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Publisher Summary This chapter analyzes trigonometric Fourier series, which are series of trigonometric functions. This set is chosen because the mathematics is the best developed and is the simplest to demonstrate. It will serve to illustrate the basic questions that need to be addressed for each system. One technique that is often used in solving partial differential equations is separation of variables. This method yields a set of ordinary differential equations of which the solutions are pasted together to provide a solution to the partial differential equation. In the problems, each ordinary differential equation can be considered as an eigenvalue/eigenfunction problem where the differential operator is self-adjoint. |
