differential calculus

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


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
$$ f_{i}(x_{1}, x_{2}, \ldots, x_{n})\ =\ a_{i1}x_{1} +\ a_{i2}x_{2} + \cdots +\ a_{in}x_{n} +\ b_{i}. $$


Quadratic Form Lagrange Multiplier Chain Rule Implicit Function Theorem Differential Calculus 
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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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