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Title
Abstract
The Method of Conformal Mappings
The Method of Sources and Sinks
Chaplygin's Equations and Method
The Superposition Procedure
References
All Topics
Mathematics

Foundations of Fluid Mechanics with Applications

Profile image of Evgenii VorozhtsovEvgenii Vorozhtsov

2017, Modern Birkhäuser classics

https://doi.org/10.1007/978-3-319-66149-0
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588 pages

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Abstract

Library of Congress Cataloging-in-Publication Data Kiselev, S.P. (Sergey Petrovich) Foundations of fluid mechanics with applications : problem solving using Mathematica / Sergey P. Kiselev, Evgenii V. Vorozhtsov, Vasily M. Fomin. p. em. (Modeling and simulation in science, engineering and technology) Includes bibliographical references and index.

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  144. Richtmyer, R.D. and Morton, K.W., Difference Methods for Initial-Value Problems, Second Edition, Interscience Publishers, New York, 1967.
  145. ListPlot[{yl, y2, ... }] plotsalistofvalues. Thexcoordinates for each point are taken to be 1, 2, ....
  146. ListPlot[{{x1, y1}, {x2, y2}, ... }] plots a list of values with specified x and y coordinates. Options[ListPlot] = {AspectRatio-> GoldenRatio(-l), Axes-> Automatic, AxesLabel->None, AxesOrigin -> Automatic, AxesStyle -> Automatic, Background -> Automatic, ColorOutput -> Automatic, DefaultColor-> Automatic, Epilog-> {}, Frame -> False, FrameLabel -> None, FrameStyle->Automatic, FrameTicks->Automatic, GridLines -> None, ImageSize -> Automatic, PlotJoined -> False, PlotLabel -> None, PlotRange -> Automatic, PlotRegion -> Automatic, PlotStyle->Automatic, Prolog-> {}, RotateLabel -> True, Ticks -> Automatic, DefaultFont: >$DefaultFont, Display Function: >$Display Function, Format Type: >$FormatType, TextStyle: >$TextStyle} [see also Fig. A.5 (b)].
  147. Example 26
  148. ListPlot[{{0,1},{2,1}, {1,3}, {0,1}}, Axes -> False, PlotJoined -> True] Log[z] gives the natural logarithm of z (logarithm to base e). Log[b, z] gives the logarithm to base b. Options[ParametricPlot3D] = {AmbientLight-> GrayLevel[O.], AspectRatio -> Automatic, Axes -> True, AxesEdge ->Automatic, AxesLabel->None, AxesStyle -> Automatic, Background -> Automatic, Boxed-> True, BoxRatios->Automatic, BoxStyle -> Automatic, ColorOutput -> Automatic, Compiled -> True, DefaultColor -> Automatic, Epilog-> {}, FaceGrids-> None, ImageSize -> Automatic, Lighting -> True, LightSources -> { { {1.,0.,1.}, RGBColor[l,O,O]}, { {1.,1.,1.}, RGBColor[O,l,O]}, { {0.,1.,1.}, RGBColor[O,O,l]} }, Plot3Matrix-> Automatic, PlotLabel -> None, PlotPoints->Automatic, PlotRange -> Automatic, PlotRegion -> Automatic, Polygonlntersections -> True, Prolog-> {}, RenderAll -> True, Shading-> True, SphericalRegion -> False, Ticks -> Automatic, ViewCenter -> Automatic, ViewPoint -> {1.3,-2.399999999999999,2.}, ParametricPlot3D[{2t, Sin[3t], Cos[3t]}, {t, 0, 5Pi}, Boxed -> False, Axes -> False]
  149. Pi ('rr) is the constant pi, with numerical value approximately equal to 3.14159.
  150. Plot3D[f, {x, xmin, xmax}, {y, ymin, ymax}) generates a three-dimensional plot of f as a function of x and y. Plot 3D [ { f, s}, { x, xmin, xmax}, {y, ymin, ymax}] generates a three-dimensional plot in which the height of the surface is specified by j, and the shading is specified by s. Options[Plot3D] = AmbientLight -> GrayLevel[O], AspectRatio -> Automatic, Axes -> True, AxesEdge -> Automatic, AxesLabel->None, AxesStyle -> Automatic, Background -> Automatic, Boxed -> True, BoxRatios -> {1 ,1,0.4}, BoxStyle -> Automatic, ClipFill-> Automatic, ColorFunction -> Automatic, ColorOutput -> Automatic, Compiled -> True, DefaultColor -> Automatic, Epilog -> {} , FaceGrids -> None, Sign[-1.35];
  151. References
  152. Ganzha, V.G. and Vorozhtsov, E.V., Numerical Solutions for Partial Differential Equations: Problem Solving Using Math- ematica, CRC Press, Boca Raton, 1996.
  153. Parker, L. and Christensen, S.M., MathTensor: a System for Doing Tensor Analysis by Computer, Addison-Wesley, Reading, 1994.
  154. Kythe, P.K., Puri, P., and Schaferkotter, M.R., Partial Differential Equations and M athematica, CRC Press, Boca Ra- ton, 1996.
  155. Vvedensky, D., Partial Differential Equations with Mathemat- ica, Addison-Wesley, Reading, 1993.
  156. Skeel, R.D. and Keiper, J.B., Elementary Numerical Com- puting with Mathematica, McGraw-Hill, Inc., New York, 1993.
  157. Baumann, G., Mathematica in Theoretical Physics: Selected Examples from Classical Mechanics to Fractals, TELOS/Sprin- ger-Verlag, New York, 1996.
  158. Martin, E. (Ed.), Mathematica 3.0. Standard Add-on Pack- ages, Wolfram Media, Cambridge University Press, Champaign, IL, 1996.

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