NCTS(South)/ NCKU Math Colloquium | |
DATE | 2010-03-18ˇ@15:10-16:00 |
PLACE | R204,2F,NCTS,NCKU |
SPEAKER | Prof. Reyer Sjamaarˇ]Cornell Universityˇ^ |
TITLE | Differential Equations and Lie's Theory of Continuous Groups |
ABSTRACT |
Most ordinary differential equations cannot be explicitly solved. However, in the seventeenth and eighteenth centuries countless methods were devised for solving special types of differential equations. A few of these methods are taught to this day in undergraduate mathemati cs courses. Sophus Lie, in the late nineteenth century, had the insight that almost all these classical methods can be explained by a single idea: the notion of continuous symmetries. For instance, he discovered that second-order differential equations admitting at least two continuous symmetries can be transformed to four basic types, each of which can be solved by two successive integrations. In this talk I will attempt to explain some of Lie's discoveries. |