Differential Equations, Mechanics, and Computation

Differential Equations, Mechanics, and Computation
Author: Richard S. Palais
Publisher: American Mathematical Soc.
Total Pages: 329
Release: 2009-11-13
Genre: Mathematics
ISBN: 0821821385

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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.

Computational Differential Equations

Computational Differential Equations
Author: Kenneth Eriksson
Publisher: Cambridge University Press
Total Pages: 558
Release: 1996-09-05
Genre: Mathematics
ISBN: 9780521567381

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

Partial Differential Equations

Partial Differential Equations
Author: R. M. M. Mattheij
Publisher: SIAM
Total Pages: 689
Release: 2005-01-01
Genre: Mathematics
ISBN: 0898715946

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Textbook with a unique approach that integrates analysis and numerical methods and includes modelling to address real-life problems.

Involution

Involution
Author: Werner M. Seiler
Publisher: Springer Science & Business Media
Total Pages: 663
Release: 2009-10-26
Genre: Mathematics
ISBN: 3642012876

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The book provides a self-contained account of the formal theory of general, i.e. also under- and overdetermined, systems of differential equations which in its central notion of involution combines geometric, algebraic, homological and combinatorial ideas.

Automated Solution of Differential Equations by the Finite Element Method

Automated Solution of Differential Equations by the Finite Element Method
Author: Anders Logg
Publisher: Springer Science & Business Media
Total Pages: 723
Release: 2012-02-24
Genre: Computers
ISBN: 3642230997

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This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Differential Dynamical Systems, Revised Edition

Differential Dynamical Systems, Revised Edition
Author: James D. Meiss
Publisher: SIAM
Total Pages: 392
Release: 2017-01-24
Genre: Mathematics
ISBN: 161197464X

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Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Numerical Solution of Partial Differential Equations in Science and Engineering

Numerical Solution of Partial Differential Equations in Science and Engineering
Author: Leon Lapidus
Publisher: John Wiley & Sons
Total Pages: 677
Release: 2011-02-14
Genre: Mathematics
ISBN: 1118031210

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From the reviews of Numerical Solution of PartialDifferential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, evenexhaustive, survey of the subject . . . [It] is unique in that itcovers equally finite difference and finite element methods." Burrelle's "The authors have selected an elementary (but not simplistic)mode of presentation. Many different computational schemes aredescribed in great detail . . . Numerous practical examples andapplications are described from beginning to the end, often withcalculated results given." Mathematics of Computing "This volume . . . devotes its considerable number of pages tolucid developments of the methods [for solving partial differentialequations] . . . the writing is very polished and I found it apleasure to read!" Mathematics of Computation Of related interest . . . NUMERICAL ANALYSIS FOR APPLIED SCIENCE Myron B. Allen andEli L. Isaacson. A modern, practical look at numerical analysis,this book guides readers through a broad selection of numericalmethods, implementation, and basic theoretical results, with anemphasis on methods used in scientific computation involvingdifferential equations. 1997 (0-471-55266-6) 512 pp. APPLIED MATHEMATICS Second Edition, J. David Logan.Presenting an easily accessible treatment of mathematical methodsfor scientists and engineers, this acclaimed work covers fluidmechanics and calculus of variations as well as more modernmethods-dimensional analysis and scaling, nonlinear wavepropagation, bifurcation, and singular perturbation. 1996(0-471-16513-1) 496 pp.

Theory of Differential Equations in Engineering and Mechanics

Theory of Differential Equations in Engineering and Mechanics
Author: Kam Tim Chau
Publisher: CRC Press
Total Pages: 1399
Release: 2017-09-22
Genre: Mathematics
ISBN: 1351675621

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This gives comprehensive coverage of the essential differential equations students they are likely to encounter in solving engineering and mechanics problems across the field -- alongside a more advance volume on applications. This first volume covers a very broad range of theories related to solving differential equations, mathematical preliminaries, ODE (n-th order and system of 1st order ODE in matrix form), PDE (1st order, 2nd, and higher order including wave, diffusion, potential, biharmonic equations and more). Plus more advanced topics such as Green’s function method, integral and integro-differential equations, asymptotic expansion and perturbation, calculus of variations, variational and related methods, finite difference and numerical methods. All readers who are concerned with and interested in engineering mechanics problems, climate change, and nanotechnology will find topics covered in these books providing valuable information and mathematics background for their multi-disciplinary research and education.

A First Course in the Numerical Analysis of Differential Equations

A First Course in the Numerical Analysis of Differential Equations
Author: A. Iserles
Publisher: Cambridge University Press
Total Pages: 481
Release: 2009
Genre: Mathematics
ISBN: 0521734908

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lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations
Author: Vitoriano Ruas
Publisher: John Wiley & Sons
Total Pages: 376
Release: 2016-04-28
Genre: Technology & Engineering
ISBN: 1119111366

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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.