Inverse problems, central to modern applied mathematics, involve deducing unknown parameters or functions in differential equations from observed spectral data. This field is pivotal in understanding ...

Elliptic operators play a central role in the analysis of partial differential equations, underpinning a wide range of phenomena from quantum mechanics to heat conduction. In particular, the study of ...

This is the first part of a two course graduate sequence in analytical methods to solve ordinary and partial differential equations of mathematical physics. Review of Advanced ODE’s including power ...

Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space ...

In this work, we find the asymptotic formulas for the sum of the negative eigenvalues smaller than −ε (ε > 0) of a self-adjoint operator L defined by the following differential expression ℓ(y) = −(p(x ...