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Mathematical Prerequisites

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

Abstract

Lake physics cannot be described let alone understood without tailoring the statements in mathematical expressions and deducing results from these. We now wish to lay down the mathematical prerequisites that are indispensable to reach quantitative results. A systematic presentation will not be given because it is assumed that the reader is (or once has been) familiar with the subjects and only needs to be reminded of knowledge that may be somewhat dormant. Let us begin with mathematics.

Keywords

Steep Descent Cartesian Coordinate System Tensor Field Vector Product Cartesian Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Abramowitz, M. and Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York, NY (1964) (and later)Google Scholar
  2. 2.
    Arfken, G.B. and Weber, H.J.: Mathematical Methods for Physicists (6th Edition). Wiley Danvers, MA (2005)Google Scholar
  3. 3.
    Betten, J.: Tensorrechnung für Ingenieure. B.G. Teubner, Stuttgart 320 p. (1987)CrossRefGoogle Scholar
  4. 4.
    Block, H.D.: Introduction to Tensor Analysis. Charles E. Merill Books, Columbus, OH, 62 p. (1962)Google Scholar
  5. 5.
    Bowen, R.M. and Wang, C.C.: Introduction to Vectors and Tensors, Vol. 1: Linear and multilinear Algebra, Vol. 2. Vector and Tensor Analysis. Plenum New York, NY, 434 p. (1976)Google Scholar
  6. 6.
    Bronstein, I.N., Semendjajew, K.A., Musiol, G. and Mühlig, G.: Taschanbuch der Mathematik. Verlag Harri Deutsch, Germany 1. Aufl. 848 p. (1993)Google Scholar
  7. 7.
    Chadwick, P.: Continuum Mechanics, Concise Theory and Problems. George Atten & Unwin Ltd. 174 p. (1976), also Dover, New York, NY, 187 p. (1999)Google Scholar
  8. 8.
    Feynman, R.P., Leighton, R.B. and Sand, M.: The Feynman Lectures on Physics. Vol. 1, 2, 3 Addison-Wesley, Reading, MA (1966)Google Scholar
  9. 9.
    Gurtin, M.E.: An Introduction to Continuum Mechanics. Academic, New York, NY, 265 p. (1981)Google Scholar
  10. 10.
    Hutter, K. and Jöhnk, K.: Continuum Methods of Physical Modeling. Springer, Berlin, 635 p. (2004)Google Scholar
  11. 11.
    Klingbeil, E.: Tensorrechnung für Ingenieure. B. I. Wissenschaftsverlag, Mannheim 197 p. (1989)Google Scholar
  12. 12.
    Kreyszig, E.: Advanced Engineering Mathematics (9th Edition). Wiley, Hoboken, NJ, USA, (2006)Google Scholar
  13. 13.
    Liu, I.-S.: Introduction to Continuum Mechanics. Springer, Berlin, 297 p. (2002)Google Scholar
  14. 14.
    Maiss, M.: Schwefelhexafluorid (SF) als Tracer für Mischungsprozesse im westlichen Bodensee. PhD Thesis, Ruprecht-Karls-Universität Heidelberg (1992)Google Scholar
  15. 15.
    Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler, Band 3 (3. Auflage), Vieweg, Braunschweig, Wiesbaden (1999)Google Scholar
  16. 16.
    Papula, L.: Mathematik für Ingenieure und Naturwissenschaftler, Bände 1,2 (9. Auflage). Vieweg, Braunschweig, Wiesbaden (2000)Google Scholar
  17. 17.
    Sokolnikoff, I.S. and Redheffer, R.M.: Mathematics of Physics and Modern Engineering (2nd Edition). McGraw-Hill, New York, NY (1966)Google Scholar
  18. 18.
    Spencer, A.J.M.: Continuum Mechanics. Longman, New York, NY, 183 p. (1980)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.ETH Zürich, c/o Versuchsanstalt für Wasserbau Hydrologie und GlaziologieZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  3. 3.Russian Academy of Sciences, P.P. Shirshov Institute of OceanologyKaliningradRussia

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