Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Small Ch.G. — Functional Equations and how to Solve Them
Small Ch.G. — Functional Equations and how to Solve Them

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Functional Equations and how to Solve Them

Автор: Small Ch.G.

Аннотация:

This book covers topics in the theory and practice of functional equations. Special emphasis is given to methods for solving functional equations that appear in mathematics contests, such as the Putnam competition and the International Mathematical Olympiad. This book will be of particular interest to university students studying for the Putnam competition, and to high school students working to improve their skills on mathematics competitions at the national and international level. Mathematics educators who train students for these competitions will find a wealth of material for training on functional equations problems. The book also provides a number of brief biographical sketches of some of the mathematicians who pioneered the theory of functional equations. The work of Oresme, Cauchy, Babbage, and others, is explained within the context of the mathematical problems of interest at the time.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 129

Добавлена в каталог: 14.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Abelian group      88
Abel’s equation      15 63 64 67 76
Abel’s equation, generalization      67
Acceleration      3
Aczel, J.      3 123
Alembert, J.d’      9
Alembert, J.d’, also known as Daremberg      9
Alembert, J.d’, also known as Rond, J.le      9
Alembert, J.d’, Daremberg changed to d’Alembert      9
Alembert, J.d’, d’Alembert’s equation      10 17 18 45
Alembert, J.d’, law school      9
Alembert, J.d’, parents and background      9
Alembert, J.d’, placed in orphanage      9
Alembert, J.d’, solutions to d’Alembert’s equation      10
Alembert, J.d’, supported by father financially      9
Algebra      1
Analysis      6 7
Area      6
Aristotle      2
Arithmetic f.e.      82
Arithmetic function      82
Arithmetic mean      51
Average      37
Axiom of Choice      93 96
Axiom of Choice, nonconstructive existence theorem      96
Babbage, C.      10 14 15 19 55 61
Babbage, C., analytical engine      11
Babbage, C., cowcatcher      11
Babbage, C., difference engine      11
Babbage, C., essay on calculus of functions      12
Babbage, C., flat rate postage      11
Babbage, C., skeleton keys      11
Bastille      6
Big Omega      84
Binet’s formula      20
Binomial coefficients      7
Binomial theorem      7 35 38
Black Death      1 2
Bonaparte, N.      7
Bottcher’s equation      63 66
British mathematics      11
Calculus      6—8 17 18
Calculus, differential equations      17 18
Calculus, integral equations      17
Calculus, Leibniz’s methodology      11
Calculus, Newtonian methodology      11
Cambridge Analytical Society      11
Cambridge Analytical Society, renamed Cambridge Philosophical Society      11
Canadian Mathematical Society      16
Carr, G.S.      22
Cauchy, A.-L.      6—9 18 31 93
Cauchy, A.-L., Cauchy’s equation      8—10 18 31 35
Cauchy, A.-L., Cauchy’s exponential equation      38
Cauchy, A.-L., early years      6
Cauchy, A.-L., family      7
Cauchy, A.-L., founder of analysis      7
Cauchy, A.-L., full solution to d’Alembert’s equation      10
Cauchy, A.-L., problems with republicans and Napoleonic movements      7
Cauchy, A.-L., royalist sympathies      7
Cauchy, A.-L., starting point for theory of f.e.      6
Cauchy’s equation      7 24 31 35 37—40 43 95
Cauchy’s equation for functions bounded below      34
Cauchy’s equation for monotone function      35
Cauchy’s equation on a circle      50
Cauchy’s equation, solution on rationals      33
Cauchy’s equation, solution on reals      34
Cauchy’s equation, tame solutions      96
Cauchy’s equation, two variables      43
Cauchy’s equation, two-variable solution      44
Cauchy’s equation, wild solutions      96
Cauchy’s exponential equation      8 38 39 42
Cauchy’s inequality      42 50
Challenges and puzzles      16
Circular cosine      10
Clagett translation      2
Classification of problems      18
Closure, under multiplication      88
Closure, under reciprocation      88
College of Navarre, College of      2
Combinations of forces      9
Combinatorial arguments      8
Commutative group      88
Commutativity      41
Commutativity equation      63 67 76
Commutativity equation, solutions for      67
Competition      1 16—19 22 84
Competition, 1995 Romanian Winter      80
Competition, IMO      17
Competition, IMO 1972      19
Competition, IMO 1997 shortlist      56 71 76
Competition, IMO 1998      84
Competition, IMO 2001      88
Competition, IMO 2001 jury      88
Competition, IMO 2001 shortlisted problem      87
Competition, IMO gold medal problem      84
Competition, IMO medals      84
Competition, problems      17
Competition, Putnam      17 18
Competition, Putnam 1947      18
Competition, Putnam 1955      18
Competition, Putnam 1956      18
Competition, Putnam 1959      19
Competition, Putnam 1963      19
Competition, Putnam 1966      22
Competition, Putnam 1971      62
Competition, Putnam 1972      20
Competition, Putnam 1979      70
Competition, Putnam 1988      21
Competition, Putnam 1996      59
Completely multiplicative function      83
Composition of functions      69
Computing      11
Conic sections      4 6
Conjugacy equation      15 62 64 67
Conjugacy equation, finding solutions      64
Constant of integration      17
Continued fractions      22
Cosine function      10 46 48
Cosine function, double angle formula      46
Cosine function, summation formula      48
Cosine, circular      10 48
Cosine, hyperbolic      10
Crux Mathematicorum      16
