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Item Open Access Calculus for biological scientists - OER project materials(Colorado State University. Libraries, 2023-07-25) Shriner, Jeff, authorFor interactive version and optimum user experience, please see: https://www.math.colostate.edu/~shriner/meta_frontmatter.html.Item Open Access Mathematics for computational science: lecture notes for MATH 156 - OER project materials(Colorado State University. Libraries, 2022-01-03) Hulpke, Alexander, author; Bonney, K., author; Meade, H., author; Moy, M., author; Neighbors, T., author; Tremaine, R., authorItem Open Access Eigenvalues and completeness for regular and simply irregular two-point differential operators(Colorado State University. Libraries, 2006) Locker, John, authorIn this monograph the author develops the spectral theory for an nth order two-point differential operator L in the Hilbert space L2[0,1], where L is determined by an nth order formal differential operator ℓ having variable coefficients and by n linearly independent boundary values B1,…,Bn. Using the Birkhoff approximate solutions of the differential equation (ρnI−ℓ)u=0, the differential operator L is classified as belonging to one of three possible classes: regular, simply irregular, or degenerate irregular. For the regular and simply irregular classes, the author develops asymptotic expansions of solutions of the differential equation (ρnI−ℓ)u=0, constructs the characteristic determinant and Green's function, characterizes the eigenvalues and the corresponding algebraic multiplicities and ascents, and shows that the generalized eigenfunctions of L are complete in L2[0,1]. He also gives examples of degenerate irregular differential operators illustrating some of the unusual features of this class.