Abstract
We present in §2 a general introduction on mathematical modeling. Irrespective of the case under consideration, the process of mathematical modeling has a general structure. See also references [1,–,6]. This structure comprises a sequence of stages followed again and again. An important ingredient of the modeling process is dimensional analysis . In §3 the main ideas of this technique are presented.
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References
On mathematical modeling
F.A.Bender An Introduction to Mathematical Modeling John Wiley & Sons, New York, 1978, ISBN 0-471-02951-3.
J.S.Berry D.N.Burghes I.D.Huntley (eds.), Teaching and Applying Mathematical Models Ellis Horwood, Chichester, 1985, ISBN 085312-728-X.
D.N.Burghes M.S.Borrie ,Chichester, Ellis Horwood, 1981.
R.R.Clements Mathematical Modeling a Case Study Approach Cambridge University Press, 1989, ISBN 0-521-34340-2.
D.W.Jordan P.Smith , Non-linear Ordinary Differential Equations Oxford University Press, 1977, (*).
On dimensional analysis
A.B.Tayler Mathematical Models in Applied Mechanics Clarendon Press, Oxford, 1986, ISBN 0-19-853533-3.
G.I.Barenblatt Similarity Self-Similarity and Intermediate Asymptotics Consultants Bureau, New York, 1979, ISBN 0-306-10956-5.
E.A.Bender see [1].
On similarity solutions
G.I.Barenblatt see [7].
A.G.Hansen Similarity Analyses of Boundary Value Problems in Engineering Prentice-Hall, London, 1964.
On differential geometry
A.R.Forsyth Lectures on the Differential Geometry of Curves and Surfaces Cambridge University Press, 1912.
C.E.Weatherburn Differential Geometry of Three Dimensions Cambridge University Press, 1927, (*).
D.J.Struik Lectures on Classical Differential Geometry Addison-Wesley, London, 1957, (*).
General Handbooks
A.M.Abramowitz I.A.Stegun Handbook of Mathematical Functions Dover, 1965.
I.S.Gradshteyn I.M.Ryzhik , Tables of Integrals Series and Products Academic Press, 1965.
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© 1992 Springer Science+Business Media Dordrecht
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Molenaar, J. (1992). Mathematical modeling and dimensional analysis. In: van der Burgh, A., Simonis, J. (eds) Topics in Engineering Mathematics. Mathematics and Its Applications, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1814-9_4
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DOI: https://doi.org/10.1007/978-94-011-1814-9_4
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