LEADER 04809nam 22007573u 450 001 9911007086003321 005 20230802010932.0 010 $a9780486134895 010 $a048613489X 010 $a9781621986447 010 $a1621986446 035 $a(CKB)2550000001186569 035 $a(EBL)1894782 035 $a(SSID)ssj0001002789 035 $a(PQKBManifestationID)12449627 035 $a(PQKBTitleCode)TC0001002789 035 $a(PQKBWorkID)11016247 035 $a(PQKB)11721683 035 $a(MiAaPQ)EBC1894782 035 $a(Au-PeEL)EBL1894782 035 $a(CaONFJC)MIL565940 035 $a(OCoLC)898421370 035 $a(Perlego)110822 035 $a(EXLCZ)992550000001186569 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aVectors, Tensors and the Basic Equations of Fluid Mechanics 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (606 p.) 225 1 $aDover Books on Mathematics 300 $aDescription based upon print version of record. 311 08$a9780486661100 311 08$a0486661105 311 08$a9781306346894 311 08$a1306346894 327 $aDOVER BOOKS ON MATHEMATICS; Title Page; Copyright Page; Dedication; Preface; Table of Contents; 1 - Introduction; 1.1. Mathematical theories and engineering science; 1.2. Scalars, vectors, and tensors; 1.3. Preview; BIBLIOGRAPHY; 2 - Cartesian Vectors and Tensors: Their Algebra; 2.11. Definition of a vector; 2.12. Example of vectors; 2.13. Scalar multiplication; 2.21. Addition of vectors - Coplanar vectors; 2.22. Unit vectors; 2.23. A basis of non-coplanar vectors; 2.31. Scalar product - Orthogonality; 2.32. Vector product; 2.33. Velocity due to rigid body rotation 327 $a2.34. Triple scalar product2.35. Triple vector product; 2.36. Reciprocal base systems; 2.41. Second order tensors; 2.42. Examples of second order tensors; 2.43. Scalar multiplication and addition; 2.44. Contraction and multiplication; 2.45. The vector of an antisymmetric tensor; 2.5. Canonical form of a symmetric tensor; 2.61. Higher order tensors; 2.62. The quotient rule; 2.7. Isotropic tensors; 2.81. Dyadics and other notations; 2.82. Axial vectors; BIBLIOGRAPHY; 3 - Cartesian Vectors and Tensors: Their Calculus; 3.11. Tensor functions of a time-like variable; 3.12. Curves in space 327 $a4.12. Streamlines4.13. Streaklines; 4.21. Dilatation; 4.22. Reynolds' transport theorem; 4.3. Conservation of mass and the equation of continuity; 4.41. Deformation and rate of strain; 4.42. Physical interpretation of the deformation tensor; 4.43. Principal axes of deformation; 4.5. Vorticity, vortex lines, and tubes; 5 - Stress in Fluids; 5.11. Cauchy's stress principle and the conservation of momentum; 5.12. The stress tensor; 5.13. The symmetry of the stress tensor; 5.14. Hydrostatic pressure; 5.15. Principal axes of stress and the notion of isotropy; 5.21. The Stokesian fluid 327 $a5.22. Constitutive equations of the Stokesian fluid5.23. The Newtonian fluid; 5.24. Interpretation of the constants ? and ?; 6 - Equations of Motion and Energy in Cartesian Coordinates; 6.11. Equations of motion of a Newtonian fluid; 6.12. Boundary conditions; 6.13. The Reynolds number; 6.14. Dissipation of energy by viscous forces; 6.2. Equations for a Stokesian fluid; 6.3. The energy equation; 6.41. Re?sume? of the development of the equations; 6.42. Special cases of the equations; 6.51. Bernoulli theorems; 6.52. Some further properties of barotropic flow; 7 - Tensors 327 $a7.11. Coordinate systems and conventions 330 $a
This introductory text is geared toward engineers, physicists, and applied mathematicians at the advanced undergraduate and graduate levels. It applies the mathematics of Cartesian and general tensors to physical field theories and demonstrates them chiefly in terms of the theory of fluid mechanics. Numerous exercises appear throughout the text. 1962 edition.
410 0$aDover Books on Mathematics 606 $aFluid dynamics 606 $aCalculus of tensors 606 $aVector analysis 606 $aEngineering & Applied Sciences$2HILCC 606 $aApplied Mathematics$2HILCC 615 0$aFluid dynamics. 615 0$aCalculus of tensors. 615 0$aVector analysis. 615 7$aEngineering & Applied Sciences 615 7$aApplied Mathematics 676 $a532 700 $aAris$b Rutherford$06052 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911007086003321 996 $aVectors, tensors, and the basic equations of fluid mechanics$9127671 997 $aUNINA