Applied Mathematical Methods

Chapter 16

¹ In some contexts, Hessian is also denoted by aseparate symbol, e.g. H(x). The alternative notation ∇²f(x), as used in some texts, is discouraged, because the symbol ∇² is reserved for the Laplacian operator.

² In some calculus texts, this determinant is referred to as the Jacobian. But, we call it the Jacobian determinant, because we have reserved the term Jacobian for the corresponding matrix, according to the standard terminology.

³ Such higher order formulae may be useful in maintaining the required accuracy at the extreme points of a finite domain, where we have to resort to a forward or backward formula, since the function would ...