Method of Applied Math 1

Course Description

Vector spaces and linear systems (linear vector spaces, basis vectors, spectral theory, adjoint matrices, eigenvalue problem, Fredholm alternative theorem, least squares solutions, singular value decomposition). Function spaces (definitions, applications: Fourier series, orthogonal polynomials, finite elements). Integral equations (classification, solution methods, domain, range, adjoint, Fredholm alternative, spectral theory). Differential equations and Green’s functions (delta functions, Green¿s functions , distribution theory, weak solutions, construction of Green¿s functions, spectral theory of differential operators, adjoint, Fredholm alternative, Sturm Liouville boundary value problems and solution by eigenfunction expansions). Calculus of variations (Euler-Lagrange equations, Hamilton¿s principle, minimization of functions and relation to eigenvalues of Sturm-Liouville operators). Prerequisite: MTH306, MTH309, MTH 418 or consent of instructor

Code

MTH 539

Credits

3

Subject

Mathematics

Programs That Include This Course

• Doctoral Doctor of Philosophy in Computational and Data Enabled Sciences
• Doctoral Doctor of Philosophy in Mathematics
• Master's Master of Arts in Mathematics
• Master's Master of Science in Computational and Applied Mathematics