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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Functional Equations and How to Solve Them (Hardcover, 2007 ed.)
Loot Price: R2,407
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Functional Equations and How to Solve Them (Hardcover, 2007 ed.)
Series: Problem Books in Mathematics
Expected to ship within 10 - 15 working days
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Over the years, a number of books have been written on the theory
of functional equations. However, very little has been published
which helps readers to solve functional equations in mathematics
competitions and mathematical problem solving. This book fills that
gap. The student who encounters a functional equation on a
mathematics contest will need to investigate solutions to the
equation by finding all solutions (if any) or by showing that all
solutions have a particular property. Our emphasis will be on the
development of those tools which are most useful in giving a family
of solutions to each functional equation in explicit form. At the
end of each chapter, readers will find a list of problems
associated with the material in that chapter. The problems vary
greatly difficulty, with the easiest problems being accessible to
any high school student who has read the chapter carefully. The
most difficult problems will be a reasonable challenge to advanced
students studying for the International Mathematical Olympiad at
the high school level or the William Lowell Putnam Competition for
university undergraduates. setting that is quite inappropriate for
the most high school students. However, the abstraction of some
parts of the modern theory reflects the fact that functional
equations can occur in diverse settings: functions on the natural
numbers, the integers, the reals, or the complex numbers can all be
studied within the subject area of functional equations. Most of
the time, the functions in this book are real-valued functions of a
single real variable. However, readers will also find functions
with complex arguments and functions defined on natural numbers in
these pages. In some cases, equations for functions between circles
will also crop up. The book ends with an appendix containing topics
that provide a springboard for further investigation of the
concepts of limits, infinite series and continuity.
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