Introduction To Computation And Modeling For Differential Equations

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Introduction to Computation and Modeling for Differential Equations

Lennart Edsberg
Introduction to Computation and Modeling for Differential Equations Book PDF

Author : Lennart Edsberg
Publisher : John Wiley & Sons
Page : 285 pages
File Size : 47,6 Mb
Release : 2015-10-05
Category : Mathematics
ISBN : 9781119018445

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Introduction to Computation and Modeling for Differential Equations by Lennart Edsberg Pdf

Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.

Introduction to Computation and Modeling for Differential Equations

Lennart Edsberg
Introduction to Computation and Modeling for Differential Equations Book PDF

Author : Lennart Edsberg
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 50,9 Mb
Release : 2015-09-16
Category : Mathematics
ISBN : 9781119018469

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Introduction to Computation and Modeling for Differential Equations by Lennart Edsberg Pdf

Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.

Computational Differential Equations

Kenneth Eriksson
Computational Differential Equations Book PDF

Author : Kenneth Eriksson
Publisher : Cambridge University Press
Page : 558 pages
File Size : 46,6 Mb
Release : 1996-09-05
Category : Mathematics
ISBN : 0521567386

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Computational Differential Equations by Kenneth Eriksson Pdf

This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

An Invitation to Applied Mathematics

Carmen Chicone
An Invitation to Applied Mathematics Book PDF

Author : Carmen Chicone
Publisher : Academic Press
Page : 878 pages
File Size : 47,9 Mb
Release : 2016-09-24
Category : Mathematics
ISBN : 9780128041543

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An Invitation to Applied Mathematics by Carmen Chicone Pdf

An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested

Partial Differential Equations

R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp
Partial Differential Equations Book PDF

Author : R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp
Publisher : SIAM
Page : 697 pages
File Size : 43,5 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0898718279

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Partial Differential Equations by R. M. M. Mattheij,S. W. Rienstra,J. H. M. ten Thije Boonkkamp Pdf

Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component - modeling - to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.

Differential Equations, Mechanics, and Computation

Richard S. Palais,Robert Andrew Palais
Differential Equations Mechanics and Computation Book PDF

Author : Richard S. Palais,Robert Andrew Palais
Publisher : American Mathematical Soc.
Page : 329 pages
File Size : 52,5 Mb
Release : 2009-11-13
Category : Mathematics
ISBN : 9780821821381

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Differential Equations, Mechanics, and Computation by Richard S. Palais,Robert Andrew Palais Pdf

This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.

An Introduction to Computational Science

Allen Holder,Joseph Eichholz
An Introduction to Computational Science Book PDF

Author : Allen Holder,Joseph Eichholz
Publisher : Springer
Page : 470 pages
File Size : 45,9 Mb
Release : 2019-06-18
Category : Business & Economics
ISBN : 9783030156794

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An Introduction to Computational Science by Allen Holder,Joseph Eichholz Pdf

This textbook provides an introduction to the growing interdisciplinary field of computational science. It combines a foundational development of numerical methods with a variety of illustrative applications spread across numerous areas of science and engineering. The intended audience is the undergraduate who has completed introductory coursework in mathematics and computer science. Students gain computational acuity by authoring their own numerical routines and by practicing with numerical methods as they solve computational models. This education encourages students to learn the importance of answering: How expensive is a calculation, how trustworthy is a calculation, and how might we model a problem to apply a desired numerical method? The text is written in two parts. Part I provides a succinct, one-term inauguration into the primary routines on which a further study of computational science rests. The material is organized so that the transition to computational science from coursework in calculus, differential equations, and linear algebra is natural. Beyond the mathematical and computational content of Part I, students gain proficiency with elemental programming constructs and visualization, which are presented in MATLAB syntax. The focus of Part II is modeling, wherein students build computational models, compute solutions, and report their findings. The models purposely intersect numerous areas of science and engineering to demonstrate the pervasive role played by computational science.

Computational Differential Equations

K. Eriksson,D. Estep,P. Hansbo,C. Johnson
Computational Differential Equations Book PDF

Author : K. Eriksson,D. Estep,P. Hansbo,C. Johnson
Publisher : Cambridge University Press
Page : 554 pages
File Size : 53,8 Mb
Release : 1996-09-05
Category : Mathematics
ISBN : 0521563127

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Computational Differential Equations by K. Eriksson,D. Estep,P. Hansbo,C. Johnson Pdf

This is a two volume introduction to the computational solution of differential equations using a unified approach organized around the adaptive finite element method. It presents a synthesis of mathematical modeling, analysis, and computation. The goal is to provide the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modeling in science and engineering: How can we model physical phenomena using differential equations? What are the properties of solutions of differential equations? How do we compute solutions in practice? How do we estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The authors then widen the scope to cover the basic classes of linear partial differential equations modeling elasticity, heat flow, wave propagation and convection-diffusion-absorption problems. The book concludes with a chapter on the abstract framework of the finite element method for differential equations. Volume 2, to be published in early 1997, extends the scope to nonlinear differential equations and systems of equations modeling a variety of phenomena such as reaction-diffusion, fluid flow, many-body dynamics and reaches the frontiers of research. It also addresses practical implementation issues in detail. These volumes are ideal for undergraduates studying numerical analysis or differential equations. This is a new edition of a 1988 text of 275 pages by C. Johnson.

