Taylor expansion definition

Taylor expansion

For f in C^n, Taylor's Theorem is used by dropping the remainder term. The first-order expansion is f(x) = f(y) + grad_f(x)(x-y), and the second-order expansion is f(x) = f(y) + grad_f(x)(x-y) + ½(x-y)'H_f(x)(x-y). (See Myth NLP-1 to avoid misconception.)
Found on http://glossary.computing.society.informs.org/index.php?page=T.html

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