Catalogue en ligne Bibliothèque de l'Ecole Nationale Polytechnique

Differential equations and dynamical systems / Lawrence Perko

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Titre : Differential equations and dynamical systems
Type de document : texte imprimé
Auteurs : Lawrence Perko, Auteur
Mention d'édition : 3 éd
Editeur : Berlin : Springer-Verlag
Année de publication : 2001
Collection : Texts in applied mathematics num. 7
Importance : XIV-555 p.
Présentation : ill.
Format : 25 cm
ISBN/ISSN/EAN : 978-0-387-95116-4
Note générale : With 241 ill. Index
Langues : Anglais (eng)
Mots-clés : Dynamique différentiable
Équations différentielles non linéaires
Équations différentielles
Systèmes dynamiques
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.
Note de contenu :
- Linear systems
Uncoupled linaer systems
Diagonaliztion
Exponentials of operators
...
- Nonlinear systems: Local theory
Some preliminary concepts and definitions
The fundamental existence-Uniqueness theorem
Dependence on initial conditions and parametres
...
- Nonlinear systems: global theory
Dynamical systems and global existence theorems
Limit sets and attractors
perodic oribts, limit cycles and separatrix cycles
...
- Nonlinear systems: bifurcation theory
Structural stability and peixoto's theorem
Bifurcations at nonhyperbolic
Higher codimension bifurcations et nonhyperbolic equilibrium points
...

Differential equations and dynamical systems [texte imprimé] / Lawrence Perko, Auteur . - 3 éd . - Springer-Verlag, 2001 . - XIV-555 p. : ill. ; 25 cm. - (Texts in applied mathematics; 7) .
ISBN : 978-0-387-95116-4
With 241 ill. Index
Langues : Anglais (eng)
Mots-clés : Dynamique différentiable
Équations différentielles non linéaires
Équations différentielles
Systèmes dynamiques
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations.
Note de contenu :
- Linear systems
Uncoupled linaer systems
Diagonaliztion
Exponentials of operators
...
- Nonlinear systems: Local theory
Some preliminary concepts and definitions
The fundamental existence-Uniqueness theorem
Dependence on initial conditions and parametres
...
- Nonlinear systems: global theory
Dynamical systems and global existence theorems
Limit sets and attractors
perodic oribts, limit cycles and separatrix cycles
...
- Nonlinear systems: bifurcation theory
Structural stability and peixoto's theorem
Bifurcations at nonhyperbolic
Higher codimension bifurcations et nonhyperbolic equilibrium points
...

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Differential equations and their applications / Martin Braun

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Titre : Differential equations and their applications : an introduction to applied mathematics
Type de document : texte imprimé
Auteurs : Martin Braun, Auteur
Mention d'édition : 4 éd
Editeur : Berlin : Springer-Verlag
Année de publication : 1993
Collection : Texts in applied mathematics num. 11
Importance : 578 p.
Présentation : ill.
Format : 25 cm
ISBN/ISSN/EAN : 978-0-387-97894-9
Note générale : With 68 ill. Index
Langues : Anglais (eng)
Mots-clés : Differential equations
Équations différentielles -- Problèmes et exercices
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This text is a clearly written and complete introductory study of differential equations and their applications. Suitable for a one- or two-semester course on the subject, the material is fully comprehensible to anyone who has studied college-level calculus. This book distinguishes itself from other differential equation texts through its application of the subject matter to fascinating events and its incorporation of relatively recent developments in the field. Some applications include: a proof that the painting, "Disciples at Emmaus," bought by the Rembrandt Society of Belgium was a modern forgery; a mathematical explanation of the Tacoma Bridge disaster; a model of the blood glucose regulatory system which leads to a criterion for the diagnosis of diabetes; an explanation of why the predator portion (sharks, skates, rays, etc.) of all fish caught in the port of Fiume, Italy, rose dramatically during the years of World War I; a mathematical verification of Darwin's law that "the more similar two species are, the fiercer is the struggle for existence between them."
Note de contenu :
1 First-order differential equations
2 Second-order linear differential equations
3 Systems of differential equations
4 Qualitative theory of differential equations
5 Separation of variables and Fourier series
6 Sturm-Liouville boundary value problems

