Author : Thierry Goudon
Publisher : John Wiley & Sons
Page : 470 pages
File Size : 38,51 MB
Release : 2016-10-14
Category : Mathematics
ISBN : 1119371279
This book provides the mathematical basis for investigating numerically equations from physics, life sciences or engineering. Tools for analysis and algorithms are confronted to a large set of relevant examples that show the difficulties and the limitations of the most naïve approaches. These examples not only provide the opportunity to put into practice mathematical statements, but modeling issues are also addressed in detail, through the mathematical perspective.
Author : Addolorata Marasco
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 49,9 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461201519
Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica for Ordinary Differential Equations provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use ODEs and Mathematica in the Dynamics of rigid bodies. Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ordinary differential equations such as, phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica. Topics and Features:*Explains how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving *End-of- chapter exercise sets incorporating the use of Mathematica programs *Detailed description and explanation of the mathematical procedures underlying the programs written in Mathematica *Appendix describing the use of ten notebooks to guide the reader through all the exercises. This book is an essential text/reference for students, graduates and practitioners in applied mathematics and engineering interested in ODE's problems in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-
Author : Dianne P. O'Leary
Publisher : SIAM
Page : 376 pages
File Size : 20,30 MB
Release : 2009-03-19
Category : Mathematics
ISBN : 0898716667
This book is a practical guide to the numerical solution of linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. It treats standard problems and introduces important variants such as sparse systems, differential-algebraic equations, constrained optimization, Monte Carlo simulations, and parametric studies. Stability and error analysis are emphasized, and the Matlab algorithms are grounded in sound principles of software design and understanding of machine arithmetic and memory management. Nineteen case studies provide experience in mathematical modeling and algorithm design, motivated by problems in physics, engineering, epidemiology, chemistry, and biology. The topics included go well beyond the standard first-course syllabus, introducing important problems such as differential-algebraic equations and conic optimization problems, and important solution techniques such as continuation methods. The case studies cover a wide variety of fascinating applications, from modeling the spread of an epidemic to determining truss configurations.
Author : Santanu Manna
Publisher : Springer Nature
Page : 467 pages
File Size : 34,34 MB
Release : 2020-02-14
Category : Mathematics
ISBN : 9811513384
This book contains original research papers presented at the International Conference on Mathematical Modelling and Scientific Computing, held at the Indian Institute of Technology Indore, India, on 19–21 July 2018. Organized into 30 chapters, the book presents the recent progress and the most advanced innovations, trends, and real-world challenges encountered and solutions embraced in the applications of mathematics and scientific computing. The book will be of interests to a wide variety of researchers, students and the practicing engineers working in diverse areas of science and engineering, ranging from applied and computational mathematics, vibration problem, computer science, and numerical optimization to physics, chemistry, biology, electrical, civil, mechanical, chemical, seismology, aerospace, and medical sciences. The aim of the conference is to bring together leading academicians, scientists, researchers, engineers, and industry partners from all over the globe to exchange and share their experiences and research results on various aspects of applied mathematics and scientific computation, like, differential equation, modeling, simulation, dynamical systems, numerical analysis, matrix theory, inverse problems, and solid and fluid mechanics, computational engineering.
Author : Vinai K. Singh
Publisher : Springer Nature
Page : 441 pages
File Size : 49,86 MB
Release : 2021-08-23
Category : Mathematics
ISBN : 3030682811
This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering. The content of the book is based on talks and papers presented at the conference Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST), held at Inderprastha Engineering College in Ghaziabad, India in January 2020. A wide range of both theoretical and applied topics are covered in detail, including the conceptualization of infinity, efficient domain decomposition, high capacity wireless communication, infectious disease modeling, and more. These chapters are organized around the following areas: Partial and ordinary differential equations Optimization and optimal control High performance and scientific computing Stochastic models and statistics Recent Trends in Mathematical Modeling and High Performance Computing will be of interest to researchers in both mathematics and engineering, as well as to practitioners who face complex models and extensive computations.
Author : Jose Nathan Kutz
Publisher :
Page : 657 pages
File Size : 29,34 MB
Release : 2013-08-08
Category : Computers
ISBN : 0199660336
Combining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.
Author : Edward A. Bender
Publisher : Courier Corporation
Page : 273 pages
File Size : 26,44 MB
Release : 2012-05-23
Category : Mathematics
ISBN : 0486137120
Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Author : Bertil Gustafsson
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 16,21 MB
Release : 2011-06-11
Category : Mathematics
ISBN : 3642194958
The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior of an aircraft that has yet to be built? The answer is computer simulations based on mathematical models – sets of equations – that describe the underlying physical properties. However, these equations are usually much too complicated to solve, either by the smartest mathematician or the largest supercomputer. This problem is overcome by constructing an approximation: a numerical model with a simpler structure can be translated into a program that tells the computer how to carry out the simulation. This book conveys the fundamentals of mathematical models, numerical methods and algorithms. Opening with a tutorial on mathematical models and analysis, it proceeds to introduce the most important classes of numerical methods, with finite element, finite difference and spectral methods as central tools. The concluding section describes applications in physics and engineering, including wave propagation, heat conduction and fluid dynamics. Also covered are the principles of computers and programming, including MATLAB®.
Author : Rutherford Aris
Publisher : Courier Corporation
Page : 300 pages
File Size : 49,22 MB
Release : 1994-01-01
Category : Technology & Engineering
ISBN : 9780486681313
"Engaging, elegantly written." — Applied Mathematical Modelling. A distinguished theoretical chemist and engineer discusses the types of models — finite, statistical, stochastic, and more — as well as how to formulate and manipulate them for best results. Filled with numerous examples, the book includes three appendices offering further examples treated in more detail.
Author : Michael T. Heath
Publisher : SIAM
Page : 587 pages
File Size : 46,41 MB
Release : 2018-11-14
Category : Science
ISBN : 1611975573
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.
