Hindustan Book Agency 2009; 350 pp; hardcover ISBN10: 8185931917 ISBN13: 9788185931913 List Price: US$48 Member Price: US$38.40 Order Code: HIN/44
 The name of C. G. J. Jacobi is familiar to every student of mathematics, thanks to the Jacobion determinant, the HamiltonJacobi equations in dynamics, and the Jacobi identity for vector fields. Best known for his contributions to the theory of elliptic and abelian functions, Jacobi is also known for his innovative teaching methods and for running the first research seminar in pure mathematics. A record of his lectures on Dynamics given in 184243 at Königsberg, edited by A. Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters. A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels. Readership Graduate students and research mathematicians interested in C. G. J. Jacobi. Table of Contents  Introduction
 The differential equations of motion
 Conservation of motion of centre of gravity
 The principle of conservation of `vis viva'
 Conservation of surface area
 The principle of least action
 Further considerations on the principle of least actionThe Lagrange multipliers
 Hamilton's integral and Lagrange's second form of dynamical equations
 Hamilton's form of the equation of motion
 The principle of the last multiplier
 Survey of those properties of determinants that are used in the theory of the last multiplier
 The multiplier for systems of differential equations with an arbitrary number of variables
 Functional determinants. Their application in setting up the partial differential equation for the multiplier
 The second form of the equation defining the multiplier. The multipliers of step wise reduced differential equations. The multiplier by the use of particular integrals
 The multiplier for systems of differential equations with higher differential coefficients. Applications to a system of mass points without constraints
 Examples of the search for multipliers. Attraction of a point by a fixed centre in a resisting medium and in empty space
 The multiplier of the equations of motion of a system under constraint in the first Langrange form
 The multiplier for the equations of motion of a constrained system in Hamiltonian form
 Hamilton's partial differential equation and its extension to the isoperimetric problem
 Proof that the integral equations derived from a complete solution of Hamilton's partial differential equation actually satisfy the system of ordinary differential equations. Hamilton's equation for free motion
 Investigation of the case in which \(t\) does not occur explicitly
 Lagrange's method of integration of first order partial differential equations in two independent variables. Application to problems of mechanics which depend only on two defining parameters. The free motion of a point on a plane and the shortest line on a surface
 The reduction of the partial differential equation for those problems in which the principle of conservation of centre of gravity holds
 Motion of a planet around the sunSolution in polar coordinates
 Solution of the same problem by introducing the distances of the planet from two fixed points
 Elliptic coordinates
 Geometric significance of elliptic coordinates on the plane and in space. Quadrature of the surface of an ellipsoid. Rectification of its lines of curvature
 The shortest line on the triaxial ellipsoid. The problem of map projection
 Attraction of a point by two fixed centres
 Abel's theorem
 General investigations of the partial differential equations of the first order. Different forms of the integrability conditions
 Direct proof of the most general form of the integrability condition. Introduction of the function \(H\), which set equal to an arbitrary constant determines the \(p\) as functions of the \(q\)
 On the simultaneous solutions of two linear partial differential equations
 Application of the preceding investigation to the integration of partial differential equations of the first order, and in particular, to the case of mechanics. The theorem on the third integral derived from two given integrals of differential equations of dynamics
 The two classes of integrals which one obtains according to Hamilton's method for problems of mechanics. Determination of the value of \((\varphi, \psi)\) for them
 Perturbation theory. Supplement
