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Course Description:
Review of finite-dimensional vector spaces and elementary matrix theory. Linear transformations, change of basis, eigenspaces. Matrix representation of linear operators and diagonalization. Applications to difference equations, Markov processes, ordinary differential equations, and stability of nonlinear dynamical systems. Inner product spaces, projection operators, orthogonal bases, Gram-Schmidt orthogonalization. Least squares method, pseudo-inverses, singular value decomposition. Adjoint operators, Hermitian and unitary operators, Fredholm Alternative Theorem. Fourier series and eigenfunction expansions. Introduction to the theory of distributions and the Fourier Integral Transform. Green's functions. Application to Partial Differential Equations.
Faculty/Manager:
Oksana Katsuro-Hopkins
Contact Information:
Oksana Katsuro-Hopkins
email: onk3@columbia.eduCredits for Course: 3 Viewing Schedule: 1 lecture per week Prerequisites: Introductory Linear Algebra required. Ordinary Differential Equations recommended. Notes:
* The information contained in this syllabus is subject to change at any time.