Introduction to differential equations. Topics include methods of solutions for linear and non-linear first order differential equations, linear second order differential equations, higher order ...

We study the solutions of ordinary linear differential equations whose coefficients are analytic elements. As one application we show nonexistence of index for certain linear differential operators ...

Mathematics of Computation, Vol. 59, No. 200 (Oct., 1992), pp. 403-420 (18 pages) We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u(x, t) + f(x, ...

Differential equations are fundamental tools in physics: they are used to describe phenomena ranging from fluid dynamics to general relativity. But when these equations become stiff (i.e. they involve ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

Calculation: A representation of a network of electromagnetic waveguides (left) being used to solve Dirichlet boundary value problems. The coloured diagrams at right represent the normalized ...

Researchers from the Institute of Cosmos Sciences of the University of Barcelona (ICCUB) have developed a new framework based ...

The theory of Appell polynomials has long intrigued researchers due to its elegant algebraic structure and rich connections with differential equations. At its core, an Appell sequence is ...

All prerequisite courses must be passed with a grade of C- or better. For official course descriptions, please see the current CU-Boulder Catalog. MATH 3001 Analysis 1 Provides a rigorous treatment of ...