Vector-valued functions of several variables
In this chapter we study the differential calculus of functions of several variables with values in E n . Among the main results are the theorems about composition and inverses and the implicit function theorem. Later in the chapter, subsets of E n that are smooth manifolds are considered, and the spaces of tangent and normal vectors at a point of a smooth manifold are found. These ideas are then applied to obtain the Lagrange multiplier rule for constrained extremum problems.
KeywordsPartial Derivative Linear Transformation Tangent Vector Chain Rule Implicit Function Theorem
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