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|a 9781621986119
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|z 0486458091
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|a (OCoLC)714803389
|z (OCoLC)860812169
|z (OCoLC)961885868
|z (OCoLC)988711286
|z (OCoLC)999584005
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|a dlr
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|b .K7 2007
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|a 530.15
|2 22
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|a UAMI
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|a Kraut, Edgar A.
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|a Fundamentals of mathematical physics /
|c Edgar A. Kraut.
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|a Dover ed.
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| 260 |
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|a Mineola, N.Y. :
|b Dover Publications,
|c 2007.
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| 300 |
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|a 1 online resource (xiii, 466 pages) :
|b illustrations
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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| 504 |
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|a Includes bibliographical references and index.
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| 506 |
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|3 Use copy
|f Restrictions unspecified
|2 star
|5 MiAaHDL
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| 533 |
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|a Electronic reproduction.
|b [Place of publication not identified] :
|c HathiTrust Digital Library,
|d 2011.
|5 MiAaHDL
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| 538 |
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|a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
|u http://purl.oclc.org/DLF/benchrepro0212
|5 MiAaHDL
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| 583 |
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|a digitized
|c 2011
|h HathiTrust Digital Library
|l committed to preserve
|2 pda
|5 MiAaHDL
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|a Print version record.
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|a Machine derived contents note: chapter one vector algebra 1 -- Introduction I -- I-1 Definitions 3 -- 1-2 Equality of Vectors and Null Vectors 4 -- 1-3 Vector Operations 5 -- 1-4 Expansion of Vectors 9 -- 1-5 Vector Identities 14 -- 86 Problems and Applications 15 -- chapter two matrix and tensor algebra 17 -- 2-1 Definitions 17 -- 2-2 Equality of Matrices and Null Matrices 18 -- 2-3 Matrix Operations 19 -- 2-4 Determinants 23 -- 2-5 Special Matrices 25 -- 2-6 Systems of Linear Equations 30 -- 2-7 Linear Operators 33 -- 2-8 Eigenvalue Problems 37 -- 2-9 Diagonalization of Matrices 40 -- 2-10 Special Properties of Hermitian Matrices 46 -- 2-11 Tensor Algebra 47 -- 2-12 Tensor Operations 48 -- 2-13 Transformation Properties of Tensors 50 -- 2-14 Special Tensors 53 -- 2-15 Problems and Applications 55 -- chapter three vector calculus 59 -- 3-1 Ordinary Vector Differentiation 59 -- 3-2 Partial Vector Differentiation 64 -- 3-3 Vector Operations in Cylindrical and Spherical Coordinate Systems 68 -- 3-4 Differential Vector Identities 74 -- 3-5 Vector Integration over a Closed Surface 76 -- 3-6 The Divergence Theorem 80 -- 3-7 The Gradient Theorem 82 -- 3-8 The Curl Theorem 82 -- 3-9 Vector Integration over a Closed Curve 83 -- 3-0 The Two-dimensional Divergence Theorem 87 -- 3-11 The Two-dimensional Gradient Theorem 87 -- 3-12 The Two-dimensional Curl Theorem 88 -- 3-13 Mnemonic Operators 92 -- 3-14 Kinematics of Infinitesimal Volume, Surface, and Line Elements 93 -- 3-15 Kinematics of a Volume Integral 96 -- 3-1.6 Kinematics of a Surface Integral 97 -- 3-17 Kinematics of a Line Integral 99 -- 3-18 Solid Angle 100 -- 3-19 Decomposition of a Vector Field into Solenoidal and -- Irrotational Parts 102 -- 3-20 Integral Theorems for Discontinuous and Unbounded Functions 103 -- 3-21 Problems and Applications 115 -- chapter four functions of a complex variable 127 -- 4-1 Introduction 127 -- 4-2 Definitions 127 -- 4-3 Complex Algebra 129 -- 4-4 Domain of Convergence 130 -- 4-5 IAnalytic Functions 131 -- 4-6 Cauchy's Approach 133 -- 4-7 Cauchy's Integral Theorem 134 -- 4-8 Cauchy's integral Representation of an Analytic Function 136 -- 4-9 Taylor's Series 139 -- 4-10 Cauchy's Inequalities 140 -- 4-11 Entire Functions 140 -- 4-12 Riemann's Theory of Functions of a Complex Variable 141 -- 4-13 Physical Interpretation 142 -- 4-14 Functions Defined on Curved Surfaces 145 -- 4-15 Laurent's Series 152 -- 4-16 Singularities of an Analytic Function 154 -- 4-17 Multivalued Functions 155 -- 4-18 Residues 158 -- 4-19 Residue at Infinity 161 -- 4-20 Generalized Residue Theorem of Cauchy 162 -- 4-21 Problems and Applications 167 -- chapter five integral transforms 173 -- 5-1 Introduction 173 -- 5-2 Orthogonal Functions 174 -- 5-3 Dirac's Notation 175 -- 5-4 Analogy between Expansion in Orthogonal Functions -- and Expansion in Orthogonal Vectors 