Methods of Mathematical Physics, Volume 1
Wiley, Jan 15, 1953 - Science - 560 pages
Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.
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The Algebra of Linear Transformations and Quadratic Forms
Linear transformations with a linear parameter
Transformation to principal axes of quadratic and Hermitian
104 other sections not shown
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Methods of Mathematical Physics: Partial Differential Equations
Richard Courant,David Hilbert
Limited preview - 2008
approximated arbitrarily arbitrary associated assume asymptotic becomes bound boundary conditions called coefficients complete consider constant continuous function converges coordinates corresponding curve defined denotes depends derivatives determined differential equation domain G dx dy eigenfunctions eigenvalue problem eigenvalues equal Euler example exists expansion expression fact finite fixed follows force formula function fundamental given Green's function hence holds homogeneous identically immediately increasing independent inequality infinite integral integral equation interval kernel leads limit linear matrix maximum means method multiply n-th normalized obtain orthogonal parameter particular piecewise polynomials positive problem proof prove quadratic relation remains representation represented respect result satisfies sequence side simple solution space square subsection sufficiently surface theorem theory tion transformation uniformly valid values vanish variables variational problem vector zero