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Numerical Methods And Analysis With Mathematical Modelling


Numerical Methods And Analysis With Mathematical Modelling
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Numerical Methods And Analysis With Mathematical Modelling


Numerical Methods And Analysis With Mathematical Modelling
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Author : WILLIAM P.. WEST FOX (RICHARD D.)
language : en
Publisher:
Release Date : 2024-08-07

Numerical Methods And Analysis With Mathematical Modelling written by WILLIAM P.. WEST FOX (RICHARD D.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-07 with Mathematics categories.


What sets this book apart is the modeling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover the basic numerical analysis methods first with simple examples to illustrate the techniques and discuss possible errors. The modeling prospective reveals the practical relevance of the numerical methods in context to real world problems. At the core of this text are the real-world modeling projects. Chapters are introduced and techniques are discussed with common examples. A modeling scenario is introduced that will be solved with these techniques later in the chapter. Often the modeling problems require more than one previously covered technique presented in the book. Fundamental exercises to practice the techniques are included. Multiple modeling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modeling examples that are solved by the methods described within the chapter. The use of technology is instrumental in numerical analysis and numerical methods. In our text, we illustrate MAPLE, EXCEL, R, and Python. Our goal is not to teach technology but illustrate its power and limitations to perform algorithms and reach conclusions. This book fulfills a need in the education of all students who plan to use technology to solve problems whether using physical models or true creative mathematical modeling, like discrete dynamical systems.



Mathematical And Numerical Methods For Partial Differential Equations


Mathematical And Numerical Methods For Partial Differential Equations
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Author : Joël Chaskalovic
language : en
Publisher: Springer
Release Date : 2014-05-16

Mathematical And Numerical Methods For Partial Differential Equations written by Joël Chaskalovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-16 with Mathematics categories.


This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.



Mathematical Modeling And Numerical Techniques In Drying Technology


Mathematical Modeling And Numerical Techniques In Drying Technology
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Author : Ian Turner
language : en
Publisher: CRC Press
Release Date : 1996-09-19

Mathematical Modeling And Numerical Techniques In Drying Technology written by Ian Turner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-09-19 with Science categories.


Offers information necessary for the development of mathematical models and numerical techniques to solve specific drying problems. The book addresses difficult issues involved with the drying equations of numerical analysis, including mesh generation, discretinization strategies, the nonlinear equation set and the linearized algebraic system, convergance criteria, time step control, experimental validation, optimum methods of visualization results, and more.



Numerical Analysis And Optimization


Numerical Analysis And Optimization
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Author : Grégoire Allaire
language : en
Publisher: OUP Oxford
Release Date : 2007-05-24

Numerical Analysis And Optimization written by Grégoire Allaire and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-24 with Mathematics categories.


This text, based on the author's teaching at École Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences.



Mathematical Modelling Applied Analysis And Computation


Mathematical Modelling Applied Analysis And Computation
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Author : Jagdev Singh
language : en
Publisher: Springer Nature
Release Date : 2019-08-31

Mathematical Modelling Applied Analysis And Computation written by Jagdev Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-31 with Mathematics categories.


This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.



Numerical Methods And Modelling For Engineering


Numerical Methods And Modelling For Engineering
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Author : Richard Khoury
language : en
Publisher: Springer
Release Date : 2016-05-11

Numerical Methods And Modelling For Engineering written by Richard Khoury and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-11 with Technology & Engineering categories.


This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems.



Advanced Numerical Methods For Differential Equations


Advanced Numerical Methods For Differential Equations
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Author : Harendra Singh
language : en
Publisher: CRC Press
Release Date : 2021-07-29

Advanced Numerical Methods For Differential Equations written by Harendra Singh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-29 with Technology & Engineering categories.


Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.



Numerical Methods In Finance


Numerical Methods In Finance
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Author : L. C. G. Rogers
language : en
Publisher: Cambridge University Press
Release Date : 2008-04-24

Numerical Methods In Finance written by L. C. G. Rogers and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-24 with Mathematics categories.


Numerical methods in finance has recently emerged as a new discipline at the intersection of probability theory, finance and numerical analysis. This book describes a wide variety of numerical methods used in financial analysis: computation of option prices, especially American option prices, by finite difference and other methods; numerical solution of portfolio management strategies; statistical procedures, identification of models; Monte Carlo methods; and numerical implications of stochastic volatilities. Lucid and concise, it covers both mathematical matters and practical issues in numerical problems. This book is an ideal resource for economists, probabilists and applied mathematicians working in finance.



Numerical Analysis


Numerical Analysis
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Author : Brian Sutton
language : en
Publisher: SIAM
Release Date : 2019-04-18

Numerical Analysis written by Brian Sutton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Mathematics categories.


This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.



Numerical Mathematics


Numerical Mathematics
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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2017-01-26

Numerical Mathematics written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.


Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performances on examples and counterexamples which outline their pros and cons. This is done using the MATLAB software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLAB computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in Engineering, Mathematics, Physics and Computer Sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields.