Prerequisites: 301, ORF 309. Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, ...

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Ordinary differential equations; Sturm-Liouville theory, properties of special functions, solution methods including Laplace transforms. Fourier series: eigenvalue problems and expansions in ...

Redolfi Steven A., "Expansion in Eigenfunctions for Systems of Ordinary Differential Equations Without the Unique Continuation Property," 04/2023 (Weikard). Risk Quantitative Model Validation Analyst ...

What is Integrability? Let us begin by considering ordinary differential equations. In classical mechanics, the standard ‘Liouville’ definition of integrability is that there should exist a sufficient ...

The Helsinki Mathematical Physics Group has been in applying these ideas to a wide variety of problems including turbulence and stochastic differential equations, kinetic theory, fluctuating ...

Quantum chemistry applies quantum mechanics to the theoretical study of chemical systems. It aims, in principle, to solve the Schrödinger equation for the system under scrutiny; however, its ...

An extended class of orthogonal polynomials defined by a Sturm–Liouville problem, with David Gómez-Ullate, Niky Kamran, Journal of Mathematical Analysis and Applications 359 (2009) 352-367.

Investigation of this solution perspective establishes the close connection between complex variable theory and DEs. A different generalization of the Fourier idea leads to the development of ...

We will focus on the Liouville EQFT and its perturbations, which include the Sinh--Gordon model. The Liouville model is scale invariant, and we consider a perturbation that breaks the scale invariance ...

Liouville's theorem; canonical transformations: action-angle variables, Poisson brackets, Hamilton-Jacobi equation. Special Theory of Relativity: Lorentz transformations, relativistic kinematics ...

Ordinary differential equations: power series and Frobenius series solutions, special functions, Fourier series, Sturm-Liouville problems, qualitative analysis of nonlinear systems. Partial ...