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Ordinary Differential Equations : a Practical Guide.
A compact treatment that takes the reader from simple examples to current research involving ordinary differential equations.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2011.
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| Colección: | AIMS Library of Mathematical Sciences.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; ORDINARY DIFFERENTIAL EQUATIONS; African Institute of Mathematics Library Series; Title; Copyright; Contents; Preface; 1 First order differential equations; 1.1 General remarks about differential equations; 1.1.1 Terminology; 1.1.2 Approaches to problems involving differential equations; 1.2 Exactly solvable first order ODEs; 1.2.1 Terminology; 1.2.2 Solution by integration; 1.2.3 Separable equations; 1.2.4 Linear first order differential equations; 1.2.5 Exact equations; 1.2.6 Changing variables; 1.3 Existence and uniqueness of solutions; 1.4 Geometric methods: direction fields.
- 1.5 Remarks on numerical methods2 Systems and higher order equations; 2.1 General remarks; 2.2 Existence and uniqueness of solutions for systems; 2.3 Linear systems; 2.3.1 General remarks; 2.3.2 Linear algebra revisited; 2.4 Homogeneous linear systems; 2.4.1 The vector space of solutions; 2.4.2 The eigenvector method; 2.5 Inhomogeneous linear systems; 3 Second order equations and oscillations; 3.1 Second order differential equations; 3.1.1 Linear, homogeneous ODEs with constant coefficients; 3.1.2 Inhomogeneous linear equations; 3.1.3 Euler equations; 3.1.4 Reduction of order.
- 3.2 The oscillating spring3.2.1 Deriving the equation of motion; 3.2.2 Unforced motion with damping; 3.2.3 Forced motion with damping; 3.2.4 Forced motion without damping; 4 Geometric methods; 4.1 Phase diagrams; 4.1.1 Motivation; 4.1.2 Definitions and examples; 4.1.3 Phase diagrams for linear systems; 4.2 Nonlinear systems; 4.2.1 The Linearisation Theorem; 4.2.2 Lyapunov functions; 5 Projects; 5.1 Ants on polygons; 5.2 A boundary value problem in mathematical physics; 5.3 What was the trouble with the Millennium Bridge?; 5.4 A system of ODEs arising in differential geometry.
- 5.5 Proving the Picard-Lindelöf Theorem5.5.1 The Contraction Mapping Theorem; 5.5.2 Strategy of the proof; 5.5.3 Completing the proof; References; Index.