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隐函数定理-(影印版) 内容简介
the implicit function theorem is. along with its close cousin
the inverse func- tion theorem， one of the most important， and one
of the oldest， paradigms in modcrn mathemarics. one can see the
germ of the idea for the implicir func tion theorem in the writings
of isaac newton （1642-1727）， and gottfried leib-niz's （1646-1716）
work cxplicitty contains an instance of implicit
differentiation.
whilc joseph louis lagrange （1736-1813） found a theorcm that is
essentially a version of the inverse function theorem， ic was
augustin-louis cauchy （1789-1857） who approached the implicit
function theorem with mathematical rigor and it is he who is
gencrally acknowledgcd as the discovcrer of the theorem. in
chap-ter 2， we will give details of the contributions of newton，
lagrange， and cauchy to the development of the implicit function
theorem.
隐函数定理-(影印版) 目录
preface
1 introduction to the implicit function theorem
1.1 implicit functions
1.2 an informal version ofthe implicit function theorem
1.3 thelmplicit function theorem paradigm
2 history
2.1 historicallntroduction
2.2 newton
2.3 lagrange
2.4 cauchy
3 basfcldeas
3.1 introduction
3.2 the inductive proof of the implicit function theorem
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