus then shifts to the solution of engineering problems via iteration procedures, differential equations via Laplace transforms, and stress analysis problems via the finite element method. The final chapter examines control systems theory, including the design of single-input single-output (SISO) systems. Two Courses in One Textbook: The first six chapters are appropriate for a lower level course at the sophomore level. The remaining chapters are ideal for a course at the senior undergraduate or first-year graduate level. Most of the chapters contain projects that require students to write a computer program in MATLAB that produces tables, graphs, or both. Many sample MATLAB programs (scripts) in the text provide guidance on completing these projects.

Timmy Siauw, Alexandre Bayen ... 
340 pages - Publisher: Academic Press; 1st edition (May, 2014) ...
Language: English - ISBN-10: 0124202284 - ISBN-13: 978-0124202283 ...

Assuming no prior background in linear algebra or real analysis, An Introduction to MATLAB® Programming and Numerical Methods for Engineers enables you to develop good computational problem solving techniques through the use of numerical methods and the MATLAB® programming environment. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level allowing you to quickly apply results in practical settings. Tips, warnings, and "try this" features within each chapter help the reader develop good programming practices + Chapter summaries, key terms, and functions and operators lists at the end of each chapter allow for quick access to important information  + At least three different types of end of chapter exercises - thinking, writing, and coding - let you assess your understanding and practice what you've learned.

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