LEADER 05143nam 2200673 450 001 9910134845103321 005 20221015211206.0 010 $a9786611843052 010 $a0-470-17985-6 010 $a3-527-61723-X 010 $a3-527-61724-8 010 $a0-585-32148-5 035 $a(CKB)111004366688712 035 $a(EBL)481645 035 $a(OCoLC)609855380 035 $a(SSID)ssj0000201988 035 $a(PQKBManifestationID)11171596 035 $a(PQKBTitleCode)TC0000201988 035 $a(PQKBWorkID)10245878 035 $a(PQKB)11683642 035 $a(MiAaPQ)EBC481645 035 $a(MiAaPQ)EBC6913653 035 $a(Au-PeEL)EBL6913653 035 $a(PPN)152415297 035 $a(EXLCZ)99111004366688712 100 $a20221015d1962 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMethods of mathematical physics /$fRichard Courant, David Hilbert 210 1$aNew York :$cInterscience Publishers,$d[1962] 210 4$dİ1962 215 $a1 online resource (854 p.) 225 1 $aWiley Classics Library ;$vv.86 300 $aDescription based upon print version of record. 311 $a0-471-50439-4 320 $aIncludes bibliographical references and index. 327 $aMETHODS OF MATHEMATICAL PHYSICS; CONTENTS; I . Introductory Remarks; 1 . General Information about the Variety of Solutions; 1 . Examples; 2 . Differential Equations for Given Families of Functions; 2 . Systems of Differential Equations; 1 . The Question of Equivalence of a System of Differential Equations and a Single Differential Equation; 2 . Elimination from a Linear System with Constant Coefficients; 3 . Determined, Overdetermined, Underdetermined Systems; 3 . Methods of Integration for Special Differential Equations; 1 . Separation of Variables 327 $a2 . Construction of Further Solutions by Superposition . Fundamental Solution of the Heat Equation . Poisson's Integral4 . Geometric Interpretation of a First Order Partial Differential Equation in Two Independent Variables . The Complete Integral; 1 . Geometric Interpretation of a First Order Partial Differential Equation in Two Independent Variables. The Complete Integral; 2 . The Complete Integral; 3 . Singular Integrals; 4 . Examples; 5 . Theory of Linear and Quasi-Linear Differential Equations of First Order; 1 . Linear Differential Equations; 2 . Quasi-Linear Differential Equations 327 $a6 . The Legendre Transformation1 . The Legendre Transformation for Functions of Two Variables; 2 . The Legendre Transformation for Functions of n Variables; 3 . Application of the Legendre Transformation to Partial Differential Equations; 7 . The Existence Theorem of Cauchy and Kowalewsky; 1 . Introduction and Examples; 2 . Reduction to a System of Quasi-Linear Differential Equations; 3 . Determination of Derivatives Along the Initial Manifold; 4 . Existence Proof for Solutions of Analytic Differential Equations; 4a . Observation About Linear Differential Equations 327 $a4b. Remark About Nonanalytic Differential Equations5. Remarks on Critical Initial Data. Characteristics; Appendix 1 to Chapter I . Laplace's Differential Equation for the Support Function of a Minimal Surface; Appendix 2 to Chapter I . Systems of Differential Equations of First Order and Differential Equations of Higher Order; 1. Plausibility Considerations; 2. Conditions of Equivalence for Systems of Two First Order Partial Differential Equations and a Differential Equation of Second Order; II. General Theory of Partial Differential Equations of First Order 327 $a1. Geometric Theory of Quasi-Linear Differential Equations in Two Independent Variables1. Characteristic Curves; 2. Initial Value Problem; 3. Examples; 2. Quasi-Linear Differential Equations in n Independent Variables; 3. General Differential Equations in Two Independent Variables; 1. Characteristic Curves and Focal Curves. The Monge Cone; 2. Solution of the Initial Value Problem; 3. Characteristics as Branch Elements. Supplementary Integral Conoid. Caustics; 4. The Complete Integral; 5. Focal Curves and the Monge Equation; 6. Examples 327 $a1. The Differential Equation of Straight Light Rays, (grad u)2 = 1 330 $aSince the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961. 410 0$aWiley Classics Library 606 $aMathematical physics 615 0$aMathematical physics. 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 $a9910134845103321 996 $aMethods of mathematical physics$92942416 997 $aUNINA