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Vector-valued functions of several variables

  • Wendell Fleming
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

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.

Keywords

Partial Derivative Linear Transformation Tangent Vector Chain Rule Implicit Function Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Wendell Fleming
    • 1
  1. 1.Department of MathematicsBrown UniversityProvidenceUSA

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