Buck, R. Creighton (Robert Creighton) 1920
Overview
Works:  50 works in 239 publications in 5 languages and 4,525 library holdings 

Genres:  Programmed instructional materials Textbooks 
Roles:  Author, Editor, Other 
Classifications:  QA303, 517 
Publication Timeline
.
Most widely held works by
R. Creighton Buck
Advanced calculus by
R. Creighton Buck(
Book
)
82 editions published between 1956 and 2003 in 4 languages and held by 1,927 WorldCat member libraries worldwide
Seths and functions; Continuity; Defferentiation; Integration; Series; Uniform convergence; Diferentiation of transformations; Aplications to geometry and analysis; Differential geometry and vector calculus; Numerical methods
82 editions published between 1956 and 2003 in 4 languages and held by 1,927 WorldCat member libraries worldwide
Seths and functions; Continuity; Defferentiation; Integration; Series; Uniform convergence; Diferentiation of transformations; Aplications to geometry and analysis; Differential geometry and vector calculus; Numerical methods
Studies in modern analysis by
R. Creighton Buck(
Book
)
29 editions published between 1912 and 1962 in 4 languages and held by 1,036 WorldCat member libraries worldwide
29 editions published between 1912 and 1962 in 4 languages and held by 1,036 WorldCat member libraries worldwide
Polynomial expansions of analytic functions by
Ralph P Boas(
Book
)
47 editions published between 1958 and 1964 in 4 languages and held by 768 WorldCat member libraries worldwide
This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH'S mono graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J.M
47 editions published between 1958 and 1964 in 4 languages and held by 768 WorldCat member libraries worldwide
This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH'S mono graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J.M
Calculus of several variables by
R. Creighton Buck(
Book
)
8 editions published in 1971 in English and French and held by 270 WorldCat member libraries worldwide
8 editions published in 1971 in English and French and held by 270 WorldCat member libraries worldwide
Introduction to differential equations by
R. Creighton Buck(
Book
)
7 editions published in 1976 in English and held by 263 WorldCat member libraries worldwide
7 editions published in 1976 in English and held by 263 WorldCat member libraries worldwide
Solutions manual [for] Calculus of several variables by
R. Creighton Buck(
Book
)
1 edition published in 1971 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 1971 in English and held by 16 WorldCat member libraries worldwide
Solutions manual [for] introduction to differential equations by
R. Creighton Buck(
Book
)
2 editions published in 1976 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 1976 in English and held by 14 WorldCat member libraries worldwide
Programed first course in algebra : revised form H, student's response booklet by
School Mathematics Study Group(
Book
)
1 edition published in 1965 in English and held by 12 WorldCat member libraries worldwide
1 edition published in 1965 in English and held by 12 WorldCat member libraries worldwide
Programed first course in algebra : revised form H, student's text by
School Mathematics Study Group(
Book
)
in English and held by 12 WorldCat member libraries worldwide
in English and held by 12 WorldCat member libraries worldwide
Programmed first course in algebra : preliminary form H by
School Mathematics Study Group(
Book
)
1 edition published in 1963 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1963 in English and held by 7 WorldCat member libraries worldwide
Programed first course in algebra. Form CR by
School Mathematics Study Group(
Book
)
2 editions published in 1962 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 1962 in English and held by 6 WorldCat member libraries worldwide
Programmed first course in algebra, revised form H. Student's text by
School Mathematics Study Group(
Book
)
1 edition published in 1965 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1965 in English and held by 6 WorldCat member libraries worldwide
Miss R.C. Buck and Miss M.H. Cornelius propose to open, at Newton Corner, Mass., a family school for girls. The number of
pupils will not exceed sixteen ; and those under the age of fifteen will be preferred. ... The first term of this school will
commence Jan. 6, 1858, and continue sixteen weeks, until April 28. ... Tuition in English branches, in the Latin and French
languages, with board, will be $350 per year. by
R. Creighton Buck(
Book
)
2 editions published in 1857 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1857 in English and held by 5 WorldCat member libraries worldwide
Approximation properties of vector valued functions by
R. Creighton Buck(
Book
)
5 editions published in 1973 in English and held by 5 WorldCat member libraries worldwide
Set theory, Topology, TheoremsWeierstrass theorem, Modules(Mathematics)Let M be a closed C(X) submodule of the space C(X:E) of all bounded continuous functions on the compact space X with values in the normed linear space E. Then, it is shown that the linear functionals phi on C(X:E) that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phi(g) = L(g(x sub 0)), where x sub 0 is a point of X and L is an extreme point of the set of functionals of norm one on E that annihilate the subspace M(x sub 0)=(all f(x sub 0) for f epsilon M). The proof uses various forms of the Weierstrass approximation theorem for modules. (Author)
5 editions published in 1973 in English and held by 5 WorldCat member libraries worldwide
Set theory, Topology, TheoremsWeierstrass theorem, Modules(Mathematics)Let M be a closed C(X) submodule of the space C(X:E) of all bounded continuous functions on the compact space X with values in the normed linear space E. Then, it is shown that the linear functionals phi on C(X:E) that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phi(g) = L(g(x sub 0)), where x sub 0 is a point of X and L is an extreme point of the set of functionals of norm one on E that annihilate the subspace M(x sub 0)=(all f(x sub 0) for f epsilon M). The proof uses various forms of the Weierstrass approximation theorem for modules. (Author)
Dispersion mapping theorems by
