The techniques that can be used to solve non-linear problems are
far different than those that are used to solve linear problems.
Many courses in analysis and applied mathematics attack linear
cases simply because they are easier to solve and do not require a
large theoretical background in order to approach them. Professor
Schechter's 2005 book is devoted to non-linear methods using the
least background material possible and the simplest linear
techniques. An understanding of the tools for solving non-linear
problems is developed whilst demonstrating their application to
problems in one dimension and then leading to higher dimensions.
The reader is guided using simple exposition and proof, assuming a
minimal set of pre-requisites. For completion, a set of appendices
covering essential basics in functional analysis and metric spaces
is included, making this ideal as an accompanying text on an
upper-undergraduate or graduate course, or even for self-study.
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