Functional equations and how to solve them:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2007
|
| Schriftenreihe: | Problem books in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XII, 129 S. Ill., graph. Darst. |
| ISBN: | 9780387345390 9780387489018 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804138697979854848 |
|---|---|
| adam_text | Contents
Preface
vu
1
An
historical
introduction
................................. 1
1.1
Preliminary remarks
..................................... 1
1.2
Nicole Oresme
.......................................... 1
1.3
Gregory of
Saint-Vincent.
................................. 4
1.4
Augustin-Louis Cauchy
................................... 6
1.5
What about calculus?
.................................... 8
1.6
Jean d Alembert
........................................ 9
1.7
Charles Babbage
........................................ 10
1.8
Mathematics competitions and recreational mathematics
..... 16
1.9
A contribution from Ramanujan
........................... 21
1.10
Simultaneous functional equations
......................... 24
1.11
A clarification of terminology
............................. 25
1.12
Existence and uniqueness of solutions
...................... 26
1.13
Problems
............................................... 26
2
Functional equations with two variables
.................... 31
2.1
Cauchy s equation
....................................... 31
2.2
Applications of Cauchy s equation
......................... 35
2.3
Jensen s equation
........................................ 37
2.4
Linear functional equation
................................ 38
2.5
Cauchy s exponential equation
............................ 38
2.6
Pexider s equation
....................................... 39
2.7
Vincze s equation
........................................ 40
2.8
Cauchy s inequality
...................................... 42
2.9
Equations involving functions of two variables
............... 43
2.10
Euler
s equation
......................................... 44
2.11
D Alemberťs
equation
................................... 45
2.12
Problems
............................................... 49
xii Contents
3
Functional equations with one variable
..................... 55
3.1
Introduction
............................................ 55
3.2
Linearization
............................................ 55
3.3
Some basic families of equations
........................... 57
3.4
A menagerie of conjugacy equations
....................... 62
3.5
Finding solutions for conjugacy equations
................... 64
3.5.1
The Koenigs algorithm for Schroder s equation
........ 64
3.5.2
The Levy algorithm for Abel s equation
.............. 66
3.5.3
An algorithm for
Böttcher s
equation
................ 66
3.5.4
Solving commutativity equations
.................... 67
3.6
Generalizations of Abel s and Schroder s equations
........... 67
3.7
General properties of iterative roots
........................ 69
3.8
Functional equations and nested radicals
................... 72
3.9
Problems
............................................... 75
4
Miscellaneous methods for functional equations
............ 79
4.1
Polynomial equations
.................................... 79
4.2
Power series methods
.................................... 81
4.3
Equations involving arithmetic functions
................... 82
4.4
An equation using special groups
.......................... 87
4.5
Problems
............................................... 89
5
Some closing heuristics
.................................... 91
6
Appendix:
Hamel
bases
.................................... 93
7
Hints and partial solutions to problems
.................... 97
7.1
A warning to the reader
.................................. 97
7.2
Hints for Chapter
1...................................... 97
7.3
Hints for Chapter
2......................................102
7.4
Hints for Chapter
3......................................107
7.5
Hints for Chapter
4......................................113
8
Bibliography
...............................................123
Index
..........................................................125
|
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| discipline | Mathematik |
| era | Geschichte gnd |
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| language | English |
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| title | Functional equations and how to solve them |
| title_auth | Functional equations and how to solve them |
| title_exact_search | Functional equations and how to solve them |
| title_full | Functional equations and how to solve them Christopher G. Small |
| title_fullStr | Functional equations and how to solve them Christopher G. Small |
| title_full_unstemmed | Functional equations and how to solve them Christopher G. Small |
| title_short | Functional equations and how to solve them |
| title_sort | functional equations and how to solve them |
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