Return to computing page for the first course APMA0330
Return to computing page for the second course APMA0340
Return to Mathematica tutorial for the first course APMA0330
Return to Mathematica tutorial for the second course APMA0340
Return to the main page for the first course APMA0330
Return to the main page for the second course APMA0340
Return to Part V of the course APMA0340
Introduction to Linear Algebra with Mathematica

Glossary

Preface

Inthe previous section, we discyssed regular Sturm--Liouville problems on some finite interval |α, β| for the second order self-adjoint differential operator
\begin{equation} \label{EqSingular.1} L \left[ x, \texttt{D} \right] = - \texttt{D}\,p(x)\, \texttt{D} - q(x)\,\texttt{I} = - \frac{\text d}{{\text d}x}\,p(x)\,\frac{\text d}{{\text d}x} - q(x) , \qquad \texttt{D} = \frac{\text d}{{\text d}x} \quad \texttt{I} = \texttt{D}^0 . \end{equation}
In its definition, we assumed that coefficients q(x), p(x), and its derivative dp(x)/dx are continuous and bounded functions on a finite closed interval [α, β].

 

  1. Everitt, W.N., A Catalogue of Sturm-Liouville Differential Equations, In: Sturm-Liouville Theory: Past and Present, pp. 271–331. Ed. W.O. Amrein, A.M. Hinz, D.B. Pearson, 2005, Birkhauser Verlag, Basel/Switzerland.
  2. Herron, I.H., Solving singular boundary value problems for ordinary differential equations, Caribbean Journal of Mathematical and Computing Sciences, 2013, 15, pp. 1--30.
  3. Krall, A.M., (1986). The Singular Sturm--Liouville Problem. In: Applied Analysis. Mathematics and Its Applications, vol 31. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4748-1_12
  4. Lützen, J. Sturm and Liouville’s work on ordinary linear differential equations. The emergence of Sturm-Liouville theory, Archive for History of Exact Sciences, 1984, volume 29, pages 309–376. https://doi.org/10.1007/BF00348405
  5. Philip, P., The Green's Function for a Singular Boundary Value Problem, M.S. Thesis, Department of Mathematics, Howard University, Washington D.C., 1975.
  6. Stakgold, I., Green's Functions and Boundary Value Problems, 1998, Second edition, Wiley Interscience, New York.
  7. Titchmarsh, E.C., Eigenfunction Expansions Associated with Second-order Differential Equations, 1946, Clarendon, Oxford.
  9. Zettl, A., Sturm--Liouville Theory, 2005, American Mathematical Sosiety, Providence, RI.

 

Return to Mathematica page
Return to the main page (APMA0340)
Return to the Part 1 Matrix Algebra
Return to the Part 2 Linear Systems of Ordinary Differential Equations
Return to the Part 3 Non-linear Systems of Ordinary Differential Equations
Return to the Part 4 Numerical Methods
Return to the Part 5 Fourier Series
Return to the Part 6 Partial Differential Equations
Return to the Part 7 Special Functions