LEADER 05026nam 2200649 450 001 9910134844303321 005 20221015211943.0 010 $a9786611843045 010 $a0-470-17952-X 010 $a3-527-61721-3 010 $a3-527-61722-1 010 $a0-585-29428-3 035 $a(CKB)111004366688714 035 $a(EBL)481644 035 $a(OCoLC)609855376 035 $a(SSID)ssj0000201989 035 $a(PQKBManifestationID)11954391 035 $a(PQKBTitleCode)TC0000201989 035 $a(PQKBWorkID)10245853 035 $a(PQKB)10759998 035 $a(MiAaPQ)EBC481644 035 $a(MiAaPQ)EBC6913649 035 $a(Au-PeEL)EBL6913649 035 $a(PPN)152408312 035 $a(EXLCZ)99111004366688714 100 $a20221015h20041937 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMethods of mathematical physics /$fRichard Courant, David Hilbert 210 1$aWeinheim, Germany :$cWiley-VCH GmbH,$d[2004] 210 4$dİ1937 215 $a1 online resource (578 p.) 300 $aDescription based upon print version of record. 311 $a0-471-50447-5 320 $aIncludes bibliographical references and index. 327 $aMETHODS OF MATHEMATICAL PHYSICS; CONTENTS; I . The Algebra of Linear Transformations and Quadratic Forms; 1 . Linear equations and linear transformations; 1 . Vectors; 2 . Orthogonal systems of vectors . Completeness; 3 . Linear transformations . Matrices; 4 . Bilinear, Quadratic, and Hermitian forms; 5 . Orthogonal and unitary transformations; 2 . Linear transformations with a linear parameter; 3 . Transformation to principal axes of quadratic and Hermitian forms; 1 . Transformation to principal axes on the basis of a maximum principle; 2 . Eigenvalues 327 $a3 . Generalization to Hermitian forms4 . Inertial theorem for quadratic forms; 5 . Representation of the resolvent of a form; 6 . Solution of systems of linear equations associated with forms; 4 . Minimum-maximum property of eigenvalues; 1 . Characterization of eigenvalues by a minimum-maximum problem; 2 . Applications . Constraints; 5 . Supplement and problems; 1 . Linear independence and the Gram determinant; 2 . Hadamard's inequality for determinants; 3 . Generalized treatment of canonical transformations; 4 . Bilinear and quadratic forms of infinitely many variables 327 $a5 . Infinitesimal linear transformations6 . Perturbations; 7 . Constraints; 8 . Elementary divisors of a matrix or a bilinear form; 9 . Spectrum of a unitary matrix; References; II . Series Expansions of Arbitrary Functions; 1 . Orthogonal systems of functions; 1 . Definitions; 2 . Orthogonalization of functions; 3 . Bessel's inequality . Completeness relation . Approximation in the mean; 4 . Orthogonal and unitary transformations with infinitely many variables; 5 . Validity of the results for several independent variables . More general assumptions 327 $a6 . Construction of complete systems of functions of several variables2 . The accumulation principle for functions; 1 . Convergence in function space; 3 . Measure of independence and dimension number; 1 . Measure of independence; 2 . Asymptotic dimension of a sequence of functions; 4 . Weierstrass's approximation theorem . Completeness of powers and of trigonometric functions; 1 . Weierstrass's approximation theorem; 2 . Extension to functions of several variables; 3 . Simultaneous approximation of derivatives; 4 . Completeness of the trigonometric functions; 5 Fourier series 327 $a1 . Proof of the fundamental theorem2 . Multiple Fourier series; 3 . Order of magnitude of Fourier Coefficients; 4 . Change in length of Basic Interval; 5 . Examples; 6 . The Fourier integral; 1 . The fundamental theorem; 2 . Extension.of the result to several variables; 3 . Reciprocity formulas; 7 . Examples of Fourier integrals; 8 . Legendre polynomials; 1 . Construction of the Legendre polynomials by orthogonalization of the powers 1,x, x2; 2 . The generating function; 3 . Other properties of the Legendre polynomials; (a) Recursion formula; (b) Differential equation 327 $a(c) Minimum property 330 $aSince 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. 606 $aMathematics 615 0$aMathematics. 676 $a530.151 700 $aCourant$b Richard$f1888-1972,$0447721 702 $aHilbert$b David$f1862-1943, 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910134844303321 996 $aMethods of mathematical physics$92942416 997 $aUNINA