177 -- 5-5 Linear Independence of Functions 179 -- 5-6 Mean-square Convergence of an Expansion -- in Orthogonal Functions 180 -- 5-7 In tgration and Differentiation of Orthogonal Expansions 185 -- 5-8 Pointwise Convergence of an Orthogonal Expansion 185 -- 5-9 Gibbs's bhenorenon 186 -- 5-10 The inite Sine Transform 187 -- 5411 The Finite Cosine Transform 190 -- 5-12 Properties of Finite Fourier Transforms 191 -- 5-13 Connection with Classical Theory of Fourier Series 192 -- 5-14 Applications of Finite Fourier Transforms 194 -- 5i-5 Infinite-range Fourier Transforms 206 -- 5-16 Condiions for the Applicability of the Fourier Transformation 210 -- 5-17 Fourier Sin and Cosine Transforms 211 -- 5-18 Fourier Transforms in n Dimensions 213 -- 5-19 Properties of Fourier Transforms 214 -- 5-20 Physical Interpretation of the Fourier Transform 216 -- 5-21 Applications of the Infinite-range Fourier Transform 218 -- 5-22 The L, avlace Transform 223 -- 5-23 Properties of Laplace Transforms 226 -- 5-24 Application of the Laplace Transform 228 -- 5-25 Problems and Applications 232 -- chapter six linear differential equations 239 -- 6-1 Introduction 239 -- 6-2 Linear Differential Equations with Constant Coefficients 240 -- 6-3 The Theory of the Seismograph 246 -- 6-4 Linear Differential Equations with Variable Coeffcients 252 -- 6-5 The Special Functions of Mathematical Physics 255 -- 6-6 The Gamma Function 256 -- 6-7 The Beta Function 259 -- 6-8 The Bessel Functions 261 -- 6-9 The Neumann Functions 264 -- 6 -0 Bessel Funetions of Arbitrary Order 267 -- 6-11 The Hankel Functions 269 -- "6-12 The Hyperbolic Bessel Functions 270 -- 6-13 The Associated Legendre Functions 272 -- 6-14 Representation of Associated Legendre Functions -- in Terms of Legendre Polynomials 275 -- 6-15 Spherical Harmonies 276 -- 6-16 Spherical Bessel Functions 279 -- 6-17 Hermite Polynomials 281 -- 6-18 General Properties of Linear Second-order Differential Equations -- with Variable Coefficients 287 -- 6-19 Evaluation of the Wronskian 291 -- 6-20 General Solution of a Homogeneous Equation -- Using Abels Formula 292 -- 6-21 Solution of an Inhomogeneous Equation -- Using Abel's Formula 293 -- 6-22 Green's Function 295 -- 6-23 Use of the Green's Function g(xjx') 296 -- 6-24 The Sturm-Liouville Problem 299 -- 6-25 Solution of Ordinary Differential Equations with Variable -- Coefficients by Transform Methods 303 -- 6-26 Problems and Applications 306 -- chapter seven partial differential equations 317 -- 7-1 Introduction 317 -- 7-2 The Role of the Laplacian 317 -- 7-3 Laplace's Equation 318 -- 7-4 Poisson's Equation 318 -- 7-5 The Diffusion Equation 319 -- 7-6 The Wave Equation 321 -- 7-7 A Few General Remarks 322 -- 7-8 Solution of Potential Problems in Two Dimensions 323 -- 7-9 Separation of Variables 333 -- 7-10 The Solution of Laplace's Equation in a Half Space 338 -- 7-11 Laplace's Equation in Polar Coordinates 343 -- 7-12 Construction of a Green's Function in Polar Coordinates 344 -- 7-13 The Exterior Dirichlet Problem for a Circle 352 -- 7-14 Laplace's Equation in Cylindrical Coordinates 354 -- 7-15 Construction of the Green's Function 356 -- 7-16 An Alternative Method of Solving Boundary-value Problems 360 -- 17 Laplace's Equation in Spherical Coordinates 363 -- 7-18 Construction of the Green's Function 365 -- 7-19 Solution of the Interior and Exterior Dirichlet Problems -- for a Grounded Conducting Sphere 368 -- "7-20 The One-dimensional Wave Equation 371 -- 7-21 The Two-dimensional Wave Equation 377 -- 7-22 The Helmholtz Equation in Cylindrical Coordinates 382 -- 7-23 The Helmholtz Equation in Rectangular Cartesian Coordinates 392. -- 7-24 The Helmholtz Equation in Spherical Coordinates 400 -- 7-25 Interpretation of the Integral Solution of Helmholtz's Equation 403 -- 7-26 The Sommerfeld Radiation Condition 405 -- 7-27 Time-dependent Problems 409 -- 7-28 Poisson's Solution of the Wave Equation 413 -- 7-29 The Diffusion Equation 420 -- 7-30 General Solution of the Diffusion Equation 422 -- 7-31 Construction of the Infinite-medium Green's Function -- for the Diffusion Equation 423 -- 7-32 Problems and Applications 427.
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|a Knovel
|b ACADEMIC - General Engineering & Project Administration
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| 650 |
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|a Mathematical physics.
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| 650 |
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|a Physique mathématique.
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| 650 |
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|a Mathematical physics
|2 fast
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|i Print version:
|w (DLC) 2006051798
|w (OCoLC)74988523
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| 856 |
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|u https://appknovel.uam.elogim.com/kn/resources/kpFMP00001/toc
|z Texto completo
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|b YANK
|n 12215318
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|a 92
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