LEADER 05326nam 2200637 a 450 001 9910141646603321 005 20230803025553.0 010 $a3-527-65363-5 010 $a3-527-65361-9 010 $a1-299-24132-8 010 $a3-527-65364-3 035 $a(CKB)2670000000337934 035 $a(EBL)1132847 035 $a(OCoLC)829459887 035 $a(SSID)ssj0000904755 035 $a(PQKBManifestationID)11476836 035 $a(PQKBTitleCode)TC0000904755 035 $a(PQKBWorkID)10924492 035 $a(PQKB)10179312 035 $a(MiAaPQ)EBC1132847 035 $a(Au-PeEL)EBL1132847 035 $a(CaPaEBR)ebr10667427 035 $a(CaONFJC)MIL455382 035 $a(EXLCZ)992670000000337934 100 $a20130312d2013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDistribution theory$b[electronic resource] $ewith applications in engineering and physics /$fPetre P. Teodorescu, Wilhelm W. Kecs, and Antonela Toma 210 $aWeinheim, Germany $cWiley$d2013 215 $a1 online resource (395 p.) 300 $aDescription based upon print version of record. 311 $a3-527-41083-X 320 $aIncludes bibliographical references and index. 327 $aDistribution Theory; Contents; Preface; 1 Introduction to the Distribution Theory; 1.1 Short History; 1.2 Fundamental Concepts and Formulae; 1.2.1 Normed Vector Spaces: Metric Spaces; 1.2.2 Spaces of Test Functions; 1.2.3 Spaces of Distributions; 1.2.4 Characterization Theorems of Distributions; 1.3 Operations with Distributions; 1.3.1 The Change of Variables in Distributions; 1.3.2 Translation, Symmetry and Homothety of Distributions; 1.3.3 Differentiation of Distributions; 1.3.4 The Fundamental Solution of a Linear Differential Operator; 1.3.5 The Derivation of the Homogeneous Distributions 327 $a1.3.6 Dirac Representative Sequences: Criteria for the Representative Dirac Sequences1.3.7 Distributions Depending on a Parameter; 1.3.8 Direct Product and Convolution Product of Functions and Distributions; 1.3.9 Partial Convolution Product of Functions; 2 Integral Transforms of Distributions; 2.1 Fourier Series and Series of Distributions; 2.1.1 Sequences and Series of Distributions; 2.1.2 Expansion of Distributions into Fourier Series; 2.1.3 Expansion of Singular Distributions into Fourier Series; 2.2 Fourier Transforms of Functions and Distributions; 2.2.1 Fourier Transforms of Functions 327 $a2.2.2 Fourier Transform and the Convolution Product2.2.3 Partial Fourier Transform of Functions; 2.2.4 Fourier Transform of Distributions from the Spaces S and D(Rn); 2.3 Laplace Transforms of Functions and Distributions; 2.3.1 Laplace Transforms of Functions; 2.3.2 Laplace Transforms of Distributions; 3 Variational Calculus and Differential Equations in Distributions; 3.1 Variational Calculus in Distributions; 3.1.1 Equations of the Euler-Poisson Type; 3.2 Ordinary Differential Equations; 3.3 Convolution Equations; 3.3.1 Convolution Algebras 327 $a3.3.2 Convolution Algebra D'+: Convolution Equations in D'+3.4 The Cauchy Problem for Linear Differential Equations with Constant Coefficients; 3.5 Partial Differential Equations: Fundamental Solutions and Solving the Cauchy Problem; 3.5.1 Fundamental Solution for the Longitudinal Vibrations of Viscoelastic Bars of Maxwell Type; 3.6 Wave Equation and the Solution of the Cauchy Problem; 3.7 Heat Equation and Cauchy Problem Solution; 3.8 Poisson Equation: Fundamental Solutions; 3.9 Green's Functions: Methods of Calculation; 3.9.1 Heat Conduction Equation 327 $a3.9.2 Green's Function for the Vibrating String4 Representation in Distributions of Mechanical and Physical Quantities; 4.1 Representation of Concentrated Forces; 4.2 Representation of Concentrated Moments; 4.2.1 Concentrate Moment of Linear Dipole Type; 4.2.2 Rotational Concentrated Moment (Center of Rotation); 4.2.3 Concentrated Moment of Plane Dipole Type (Center of Dilatation or Contraction); 4.3 Representation in Distributions of the Shear Forces and the Bending Moments; 4.3.1 Concentrated Force of Magnitude P Applied at the Point c in [a,b] 327 $a4.3.2 Concentrated Moment of Magnitude m Applied at the Point c in [a,b] 330 $aIn this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail.They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mec 606 $aDistribution (Probability theory) 615 0$aDistribution (Probability theory) 676 $a515.782 700 $aTeodorescu$b P. P$0932126 701 $aKecs$b Wilhelm W$041423 701 $aToma$b Antonela$0932127 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910141646603321 996 $aDistribution theory$92096776 997 $aUNINA