Advanced Mathematical Methods With Maple -

: Expanding functions in terms of orthonormal systems, such as Legendre, Hermite, and Laguerre polynomials.

Advanced mathematical methods with Maple focus on using the software's symbolic, numerical, and graphical capabilities to solve complex problems in the physical sciences and engineering. Maple serves as a powerful engine for visualizing mathematics and implementing approximate analytical techniques that would be algebraically impossible by hand. Core Mathematical Concepts & Maple Implementation Advanced mathematical methods with Maple

: Developing systematic ways to find approximate solutions to problems that cannot be solved exactly by starting from the exact solution of a related, simpler problem. : Expanding functions in terms of orthonormal systems,

: Applying advanced integral approximation methods used extensively in diffraction theory and wave propagation. Applications in Dynamical Systems This includes asymptotic expansions of integrals and the

: Investigating the behavior of functions as a parameter approaches a limit (e.g., infinity). This includes asymptotic expansions of integrals and the use of Watson’s Lemma .

The following advanced methods are standard components of curriculum and research using Maple :

Maple is particularly favored for studying because it can automate laborious tasks like finding fixed points and assessing stability. Advanced Mathematical Methods | Open University | M833