Introduction to Symmetry Analysis with CD-ROM. Cambridge Texts in Applied Mathematics Part No. 29

  • ID: 2128759
  • Book
  • 654 Pages
  • Cambridge University Press
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Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.
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1. Introduction to symmetry
2. Dimensional analysis
3. Systems of ODE's, first order PDE's, state-space analysis
4. Classical dynamics
5. Introduction to one-parameter Lie groups
6. First order ordinary differential equations
7. Differential functions and notation
8. Ordinary differential equations
9. Partial differential equations
10. Laminar boundary layers
11. Incompressible flow
12. Compressible flow
13. Similarity rules for turbulent shear flows
14. Lie-Bäcklund transformations
15. Invariance condition for integrals, variational symmetries
16. Bäcklund transformations and non-local groups
Appendix 1. Review of calculus and the theory of contact
Appendix 2. Invariance of the contact conditions under Lie point transformation groups
Appendix 3. Infinite-order structure of Lie-Bäcklund transformations
Appendix 4. Symmetry analysis software.
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Brian J. Cantwell. Stanford University, California

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