R. Creighton Buck(
Book
)
4 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
A function of three variables is often regarded as inherently simpler than a function of five variables, and there has been much attention given to the nature of complicated functions that can be expressed exactly in various ways in terms of simpler functions. From the viewpoint of computation, however, it is sufficient if a function F can be approximated arbitrarily well by combinations of simple functions. This paper deals with the general structure of this process, and obtains specific theorems that help to describe its limitations, and necessary conditions on the functions F for which this is possible. More detailed applications will be made in the future
4 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
A function of three variables is often regarded as inherently simpler than a function of five variables, and there has been much attention given to the nature of complicated functions that can be expressed exactly in various ways in terms of simpler functions. From the viewpoint of computation, however, it is sufficient if a function F can be approximated arbitrarily well by combinations of simple functions. This paper deals with the general structure of this process, and obtains specific theorems that help to describe its limitations, and necessary conditions on the functions F for which this is possible. More detailed applications will be made in the future
The solutions to a smooth PDE can be dense in C[I] by
R. Creighton Buck(
Book
)
3 editions published in 1980 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1980 in English and held by 4 WorldCat member libraries worldwide
Extreme Functionals on Spaces of Vector Valued Functions by
R. Creighton Buck(
Book
)
4 editions published between 1972 and 1973 in English and held by 4 WorldCat member libraries worldwide
The space C(X : E) of E valued bound continuous functions on a compact space X is represented as a subspace of C(X x B sub E) and the extreme linear functionals phi of norm 1 on C(X : E) arise as the product of the points of X and extreme points of B sub E, the dual ball of E. This is generalized, using the BuckPhelps Theorem to identify extreme functionals phi in the set of those that annihilate certain submodules of C(X : E). (Author)
4 editions published between 1972 and 1973 in English and held by 4 WorldCat member libraries worldwide
The space C(X : E) of E valued bound continuous functions on a compact space X is represented as a subspace of C(X x B sub E) and the extreme linear functionals phi of norm 1 on C(X : E) arise as the product of the points of X and extreme points of B sub E, the dual ball of E. This is generalized, using the BuckPhelps Theorem to identify extreme functionals phi in the set of those that annihilate certain submodules of C(X : E). (Author)
Approximate Complexity and Functional Representation by
R. Creighton Buck(
Book
)
3 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
Results are obtained dealing with the exact and the approximate representation of a function F as a superposition, in designated formats, of functions of fewer variables. Two main cases are considered. In the classical nomographic case one seeks criteria for deciding if a function can be expressed in the form f(phi(x) + psi(y)), or as a uniform limit of such functions. The second case is also related to the solution of Hilbert's 13th problem, and deals with the format F(x) = f(phi(x)) where x lies in an ncell I and phi is a real valued continuous function on I, and f is a function on R taking values in a chosen normed space epsilon. The use of these criteria is illustrated with several specific functions
3 editions published in 1976 in English and held by 3 WorldCat member libraries worldwide
Results are obtained dealing with the exact and the approximate representation of a function F as a superposition, in designated formats, of functions of fewer variables. Two main cases are considered. In the classical nomographic case one seeks criteria for deciding if a function can be expressed in the form f(phi(x) + psi(y)), or as a uniform limit of such functions. The second case is also related to the solution of Hilbert's 13th problem, and deals with the format F(x) = f(phi(x)) where x lies in an ncell I and phi is a real valued continuous function on I, and f is a function on R taking values in a chosen normed space epsilon. The use of these criteria is illustrated with several specific functions
Polynomial expansions of analytic functions, by R.P. Boas and R.C. Buck. by
Ralph P Boas(
Book
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
Advanced calculus [by] R. Creighton Buck with the collaboration of Ellen F. Buck by
R. Creighton Buck(
Book
)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 Buck, Ellen F. Other
 Boas, Ralph P. (Ralph Philip) 19121992 Author
 Willcox, Alfred B. 1925
 Boas, Ralph Philip (19121992) Author
 School Mathematics Study Group
 Pérez Vilaplana, José
 McShane, Edward James
 WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
 University of WisconsinMadison Mathematics Research Center
 Mathematical Association of America Editor
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Associated Subjects
Algebra Analytic functions Approximation theory Boarding schools Calculus Differential equations Differential equations, Partial EducationCurricula Functional analysis Functions Functions of several real variables Global analysis (Mathematics) Harvard University MassachusettsNewton Mathematical analysis Mathematics MathematicsStudy and teaching (Secondary) Polynomials Programmed instruction Vector valued functions
Alternative Names
Buck, R. C.
Buck, R. Creighton 1920...
Buck, Robert C. 19201998
Buck, Robert Creighton.
Buck, Robert Creighton 1920
Buck, Robert Creighton 19201998
Creighton Buck Robert
Robert Creighton Buck American mathematician
Robert Creighton Buck Amerikaans wiskundige (19201998)
Robert Creighton Buck amerikansk matematikar
Robert Creighton Buck amerikansk matematiker
Robert Creighton Buck matemático estadounidense
Robert Creighton Buck matematico statunitense
Robert Creighton Buck USamerikanischer Mathematiker
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