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The objective of this course is to provide an accessible
introduction to approximation methods for undergraduate
students with calculus background only, emphasizing
approximation viewpoints, error criteria, convergence
behavior, and representative tools from classical
approximation theory. The course is not intended to be a
general numerical analysis course; instead, it focuses on
core approximation topics such as best uniform
approximation, orthogonal polynomials and their
structural/extremal properties, minimax approximation and
the exchange algorithm, alternative approximation criteria
(including ?1 and discrete viewpoints), and introductory
rational approximation in a real-variable setting.
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