Differential equations and their applications : an introduction to applied mathematics [texte imprimé] / Martin Braun, Auteur . - 4 éd . - Springer-Verlag, 1993 . - 578 p. : ill. ; 25 cm. - (Texts in applied mathematics; 11) .
ISBN : 978-0-387-97894-9
With 68 ill. Index
Langues : Anglais (eng)
Mots-clés : Differential equations
Équations différentielles -- Problèmes et exercices
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This text is a clearly written and complete introductory study of differential equations and their applications. Suitable for a one- or two-semester course on the subject, the material is fully comprehensible to anyone who has studied college-level calculus. This book distinguishes itself from other differential equation texts through its application of the subject matter to fascinating events and its incorporation of relatively recent developments in the field. Some applications include: a proof that the painting, "Disciples at Emmaus," bought by the Rembrandt Society of Belgium was a modern forgery; a mathematical explanation of the Tacoma Bridge disaster; a model of the blood glucose regulatory system which leads to a criterion for the diagnosis of diabetes; an explanation of why the predator portion (sharks, skates, rays, etc.) of all fish caught in the port of Fiume, Italy, rose dramatically during the years of World War I; a mathematical verification of Darwin's law that "the more similar two species are, the fiercer is the struggle for existence between them."
Note de contenu :
1 First-order differential equations
2 Second-order linear differential equations
3 Systems of differential equations
4 Qualitative theory of differential equations
5 Separation of variables and Fourier series
6 Sturm-Liouville boundary value problems

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Elliptic partial differential equations of second order / David Gilbarg

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Titre : Elliptic partial differential equations of second order
Type de document : texte imprimé
Auteurs : David Gilbarg ; Neil S. Trudinger, Auteur
Editeur : Berlin : Springer-Verlag
Année de publication : 2001
Collection : Classics in mathematics, ISSN 1431-0821
Importance : XIII-513 p.
Format : 24 cm
ISBN/ISSN/EAN : 978-3-540-41160-4
Note générale : Bibliogr. Index
Langues : Anglais (eng)
Mots-clés : Differential equations, Elliptic
Équations différentielles elliptiques
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures
Note de contenu :
- Linear Equations
Laplace's Equation
The Classical Maximum Principle
Poisson's Equation and the Newtonian Potential
Banach and Hilbert Spaces
- Quasilinear Equations
Maximum and Comparison Principles
Topological Fixed Point Theorems and Their Application
Equations in Two Variables
Hölder Estimates for the Gradient
Boundary Gradient Estimates
...

Elliptic partial differential equations of second order [texte imprimé] / David Gilbarg ; Neil S. Trudinger, Auteur . - Springer-Verlag, 2001 . - XIII-513 p. ; 24 cm. - (Classics in mathematics, ISSN 1431-0821) .
ISBN : 978-3-540-41160-4
Bibliogr. Index
Langues : Anglais (eng)
Mots-clés : Differential equations, Elliptic
Équations différentielles elliptiques
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures
Note de contenu :
- Linear Equations
Laplace's Equation
The Classical Maximum Principle
Poisson's Equation and the Newtonian Potential
Banach and Hilbert Spaces
- Quasilinear Equations
Maximum and Comparison Principles
Topological Fixed Point Theorems and Their Application
Equations in Two Variables
Hölder Estimates for the Gradient
Boundary Gradient Estimates
...

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Integral transforms and their applictions / Brian Davies

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Titre : Integral transforms and their applictions
Type de document : texte imprimé
Auteurs : Brian Davies, Auteur
Mention d'édition : 3th ed
Editeur : Berlin : Springer-Verlag
Année de publication : 2002
Collection : Texts in applied mathematics num. 41
Importance : 367 p.
Présentation : ill.
Format : 25 cm
ISBN/ISSN/EAN : 978-0-387-95314-4
Note générale : Bibliogr. p. [357]-362. Index
Langues : Anglais (eng)
Mots-clés : Integral transforms
Transformations intégrales
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé :
This book is an introduction and reference for the applications of integral transforms to a wide range of common mathematical problems. Emphasis is placed on the development of techniques and on the connection between properties of transforms and the kinds of problems for which they provide tools. Over 400 problems accompany the text, illustrating areas of applications. This third edition has been substantially updated, extended, and reorganized. Graduate students and researchers working in mathematics and physics will find this book useful.
Note de contenu :
* Functions of a Complex Variable.
* The Laplace Transform.
* The Inversion Integral.
* Ordinary Differential Equations.
* Partial Differential Equations I.
* Integral Equations.
* The Fourier Transform.
* Partial Differential Equations II.
* Generalized Functions.
* Green's Functions.
...

