Date of Graduation
Master of Science in Mathematics
wave equation, energy, Fourier series, Fourier coeﬃcients, partial diﬀerential equations
Partial Differential Equations
The focus of this thesis is to show how methods of Fourier analysis, in particular Parseval’s equality, can be used to provide explicit energy calculations for solutions of wave equations in one dimension. These calculations are discussed for simple examples and then extended to ﬁt the general wave equation with Robin boundary conditions. Ideas from Sobolev space theory are used to provide justiﬁcation of the method.
© Ellen R. Hunter
Hunter, Ellen R., "Energy Calculations and Wave Equations" (2018). MSU Graduate Theses. 3232.