

Contents


Week 1: 
Vector spaces, subspaces, linear transformations 
Week 2: 
Dual spaces, multilinear functionals 
Week 3: 
Symplectic vector spaces 
Week 4: 
Symplectic transformations 
Week 5: 
Hamilton’s equations 
Week 6: 
Hamiltonian flows 
Week 7: 
Poisson brackets 
Week 8: 
KdV Eq., Wave Eq., Schrödinger Eq., SineGordon Eq. 
Week 9: 
Midterm exam 
Week 10: 
Manifolds 
Week 11: 
Vector fields and differential forms 
Week 12: 
Symplectic manifolds, Hamiltonian systems, Canonical maps 
Week 13: 
Poisson brackets on symplectic manifolds 
Week 14: 
The canonical Hamiltonian systems on cotangent bundles 
Week 15*: 
Review 
Week 16*: 
Final Exam 
Textbooks and materials: 
• Marsden, J. E., & Ratiu, T. (1999), Introduction to mechanics and symmetry, Second edition, Texts in Applied Mathematics 17, SpringerVerlag, New York. • Libermann, P., & Marle, C. M. (2012), Symplectic geometry and analytical mechanics (Vol. 35), Springer. • Abraham, R. & Marsden, J. E. (1978), Foundations of mechanics, Benjamin/Cummings Publishing Company, Reading, Massachusetts.

Recommended readings: 
• Arnold, V.I. (2013) Mathematical methods of classical mechanics (Vol. 60), Springer • Holm, D.D. (2008) Geometric Mechanics. Part I and Part II, Imperial College Press, London, • Holm, D.D., Schmah, T. & Stoica C. (2009) Geometric Mechanics and Symmetry. From Finite to Infinite Dimensions, Oxford University Press,


* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

