Calculus of Variations: With Applications to Physics and EngineeringCourier Corporation, 1974 M01 1 - 326 páginas This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat's principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. "I regard this as a very useful book which I shall refer to frequently in the future." J. L. Synge, Bulletin of the American Mathematical Society. |
Otras ediciones - Ver todas
Calculus of Variations: With Applications to Physics and Engineering Robert Weinstock Vista de fragmentos - 1952 |
Calculus of Variations - With Applications to Physics and Engineering Robert Weinstock Sin vista previa disponible - 2008 |
Términos y frases comunes
according applied approximation arbitrary constants atom axis boundary conditions boundary edge C₁ calculus calculus of variations cartesian chapter configuration continuously differentiable coordinates corresponding curve defined definition denote described differentiable functions differential equation dx dy dy dz eigenfunctions eigenvalue eigenvalue-eigenfunction problem elastic eligible functions end-chapter exercise end-point conditions equations of motion Euler-Lagrange equation extremizing function extremum Fermat's principle finite number fixed follows func functions eligible given Green's theorem Hamilton's principle HINT identically independent variable integral integrand isoperimetric problem Lagrange multiplier line integral linear membrane method minimization normal obtain orthogonal partial derivatives particle plane plate positive potential energy prescribed proof prove replaced respect to functions result Ritz method satisfy Schrödinger equation Show solution strain string Sturm-Liouville substitution surface t₁ theory tion transformation values vanish velocity vibrating vibrating-string zero λε λι Να(λ ди ду дх дхз