Second-order ordinary differential equations Special functions, Sturm-Liouville theory and transforms
Publisher: Bookboon
Published: 2013
ISBN-13: 9788776819729
Table of contents: title: Sisältö; title: Power-series solution of ODEs; title: Series solution: essential ideas; title: ODEs with regular singular points; title: Exercises 1; title: The method of Frobenius; title: The basic method; title: The two special cases; title: Exercises; title: The Bessel equation and Bessel functions; title: First solution; title: The second solution; title: The modified Bessel equation; title: The Legendre polynomials; title: Exercises 4; title: The Hermite polynomials; title: Exercises 5; title: Generating functions; title: Legendre polynomials; title: Hermite polynomials; title: Bessel functions; title: Exercises 6; title: Answers; title: Part II: An introduction to Sturm-Liouville theory; title: Preface; title: List of Equations; title: Introduction and Background; title: The second-order equations; title: The boundary-value problem; title: Self-adjoint equations; title: Exercises 1; title: The Sturm-Liouville problem: the eigenvalues; title: Real eigenvalues; title: Simple eigenvalues; title: Ordered eigenvalues; title: Exercises 2; title: The Sturm-Liouville problem: the eigenfunctions; title: The fundamental oscillation theorem; title: Using the fundamental oscillation theorem; title: Orthogonality; title: Eigenfunction expansions; title: Exercises 3; title: Inhomogeneous equations; title: Exercise 4; title: Answers; title: Part III: Integral transforms; title: Preface; title: List of Problems; title: Introduction; title: The appearance of an integral transform from a PDE; title: The appearance of an integral transform from an ODE; title: Exercise 1; title: The Laplace Transform; title: LTs of some elementary functions; title: Some properties of the LT; title: Inversion of the Laplace Transform; title: Applications to the solution of differential and integral equations; title: Exercises 2; title: The Fourier Transform; title: FTs of some elementary functions; title: Some properties of the FT; title: Inversion of the Fourier Transform; title: Applications to the solution of differential and integral equations; title: Exercises 3; title: The Hankel Transform; title: HTs of some elementary functions; title: Some properties of the HT; title: Application to the solution of a PDE; title: Exercises 4; title: The Mellin Transform; title: MTs of some elementary functions; title: Some properties of the MT; title: Applications to the solution of a PDE; title: Exercises 5; title: Tables of a few standard Integral Transforms; title: Answers; title: Index