Differential Equations

Charles Henry Edwards,David E. Penney,David Calvis
Differential Equations Book PDF

Author : Charles Henry Edwards,David E. Penney,David Calvis
Publisher : Unknown
Page : 600 pages
File Size : 44,5 Mb
Release : 2007-07-18
Category : Differential equations
ISBN : 013600038X

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Differential Equations by Charles Henry Edwards,David E. Penney,David Calvis Pdf

For introductory courses in Differential Equations. This text provides the conceptual development and geometric visualization of a modern differential equations course that is still essential to science and engineering students. It reflects the new emphases that permeate the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; its focus has shifted from the traditional manual methods to new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.

Modelling with Ordinary Differential Equations

T.P. Dreyer
Modelling with Ordinary Differential Equations Book PDF

Author : T.P. Dreyer
Publisher : Routledge
Page : 190 pages
File Size : 45,6 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351430692

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Modelling with Ordinary Differential Equations by T.P. Dreyer Pdf

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

Introduction to Fractional Differential Equations

Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado
Introduction to Fractional Differential Equations Book PDF

Author : Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado
Publisher : Springer
Page : 188 pages
File Size : 43,7 Mb
Release : 2018-10-28
Category : Technology & Engineering
ISBN : 9783030008956

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Introduction to Fractional Differential Equations by Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado Pdf

This book introduces a series of problems and methods insufficiently discussed in the field of Fractional Calculus – a major, emerging tool relevant to all areas of scientific inquiry. The authors present examples based on symbolic computation, written in Maple and Mathematica, and address both mathematical and computational areas in the context of mathematical modeling and the generalization of classical integer-order methods. Distinct from most books, the present volume fills the gap between mathematics and computer fields, and the transition from integer- to fractional-order methods.

Differential Equations and Boundary Value Problems

Charles Henry Edwards,David E. Penney,David Calvis
Differential Equations and Boundary Value Problems Book PDF

Author : Charles Henry Edwards,David E. Penney,David Calvis
Publisher : Unknown
Page : 128 pages
File Size : 44,7 Mb
Release : 2023
Category : Boundary value problems
ISBN : 0137540124

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Differential Equations and Boundary Value Problems by Charles Henry Edwards,David E. Penney,David Calvis Pdf

"This is a textbook for the standard introductory differential equations course taken by science and engineering students. Its updated content reflects the wide availability of technical computing environments like Maple, Mathematica, and MATLAB that now are used extensively by practicing engineers and scientists. The traditional manual and symbolic methods are augmented with coverage also of qualitative and computer-based methods that employ numerical computation and graphical visualization to develop greater conceptual understanding. A bonus of this more comprehensive approach is accessibility to a wider range of more realistic applications of differential equations"--

An Introduction to Differential Equations

Anil G Ladde,G S Ladde
An Introduction to Differential Equations Book PDF

Author : Anil G Ladde,G S Ladde
Publisher : World Scientific Publishing Company
Page : 636 pages
File Size : 50,8 Mb
Release : 2013-01-11
Category : Mathematics
ISBN : 9789814397391

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An Introduction to Differential Equations by Anil G Ladde,G S Ladde Pdf

Volume 1: Deterministic Modeling, Methods and Analysis For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. The advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background. An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 (“An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis”). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus. Errata Errata (32 KB)

Modelling with Ordinary Differential Equations

Alfio Borzì
Modelling with Ordinary Differential Equations Book PDF

Author : Alfio Borzì
Publisher : CRC Press
Page : 405 pages
File Size : 45,8 Mb
Release : 2020-04-13
Category : Mathematics
ISBN : 9781351190381

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Modelling with Ordinary Differential Equations by Alfio Borzì Pdf

Modelling with Ordinary Differential Equations: A Comprehensive Approach aims to provide a broad and self-contained introduction to the mathematical tools necessary to investigate and apply ODE models. The book starts by establishing the existence of solutions in various settings and analysing their stability properties. The next step is to illustrate modelling issues arising in the calculus of variation and optimal control theory that are of interest in many applications. This discussion is continued with an introduction to inverse problems governed by ODE models and to differential games. The book is completed with an illustration of stochastic differential equations and the development of neural networks to solve ODE systems. Many numerical methods are presented to solve the classes of problems discussed in this book. Features: Provides insight into rigorous mathematical issues concerning various topics, while discussing many different models of interest in different disciplines (biology, chemistry, economics, medicine, physics, social sciences, etc.) Suitable for undergraduate and graduate students and as an introduction for researchers in engineering and the sciences Accompanied by codes which allow the reader to apply the numerical methods discussed in this book in those cases where analytical solutions are not available

Numerical Methods for Partial Differential Equations

Vitoriano Ruas
Numerical Methods for Partial Differential Equations Book PDF

Author : Vitoriano Ruas
Publisher : John Wiley & Sons
Page : 376 pages
File Size : 51,9 Mb
Release : 2016-04-28
Category : Technology & Engineering
ISBN : 9781119111368

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Numerical Methods for Partial Differential Equations by Vitoriano Ruas Pdf

Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.