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Books on the topic 'Transformations (Mathematics) Conformal mapping'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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Consult the top 18 books for your research on the topic 'Transformations (Mathematics) Conformal mapping.'

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1

Kythe, Prem K. Computational Conformal Mapping. Boston, MA: Birkhäuser Boston, 1998.

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2

A, Laura Patricio A., ed. Conformal mapping: Methods and applications. Amsterdam: Elsevier, 1991.

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3

Conformal transformations in electrical engineering. London: Chapman & Hall, 1985.

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4

Poder, K. Some conformal mappings and transformations for geodesy and topographic cartography. København: Kort & Matrikelstyrelsen, 1998.

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5

Bell, Steven Robert. The Cauchy transform, potential theory, and conformal mapping. Boca Raton, Fl: CRC Press, 1992.

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6

Carabineanu, Adrian. Metoda transformărilor conforme pentru domenii vecine cu aplicații în mecanica fluidelor. București: Editura Academiei Române, 1993.

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7

Conformally invariant processes in the plane. Providence, R.I: American Mathematical Society, 2005.

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8

Grafarend, Erik W. Map projections: Cartographic information systems. Berlin: Springer, 2006.

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9

Advanced engineering mathematics. Englewood Cliffs, N.J: Prentice Hall, 1988.

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10

Advanced engineering mathematics. 2nd ed. Upper Saddle River, N.J: Prentice Hall, 1998.

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11

service), SpringerLink (Online, ed. Green's Functions and Infinite Products: Bridging the Divide. Boston: Springer Science+Business Media, LLC, 2011.

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12

Laura, Patricio A. A., and Roland Schinzinger. Conformal Mapping: Methods and Applications. Dover Publications, 2003.

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13

Ostrowski, A. Collected Mathematical Papers: Vol. 6 XIV Conformal Mapping; XV Numerical Analysis; XVI Miscellany. Birkhauser, 2013.

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14

Krumm, Friedrich W., and Erik W. Grafarend. Map Projections. Springer, 2006.

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15

Map Projections: Cartographic Information Systems. Springer, 2014.

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16

Grafarend, Erik W., Rey-Jer You, and Rainer Syffus. Map Projections: Cartographic Information Systems. Springer, 2017.

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17

Melnikov, Yuri A. Green's Functions and Infinite Products: Bridging the Divide. Birkhäuser, 2011.

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18

Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator is studied using an example by Trefethen et al. The integrable models (KdV, Hasimoto’s vortex soliton) and their hamiltonian formalism are studied. Delving into deeper mathematics, geodesics on Lie groups are studied: first using the Lie algebra and then using Milnor’s approach to the curvature of the Lie group. Arnold’s deep idea that Euler’s equations are the geodesic equations on the diffeomorphism group is then explained and its curvature calculated. The next three chapters are an introduction to numerical methods: spectral methods based on Chebychev functions for ODEs, their application by Orszag to solve the Orr–Sommerfeld equation, finite difference methods for elementary PDEs, the Magnus formula and its application to geometric integrators for ODEs. Two appendices give an introduction to dynamical systems: Arnold’s cat map, homoclinic points, Smale’s horse shoe, Hausdorff dimension of the invariant set, Aref ’s example of chaotic advection. The last appendix introduces renormalization: Ising model on a Cayley tree and Feigenbaum’s theory of period doubling.

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