Vector-valued functions of several variables

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


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.


Partial Derivative Linear Transformation Tangent Vector Chain Rule Implicit Function Theorem 
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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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