Abstract
This chapter discusses multivariable differential calculus and the differential calculus of mappings from one Euclidean space to another. The basic idea of multivariable differential calculus is the approximation of nonlinear mappings by linear ones. The chapter describes Lagrange multipliers and the classification of critical points for functions of two variables. A quadratic form is called positive-definite if f(x, y) > 0 unless x = y = 0, negative-definite if f(x, y) < 0 unless x = y = 0, and nondefinite if it has both positive and negative values. Taylor's formula provides polynomial approximations to general functions.
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