Guldberg, A.: Sur les équations différentielles que possedent un système fundamental d'intégrales, C.R. Vessiot, E.: Sur une classe d'équations différentielles, Ann. E.: Introduction to Lie Algebras and Representation Theory, Springer, New York, 1972. Jacobson, N.: Lie Algebras, Interscience Publishers, New York, 1961. and Winternitz, P.: Classification of systems of ordinary differential equations with superposition principles, J. Winternitz, P.: Comments on superposition rules for nonlinear coupled first-order differential equations, J. Wolf (ed.), Nonlinear Phenomena, Lecture Notes in Phys. Winternitz, P.: Lie groups and solutions of nonlinear differential equations, In: K. and Marle, Ch.-M.: Symplectic Geometry and Analytical Mechanics, D. Lie, S.: Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen (revised and edited by Dr G. and Norman, E.: On global representations of the solutions of linear differential equations as a product of exponentials, Mem. and Norman, E.: Lie algebraic solution of linear differential equations, J. and Ramos, A.: Integrability of Riccati equation from a group theoretical viewpoint, Internat. F.: Related operators and exact solutions of Schrödinger equations, Internat. and Nasarre, J.: The nonlinear superposition principle and the Wei-Norman method, Internat. M.: A generalization of Lie's 'counting' theorem for second-order ordinary differential equations, J. Homework problems contain all the main types of possible exam questions.Anderson, R. Here is a few review problems to make sure you haven't overlooked an important topic:Ĥ.Rev: 3, 4, 6, 7, 9, 11, 13, 22, 25, 26, 32 5.Rev: 2, 3, 5, 6, 11, 12, 17, 18 6.Rev: 3, 4, 7, 8, 15 (find the formula for the coefficients, and write out explicitly the first few terms) 19, 20.
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