Bibliography, etc. Note
Includes bibliographical references (p. -159) and index.
Formatted Contents Note
Implicit functions An informal version of the implicit function theorem The implicit function theorem paradigm Historical introduction Newton Lagrange Cauchy The inductive proof of the implicit function theorem The classical approach to the implicit function theorem The contraction mapping fixed point principle The rank theorem and the decomposition theorem A counterexample Ordinary differential equations Numerical homotopy methods Equivalent definitions of a smooth surface Smoothness of the distance function The Weierstrass preparation theorem Implicit function theorems without differentiability An inverse function theorem for continuous mappings Some singular cases of the implicit function theorem Analytic implicit function theorems Hadamard's global inverse function theorem The implicit function theorem via the Newton-Raphson method the Nash-Moser implicit function theorem.