Differentiation of real valued functions

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


We now begin the differential calculus for real valued functions of several variables. The first step is to define the notions of directional derivative and partial derivative. Then the concept of differentiable function is introduced, by linear approximation to the increments of a function. Taylor’s formula with remainder is obtained for functions of class C(q); such functions have continuous partial derivatives of orders 1, 2,..., q. It is then applied to problems of relative extrema and to the characterization of convex functions of class C(2).


Partial Derivative Convex Function Extreme Point Differentiable Function Tangent Plane 
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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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