University of California, Berkeley Spring Semester 2010Department of Mechanical Engineering Instructor: P. Papadopoulos ME281 - Methods of Tensor Calculus and Differential Geometry SELECTED BIBLIOGRAPHY I. Classical tensor calculus [1] T. Levi-Civita. The Absolute Differential Calculus. Blackie, London, 1927. [2] A.J. McConnell. Applications of the Absolute Differential Calculus. Blackie, London, 1931. [3] C.E. Weatherburn. An Introduction to Riemannian Geometry and the Tensor Calculus. The University Press, Cambridge, 1938. [4] L.P. Eisenhart. An Introduction to Differential Geometry, with Use of the Tensor Calculus. Princeton University Press, Princeton, 1947. [5] A.D. Michal. Matrix and Tensor Calculus with Applications to Mechanics, Elasticity, and Aeronautics. John Wiley, New York, 1947. [6] J.L. Synge and A. Schild. Tensor Calculus. University of Toronto Press, Toronto, 1949. [7] G.E. Hay. Vector and Tensor Analysis. Dover, New York, 1953. [8] J.A. Schouten. Ricci-Calculus. Springer-Verlag, Berlin, 2nd edition, 1954. [9] J.A. Schouten. Tensor Analysis for Physicists. Clarendon Press, Oxford, 2nd edition, 1959. [10] B. Spain. Tensor Calculus. Edinburg, Oliver and Boyd, New York, 3rd edition, 1960. [11] J.L. Ericksen. Tensor fields. In S. Fl¨ ugge, editor, Handbuch der Physik III/1, pages 794–858. Springer-Verlag, Berlin, 1960. [12] A. Lichnerowicz. Elements of Tensor Calculus. Wiley, New York, 1962. [13] L. Brillouin. Tensors in Mechanics and Elasticity. Academic Press, New York, 1964. [14] I.S. Sokolnikoff. Tensor Analysis, Theory and Applications to Geometry and Mechanics of Continua. Wiley, New York, 2nd edition, 1964. (R) [15] W. Fl¨ ugge. Tensor Analysis and Continuum Mechanics. Springer-Verlag, Berlin, 1972. geometry text ME281 Auslander. (R) [6] S. Redwood City. [18] M. geometry text ME281 . Miles. Addison-Wesley. Reading. [4] L. New York. 1968. 1988.G.E. Abraham. Stoker. Math 140 notes. [2] D. Analysis on Manifolds. 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SpringerVerlag. Differential Geometry. Munkres. Introduction to differential geometry. 1991. Wiley. 1967. Springer-Verlag. Boston. Willmore. Clarendon Press. Nomizu. Differential Geometry. 1983. A Brief on Tensor Analysis. New York. 1961.Ratiu. and Applications. Tensor Analysis. Springer-Varlag. Bowen and C. Struik. New York. New York. Riemannian Geometry. New York. [14] M. 1990.J. Wiley. Bishop and S.I. Thorpe. 2nd edition. Wang. [17] R. Publish or Perish. [8] S. Oxford. Elsevier. Spivak. 1994. 1979. Manifolds. [9] M.-C. [9] R. AMS. Mathematical Foundations of Elasticity. 1975. 1987. (R) [4] B. C. Rund. [12] Y. New York.E. Differential Geometry with Applications to Mechanics and Physics. World Scientific. Flanders. DeWitt-Morette. Marcel Dekker. Oxford University Press. 2001.E. Differential Forms. 2000. Aubin. Tensors and Manifolds: With Applications to Mechanics and Relativity. 1999. New York.R.J.J. 1991. Englewood Cliffs. 1983. [5] Y. 1980. geometry text ME281 . [8] C. 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