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Introduction to symmetry analysis /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2002.
|
| Colección: | Cambridge texts in applied mathematics.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Historical Preface
- Rise of the Academies
- Abel and Galois
- Lie and Klein
- 1870
- Lie's Arrest
- Gauss, Riemann, and the New Geometry
- The Erlangen Program
- Lie's Career at Leipzig
- A Falling Out
- Lie's Final Return to Norway
- After 1900
- The Ariadne Thread
- Symmetry in Nature
- Some Background
- The Discrete Symmetries of Objects
- The Principle of Covariance
- Continuous Symmetries of Functions and Differential Equations
- Some Notation Conventions
- Dimensional Analysis
- The Two-Body Problem in a Gravitational Field
- The Drag on a Sphere
- The Drag on a Sphere in High-Speed Gas Flow
- Buckingham's Pi Theorem--The Dimensional-Analysis Algorithm
- Systems of ODEs and First-Order PDEs; State-Space Analysis
- Autonomous Systems of ODEs in the Plane
- Characteristics
- First-Order Ordinary Differential Equations
- Thermodynamics; The Legendre Transformation
- Incompressible Flow in Two Dimensions
- Fluid Flow in Three Dimensions--The Dual Stream Function
- Nonlinear First-Order PDEs--The Method of Lagrange and Charpit
- Characteristics in n Dimensions
- State-Space Analysis in Two and Three Dimensions
- Classical Dynamics
- Hamilton's Principle
- Hamilton's Equations
- The Hamilton--Jacobi Equation
- Introduction to One-Parameter Lie Groups
- The Symmetry of Functions
- An Example and a Counterexample
- One-Parameter Lie Groups
- Invariant Functions
- Infinitesimal Form of a Lie Group.