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differential calculus

  • Harold M. Edwards
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

Consider the problem of solving a system of m equations in n unknowns
$$ y_{i} = f_{i}(x_{1}, x_{2}, \ldots, x_{n})\ \ (i = 1,2, \ldots, m) $$
for all possible values of \( (x_{1}, x_{2}, \ldots, x_{n}) \) given \( (y_{1}, y_{2}, \ldots, y_{m}) \). Chapter 4 deals with the solution of this problem in the special case where the functions \( f_{i} \) are affine functions, that is, functions of the form
$$ f_{i}(x_{1}, x_{2}, \ldots, x_{n})\ =\ a_{i1}x_{1} +\ a_{i2}x_{2} + \cdots +\ a_{in}x_{n} +\ b_{i}. $$

Keywords

Quadratic Form Lagrange Multiplier Chain Rule Implicit Function Theorem Differential Calculus 
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

© Harold M. Edwards 2014

Authors and Affiliations

  • Harold M. Edwards
    • 1
  1. 1.Courant InstituteNew York UniversityNew YorkUSA

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