LEADER 04531nam 22006975 450 001 9910349511603321 005 20251107172636.0 010 $a3-030-26895-0 024 7 $a10.1007/978-3-030-26895-4 035 $a(CKB)4100000009160259 035 $a(DE-He213)978-3-030-26895-4 035 $a(MiAaPQ)EBC5919520 035 $a(PPN)269145583 035 $a(EXLCZ)994100000009160259 100 $a20190830d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Primer in Tensor Analysis and Relativity /$fby Ilya L. Shapiro 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (XVIII, 324 p. 17 illus.) 225 1 $aUndergraduate Lecture Notes in Physics,$x2192-4805 311 08$a3-030-26894-2 327 $aAcknowledgements -- Preface -- Part I: Tensor Algebra and Analysis -- 1: Linear spaces, vectors and tensors -- 2: Operations over tensors, metric tensor -- 3: Symmetric, skew(anti) symmetric tensors and determinants -- 4: Curvilinear coordinates, local coordinate transformations -- 5: Derivatives of tensors, covariant derivates -- 6: Grad, div, rot and relations between them -- 7: Grad, div, rot and in cylindric and spherical coordinates -- 8: Curvilinear, surface and D-dimensional integrals -- 9: Theorems of Green, Stokes and Gauss -- 10: Solutions to the exercises from Part 1 -- Part II: Elements of Electrodynamics and Special Relativity -- 11 Maxwell equations and Lorentz transformations -- 12 Laws of relativistic mechanics -- 13 Maxwell equations in relativistic form -- Part III Applications to General Relativity -- 14 Equivalence principle, covariance and curvature tensor -- 15 Einstein equations, Schwarzschild solution and gravitational waves -- 16 Basic elements of cosmology -- 17 Special sections -- Index. 330 $aThis undergraduate textbook provides a simple, concise introduction to tensor algebra and analysis, as well as special and general relativity. With a plethora of examples, explanations, and exercises, it forms a well-rounded didactic text that will be useful for any related course. The book is divided into three main parts, all based on lecture notes that have been refined for classroom teaching over the past two decades. Part I provides students with a comprehensive overview of tensors. Part II links the very introductory first part and the relatively advanced third part, demonstrating the important intermediate-level applications of tensor analysis. Part III contains an extended discussion of general relativity, and includes material useful for students interested primarily in quantum field theory and quantum gravity. Tailored to the undergraduate, this textbook offers explanations of technical material not easily found or detailed elsewhere, includingan understandable description of Riemann normal coordinates and conformal transformations. Future theoretical and experimental physicists, as well as mathematicians, will thus find it a wonderful first read on the subject. 410 0$aUndergraduate Lecture Notes in Physics,$x2192-4805 606 $aMathematical physics 606 $aGravitation 606 $aElectrodynamics 606 $aElementary particles (Physics) 606 $aQuantum field theory 606 $aMathematical Methods in Physics 606 $aClassical and Quantum Gravity 606 $aClassical Electrodynamics 606 $aMathematical Physics 606 $aTheoretical, Mathematical and Computational Physics 606 $aElementary Particles, Quantum Field Theory 615 0$aMathematical physics. 615 0$aGravitation. 615 0$aElectrodynamics. 615 0$aElementary particles (Physics). 615 0$aQuantum field theory. 615 14$aMathematical Methods in Physics. 615 24$aClassical and Quantum Gravity. 615 24$aClassical Electrodynamics. 615 24$aMathematical Physics. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aElementary Particles, Quantum Field Theory. 676 $a512.57 676 $a515.63 700 $aShapiro$b Ilya L$4aut$4http://id.loc.gov/vocabulary/relators/aut$0892058 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910349511603321 996 $aPrimer in Tensor Analysis and Relativity$92585119 997 $aUNINA