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Cover: 9780387345390 | Functional Equations and How to Solve Them | Christopher G. Small
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Functional Equations and How to Solve Them
Taschenbuch von Christopher G. Small
Sprache: Englisch

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Beschreibung
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, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning 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, 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. The book ends with an appendix containing topics that provide a springboard for further investigation of the concepts of limits, infinite series and continuity.
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, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning 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, 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. The book ends with an appendix containing topics that provide a springboard for further investigation of the concepts of limits, infinite series and continuity.
Zusammenfassung
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, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning a family of solutions to each functional equation in explicit form.
Inhaltsverzeichnis
An historical introduction.- Functional equations with two variables.- Functional equations with one variable.- Miscellaneous methods for functional equations.- Some closing heuristics.- Appendix: Hamel bases.- Hints and partial solutions to problems.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 144
Reihe: Problem Books in Mathematics
Inhalt: xii
131 S.
14 s/w Illustr.
ISBN-13: 9780387345390
ISBN-10: 0387345396
Sprache: Englisch
Herstellernummer: 11592402
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Small, Christopher G.
Auflage: 2007
Hersteller: Springer New York
Springer US, New York, N.Y.
Problem Books in Mathematics
Maße: 235 x 155 x 9 mm
Von/Mit: Christopher G. Small
Erscheinungsdatum: 08.08.2007
Gewicht: 0,23 kg
preigu-id: 102046511
Zusammenfassung
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, or by showing that all solutions have a particular property. The emphasis here will be on the development of those tools which are most useful in assigning a family of solutions to each functional equation in explicit form.
Inhaltsverzeichnis
An historical introduction.- Functional equations with two variables.- Functional equations with one variable.- Miscellaneous methods for functional equations.- Some closing heuristics.- Appendix: Hamel bases.- Hints and partial solutions to problems.
Details
Erscheinungsjahr: 2007
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 144
Reihe: Problem Books in Mathematics
Inhalt: xii
131 S.
14 s/w Illustr.
ISBN-13: 9780387345390
ISBN-10: 0387345396
Sprache: Englisch
Herstellernummer: 11592402
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Small, Christopher G.
Auflage: 2007
Hersteller: Springer New York
Springer US, New York, N.Y.
Problem Books in Mathematics
Maße: 235 x 155 x 9 mm
Von/Mit: Christopher G. Small
Erscheinungsdatum: 08.08.2007
Gewicht: 0,23 kg
preigu-id: 102046511
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