| In this thesis we derive the solutions of the torsion problem of a cylinder with different cross sections bounded by simple closed curves. The torsion problem can be reduced to solving the two dimensional Dirichlet problem. Four different methods are shown.; The first method, convenient for rectangular curves, involves separation of variables and Fourier analysis. The second method, used to solve cross sections such as those bounded by an ellipse, triangle, or limacon, involves the use of complex functions. The third method, used to solve the problem for cross sections bounded by curves with equation r = cos n (&thetas; /n) or r = sinn (&thetas;/n), involves the use of combinatorial trigonometric identities. And the fourth method, used to solve the torsion problem for cross sections bounded by curvilinear polygons, involves the use of conformal mappings to arrive to solutions. |
