Introduction to Symmetry Analysis

Preface 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-Backlund transformations 15. Invariance condition for integrals, variational symmetries 16. Backlund 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-Backlund transformations Appendix 4. Symmetry analysis software.