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Bibliography
Includes bibliographical references and index.
Contents
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.