Integral transforms and their applictions [texte imprimé] / Brian Davies, Auteur . - 3th ed . - Springer-Verlag, 2002 . - 367 p. : ill. ; 25 cm. - (Texts in applied mathematics; 41) .
ISBN : 978-0-387-95314-4
Bibliogr. p. [357]-362. Index
Langues : Anglais (eng)
Mots-clés : Integral transforms
Transformations intégrales
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé :
This book is an introduction and reference for the applications of integral transforms to a wide range of common mathematical problems. Emphasis is placed on the development of techniques and on the connection between properties of transforms and the kinds of problems for which they provide tools. Over 400 problems accompany the text, illustrating areas of applications. This third edition has been substantially updated, extended, and reorganized. Graduate students and researchers working in mathematics and physics will find this book useful.
Note de contenu :
* Functions of a Complex Variable.
* The Laplace Transform.
* The Inversion Integral.
* Ordinary Differential Equations.
* Partial Differential Equations I.
* Integral Equations.
* The Fourier Transform.
* Partial Differential Equations II.
* Generalized Functions.
* Green's Functions.
...

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Introduction to partial differential equations / Aslak Tveito

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Titre : Introduction to partial differential equations : a computational approach
Type de document : texte imprimé
Auteurs : Aslak Tveito, Auteur ; Ragnar Winther, Auteur
Editeur : Berlin : Springer-Verlag
Année de publication : 1998
Collection : Texts in applied mathematics num. 29
Importance : XV-392 p.
Présentation : ill.
Format : 24 cm
ISBN/ISSN/EAN : 978-0-387-98327-1
Note générale : With 69 ill. Bibliogr. Index
Langues : Anglais (eng)
Mots-clés : Differential equations, Partial
Équations aux dérivées partielles
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This book teaches the basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles and energy estimates are included. Numerical methods are introduced in parallel to the classical theory. The numerical experiments are used to illustrate properties of differential equations and theory for finite difference approximations is developed. Numerical methods are included in the book to show the significance of computations in partial differential equations and to illustrate the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between the analytical and numerical techniques.
Note de contenu :
- Setting the Scene
- Two-Point Boundary Value Problems
- The Heat Equation
- Finite Difference Schemes For The Heat Equation
- The Wave Equation
- Maximum Principles
- Poisson’s Equation in Two Space Dimensions
- Orthogonality and General Fourier Series
...

Introduction to partial differential equations : a computational approach [texte imprimé] / Aslak Tveito, Auteur ; Ragnar Winther, Auteur . - Springer-Verlag, 1998 . - XV-392 p. : ill. ; 24 cm. - (Texts in applied mathematics; 29) .
ISBN : 978-0-387-98327-1
With 69 ill. Bibliogr. Index
Langues : Anglais (eng)
Mots-clés : Differential equations, Partial
Équations aux dérivées partielles
Index. décimale : 517.911 Questions générales. Théorèmes d'existence. Théorèmes d'unicité. Différentiabilité des solutions
Résumé : This book teaches the basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Standard topics such as separation of variables, Fourier analysis, maximum principles and energy estimates are included. Numerical methods are introduced in parallel to the classical theory. The numerical experiments are used to illustrate properties of differential equations and theory for finite difference approximations is developed. Numerical methods are included in the book to show the significance of computations in partial differential equations and to illustrate the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between the analytical and numerical techniques.
Note de contenu :
- Setting the Scene
- Two-Point Boundary Value Problems
- The Heat Equation
- Finite Difference Schemes For The Heat Equation
- The Wave Equation
- Maximum Principles
- Poisson’s Equation in Two Space Dimensions
- Orthogonality and General Fourier Series
...

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Partial differential equations / Jürgen Jost

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Solving ordinary differential equations 2 / Ernst Hairer

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