LEADER 05287nam 22006613u 450 001 9911007077603321 005 20230803022821.0 010 $a0-486-13160-2 010 $a1-62198-611-X 035 $a(CKB)2550000001185941 035 $a(EBL)1894900 035 $a(SSID)ssj0001002722 035 $a(PQKBManifestationID)12389498 035 $a(PQKBTitleCode)TC0001002722 035 $a(PQKBWorkID)11014883 035 $a(PQKB)10564888 035 $a(MiAaPQ)EBC1894900 035 $a(Au-PeEL)EBL1894900 035 $a(CaONFJC)MIL565319 035 $a(OCoLC)868270297 035 $a(EXLCZ)992550000001185941 100 $a20141222d2013|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFundamentals of Mathematical Physics 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2013 215 $a1 online resource (1001 p.) 225 1 $aDover Books on Physics 300 $aDescription based upon print version of record. 311 08$a0-486-45809-1 311 08$a1-306-34068-3 327 $aTitle Page; Copyright Page; preface; errata; Table of Contents; CHAPTER ONE - vector algebra; INTRODUCTION; 1-1 DEFINITIONS; 1-2 EQUALITY OF VECTORS AND NULL VECTORS; 1-3 VECTOR OPERATIONS; 1-4 EXPANSION OF VECTORS; 1-5 VECTOR IDENTITIES; 1-6 PROBLEMS AND APPLICATIONS; CHAPTER TWO - matrix and tensor algebra; 2-1 DEFINITIONS; 2-2 EQUALITY OF MATRICES AND NULL MATRICES; 2-3 MATRIX OPERATIONS; 2-4 DETERMINANTS; 2-5 SPECIAL MATRICES; 2-6 SYSTEMS OF LINEAR EQUATIONS; 2-7 LINEAR OPERATORS; 2-8 EIGENVALUE PROBLEMS; 2-9 DIAGONALIZATION OF MATRICES; 2-10 SPECIAL PROPERTIES OF HERMITIAN MATRICES 327 $a2-11 TENSOR ALGEBRA2-12 TENSOR OPERATIONS; 2-13 TRANSFORMATION PROPERTIES OF TENSORS; 2-14 SPECIAL TENSORS; 2-15 PROBLEMS AND APPLICATIONS; CHAPTER THREE - vector calculus; 3-1 ORDINARY VECTOR DIFFERENTIATION; 3-2 PARTIAL VECTOR DIFFERENTIATION; 3-3 VECTOR OPERATIONS IN CYLINDRICAL AND SPHERICAL COORDINATE SYSTEMS; 3-4 DIFFERENTIAL VECTOR IDENTITIES; 3-5 VECTOR INTEGRATION OVER A CLOSED SURFACE; 3-6 THE DIVERGENCE THEOREM; 3-7 THE GRADIENT THEOREM; 3-8 THE CURL THEOREM; 3-9 VECTOR INTEGRATION OVER A CLOSED CURVE; 3-10 THE TWO-DIMENSIONAL DIVERGENCE THEOREM 327 $a3-11 THE TWO-DIMENSIONAL GRADIENT THEOREM3-12 THE TWO-DIMENSIONAL CURL THEOREM; 3-13 MNEMONIC OPERATORS; 3-14 KINEMATICS OF INFINITESIMAL VOLUME, SURFACE, AND LINE ELEMENTS; 3-15 KINEMATICS OF A VOLUME INTEGRAL; 3-16 KINEMATICS OF A SURFACE INTEGRAL; 3-17 KINEMATICS OF A LINE INTEGRAL; 3-18 SOLID ANGLE; 3-19 DECOMPOSITION OF A VECTOR FIELD INTO SOLENOIDAL AND IRROTATIONAL PARTS; 3-20 INTEGRAL THEOREMS FOR DISCONTINUOUS AND UNBOUNDED FUNCTIONS; 3-21 PROBLEMS AND APPLICATIONS; CHAPTER FOUR - functions of a complex variable; 4-1 INTRODUCTION; 4-2 DEFINITIONS; 4-3 COMPLEX ALGEBRA 327 $a4-4 DOMAIN OF CONVERGENCE4-5 ANALYTIC FUNCTIONS; 4-6 CAUCHY'S APPROACH; 4-7 CAUCHY'S INTEGRAL THEOREM; 4-8 CAUCHY'S INTEGRAL REPRESENTATION OF AN ANALYTIC FUNCTION THEOREM:; 4-9 TAYLOR'S SERIES; 4-10 CAUCHY'S INEQUALITIES; 4-11 ENTIRE FUNCTIONS; 4-12 RIEMANN'S THEORY OF FUNCTIONS OF A COMPLEX VARIABLE; 4-13 PHYSICAL INTERPRETATION; 4-14 FUNCTIONS DEFINED ON CURVED SURFACES; 4-15 LAURENT'S SERIES; 4-16 SINGULARITIES OF AN ANALYTIC FUNCTION; 4-17 MULTIVALUED FUNCTIONS; 4-18 RESIDUES; 4-19 RESIDUE AT INFINITY; 4-20 GENERALIZED RESIDUE THEOREM OF CAUCHY; 4-21 PROBLEMS AND APPLICATIONS 327 $aCHAPTER FIVE - integral transforms5-1 INTRODUCTION; 5-2 ORTHOGONAL FUNCTIONS; 5-3 DIRAC'S NOTATION; 5-4 ANALOGY BETWEEN EXPANSION IN ORTHOGONAL FUNCTIONS AND EXPANSION IN ORTHOGONAL VECTORS; 5-5 LINEAR INDEPENDENCE OF FUNCTIONS; 5-6 MEAN-SQUARE CONVERGENCE OF AN EXPANSION IN ORTHOGONAL FUNCTIONS; 5-7 INTEGRATION AND DIFFERENTIATION OF ORTHOGONAL EXPANSIONS; 5-8 POINTWISE CONVERGENCE OF AN ORTHOGONAL EXPANSION; 5-9 GIBBS'S PHENOMENON; 5-10 THE FINITE SINE TRANSFORM; 5-11 THE FINITE COSINE TRANSFORM; 5-12 PROPERTIES OF FINITE FOURIER TRANSFORMS 327 $a5-13 CONNECTION WITH CLASSICAL THEORY OF FOURIER SERIES 330 $aIndispensable for students of modern physics, this text provides the necessary background in mathematics for the study of electromagnetic theory and quantum mechanics. Clear discussions explain the particulars of vector algebra, matrix and tensor algebra, vector calculus, functions of a complex variable, integral transforms, linear differential equations, and partial differential equations. This volume collects under one cover the mathematical ideas formerly available only by taking many separate courses. It offers in-depth treatments, with a minimum of mathematical formalism. Suitable for stu 410 0$aDover Books on Physics 606 $aMathematical physics 606 $aEngineering & Applied Sciences$2HILCC 606 $aApplied Physics$2HILCC 615 0$aMathematical physics. 615 7$aEngineering & Applied Sciences 615 7$aApplied Physics 676 $a530.15 700 $aKraut$b Edgar A$0149551 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911007077603321 996 $aFundamentals of Mathematical Physics$9512402 997 $aUNINA