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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 기하학 > 미분기하학
· ISBN : 9780521824767
· 쪽수 : 518쪽
목차
Introduction; Part I. Symmetries and Integrals: 1. Distributions; 2. Ordinary differential equations; 3. Model differential equations and Lie superposition principle; Part II. Symplectic Algebra: 4. Linear algebra of symplectic vector spaces; 5. Exterior algebra on symplectic vector spaces; 6. A Symplectic classification of exterior 2-forms in dimension 4; 7. Symplectic classification of exterior 2-forms; 8. Classification of exterior 3-forms on a 6-dimensional symplectic space; Part III. Monge-Ampere Equations: 9. Symplectic manifolds; 10. Contact manifolds; 11. Monge-Ampere equations; 12. Symmetries and contact transformations of Monge-Ampere equations; 13. Conservation laws; 14. Monge-Ampere equations on 2-dimensional manifolds and geometric structures; 15. Systems of first order partial differential equations on 2-dimensional manifolds; Part IV. Applications: 16. Non-linear acoustics; 17. Non-linear thermal conductivity; 18. Meteorology applications; Part V. Classification of Monge-Ampere Equations: 19. Classification of symplectic MAEs on 2-dimensional manifolds; 20. Classification of symplectic MAEs on 2-dimensional manifolds; 21. Contact classification of MAEs on 2-dimensional manifolds; 22. Symplectic classification of MAEs on 3-dimensional manifolds.