Cyclic function      61
Degree of polynomial      18 79
Dense set      47
Descartes, R.      2
Descartes, R., graphs of functions      2
Dhombres, J.      3 123
Differential equations versus f.e.      19
Differentiation      8 9
Difform intensities      2
Direct and inverse calculation      12
Direct and inverse calculation, inverse more difficult      12
Directoire      7
Distance      3
Distance, signed      3
Divergent series      22
Dubikajtis’ theorem      112
d’Alembert’s equation      45 49
Elementary methods without calculus      18
Enlightenment      2
Equation in two variables      10
Equivalence class      58
Equivalence relation      58
Equivalence relation, reflexivity      58
Equivalence relation, symmetry      58
Equivalence relation, transitivity      58
Euler’s equation      39 44
Euler’s equation, generalized      45
Euler’s equation, solution      44
Euler’s equation, solution to generalized      50
Europe      1
Exhaustion, method of      6
Extreme Value Theorem      34
Fibonacci numbers      20
Fixed point under iteration      59
Fourteenth century      1
Fractional part      58
France      7
French Revolution      6
Function of two variables      43
Function, analytic      81
Function, antisymmetric      14
Function, arithmetic      82
Function, bounded on interval      7 35 45
Function, completely multiplicative      83 84
Function, complex-valued      77
Function, constant      4 9 58
Function, continuous      7—9 18 25—28 31 33—35 37—40 43—45 49—51 58 59 69 70 75 76 78 101
Function, decreasing      35 51 69 70 89
Function, differentiable      9
Function, even      47
Function, homogeneous      44
Function, homogeneous of degree k      44
Function, increasing      3 35—37 51 69 70 89 99 107 116
Function, involution      13—15 61
Function, linear      1 3 6 7 9
Function, monotone      35 75
Function, nondecreasing      89 120
Function, nowhere continuous      9
Function, nowhere differentiable      9
Function, one-to-one      14 15
Function, periodic      77 80 92
Function, positive      39
Function, quadratic      2
Function, restricted domain      18
Function, strictly positive      21
Function, symmetric      13 52
Functional equation, commutativity equation      63 76
Functional equation, conjugacy equation      62 64
Functional equation, existence of solution      26
Functional equation, families of      57
Functional equation, miscellaneous methods      79
Functional equation, nonlinear      23
Functional equation, one variable      55
Functional equation, polynomial      18 79 80
Functional equation, simultaneous      24
Functional equation, single variable      25
Functional equation, symmetries in      91
Functional equation, too general      42
Functional equation, two or more variables      25 31
Functional equation, uniqueness of solution      26
Functional equations versus differential equations      19
Gamma function      75 107
Geometric mean      51
Golden ratio      20
Golden ratio as limiting ratio of Fibonacci sequence      20
Gottingen University      93
Group      88
Group, commutative      88
Group-theoretic methods      87
Hamel bases      35 93 95
Hamel bases, uncountable      95
Hamel bases, uniqueness of representation      94
Hamel, G.      35 93
Hamel, G., 1905 paper of Hamel bases      93
Hardy — Ramanujan number      73
Hardy, G.H.      73
Harmonic mean      51
Herschel, J.      11
Herschel, W.      11
Heuristics for solving f.e.      91
Heytesbury, William of      2
High school mathematics      16
High school students      16
Hilbert, D.      93
Hilbert’s fourth problem      93
Hints to problems      97
Hints to problems, Chapter 1      97
Hints to problems, Chapter 2      102
Hints to problems, Chapter 3      107
Hints to problems, Chapter 4      113
history      1 17 123
Hyperbola      4—6
Hyperbolic cosine      10 46 47
Hyperbolic cosine, summation formula      48
Hyperbolic sine      48
Hyperbolic tangent      48
Identity      88
Identity function      14
Indeterminate expression      18
Induction      24 31 46 47 83 85
Ingenuity in solutions      91
Integration      4
Inverse problem      12
Inverse problem, f.e.as      12
Italian Renaissance      16
Iteration      58
Iterative roots      14 15 19 55 61 69
Iterative square root      14 20
Jensen’s equation      37 38
Jensen’s equation, solution      38
Journal of the Indian mathematical society      23
Klein, F.      93
Koenigs algorithm      64 76 81
Legendre symbol      84
Levy algorithm      66
LIMIT      25 59 64 66
Linear algebra      62
Linear functional equation      38
Linear functional equation, solution      38 51
Linear functions      91
Linearization      55 92
Liouville function      84
Lisieux      2
Logarithms      4—6 8 39 91
Mathematical Association of America      16
Mathematical Mayhem      16
Mathematics Magazine      16
Mean speed theorem      2
Mechanics      2
Medieval world      2
Merton College      2
Merton theorem      2
Multiplicative group      88
Multiplicative identity      88
Multiplicative inverse      88
Natural philosophy      2
Natural sciences      2
Nested radical      21—23 72
Nested radicals      72
Newton, I.      7
Newton, I., derivation of binomial theorem      7
Nonconstructive existence      96
Nonlinear equation      23
Nth order f.e.      13
Number theory      84
Numbers, complex      77 79
Numbers, dyadic rationals      47
Numbers, Hardy — Ramanujan number      73
Numbers, perfect squares      23
Numbers, positive integers      82
Numbers, primes      84 85
Numbers, rational      32 33 50
Numbers, real      79
Orbit      58
Oresme      2
Oresme, N.      1—4 6
Oresme, N., defined functional relationship      2
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте