Tromba, Anthony
Overview
Works:  70 works in 409 publications in 7 languages and 7,319 library holdings 

Genres:  Conference proceedings Examinations, questions, etc 
Roles:  Author, Editor 
Classifications:  BH301.N3, 117 
Publication Timeline
.
Most widely held works by
Anthony Tromba
Vector calculus by
Jerrold E Marsden(
Book
)
109 editions published between 1970 and 2012 in 6 languages and held by 1,701 WorldCat member libraries worldwide
Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world. (Midwest)
109 editions published between 1970 and 2012 in 6 languages and held by 1,701 WorldCat member libraries worldwide
Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world. (Midwest)
Mathematics and optimal form by
Stefan Hildebrandt(
Book
)
25 editions published between 1984 and 1998 in 4 languages and held by 1,451 WorldCat member libraries worldwide
Studie over de vraag waarom de natuur bepaalde vormen, zoals kristalvormen, prefereert boven vele andere mathematisch mogelijke vormen
25 editions published between 1984 and 1998 in 4 languages and held by 1,451 WorldCat member libraries worldwide
Studie over de vraag waarom de natuur bepaalde vormen, zoals kristalvormen, prefereert boven vele andere mathematisch mogelijke vormen
The parsimonious universe : shape and form in the natural world by
Stefan Hildebrandt(
Book
)
16 editions published between 1995 and 1996 in English and German and held by 748 WorldCat member libraries worldwide
Can one set of basic laws account for both the recurring themes and the infinite variety of nature's designs? When it comes to shape and form, does nature simply proceed in the easiest, most efficient way? Complete answers to these questions are likely never to be discovered. Still, down through the ages, the investigation of symmetry and regularity in nature has yielded some fascinating and surprising insights. Out of this inquiry comes a specific branch of mathematics  the calculus of variations  which explores questions of optimization: Is the igloo the optimal housing form for minimizing heat loss? Do bees use the least possible amount of wax when building their hives? In The Parsimonious Universe, Stefan Hildebrandt and Anthony Tromba invite readers to join the search for the mathematical underpinnings of natural shapes and form. Moving from ancient times to the nuclear age, the book looks at centuries of evidence that the physical world adheres to the principle of the economy of means  meaning that nature achieves efficiency by being rather stingy with the energy it expends. On almost every page can be found historical discussions, striking color illustrations, and examples ranging from atomic nuclei to soap bubbles to spirals and fractals. Without using technical language, Hildebrandt and Tromba open up an intriguing avenue of scientific inquiry to an uninitiated readership, showing what can be discovered when mathematics is used to investigate the natural world
16 editions published between 1995 and 1996 in English and German and held by 748 WorldCat member libraries worldwide
Can one set of basic laws account for both the recurring themes and the infinite variety of nature's designs? When it comes to shape and form, does nature simply proceed in the easiest, most efficient way? Complete answers to these questions are likely never to be discovered. Still, down through the ages, the investigation of symmetry and regularity in nature has yielded some fascinating and surprising insights. Out of this inquiry comes a specific branch of mathematics  the calculus of variations  which explores questions of optimization: Is the igloo the optimal housing form for minimizing heat loss? Do bees use the least possible amount of wax when building their hives? In The Parsimonious Universe, Stefan Hildebrandt and Anthony Tromba invite readers to join the search for the mathematical underpinnings of natural shapes and form. Moving from ancient times to the nuclear age, the book looks at centuries of evidence that the physical world adheres to the principle of the economy of means  meaning that nature achieves efficiency by being rather stingy with the energy it expends. On almost every page can be found historical discussions, striking color illustrations, and examples ranging from atomic nuclei to soap bubbles to spirals and fractals. Without using technical language, Hildebrandt and Tromba open up an intriguing avenue of scientific inquiry to an uninitiated readership, showing what can be discovered when mathematics is used to investigate the natural world
Teichmüller theory in Riemannian geometry by
Anthony Tromba(
Book
)
14 editions published in 1992 in English and Undetermined and held by 286 WorldCat member libraries worldwide
14 editions published in 1992 in English and Undetermined and held by 286 WorldCat member libraries worldwide
Calculus by
Kenneth McAloon(
Book
)
6 editions published between 1972 and 1976 in English and Spanish and held by 251 WorldCat member libraries worldwide
Introductory course for students with a highschool background of algebra, geometry and rudiments of trigonometry
6 editions published between 1972 and 1976 in English and Spanish and held by 251 WorldCat member libraries worldwide
Introductory course for students with a highschool background of algebra, geometry and rudiments of trigonometry
The index theorem for minimal surfaces of higher genus by
Friedrich Tomi(
Book
)
12 editions published in 1995 in English and held by 225 WorldCat member libraries worldwide
12 editions published in 1995 in English and held by 225 WorldCat member libraries worldwide
Existence theorems for minimal surfaces of nonzero genus spanning a contour by
Friedrich Tomi(
Book
)
11 editions published in 1988 in English and held by 223 WorldCat member libraries worldwide
11 editions published in 1988 in English and held by 223 WorldCat member libraries worldwide
On the number of simply connected minimal surfaces spanning a curve by
Anthony Tromba(
Book
)
13 editions published in 1977 in English and held by 215 WorldCat member libraries worldwide
13 editions published in 1977 in English and held by 215 WorldCat member libraries worldwide
Basic multivariable calculus by
Jerrold E Marsden(
Book
)
19 editions published between 1993 and 2000 in 3 languages and held by 191 WorldCat member libraries worldwide
19 editions published between 1993 and 2000 in 3 languages and held by 191 WorldCat member libraries worldwide
Seminar on New Results in Nonlinear Partial Differential Equations : a publication of the MaxPlanckInstitut für Mathematik,
Bonn by
Anthony Tromba(
Book
)
17 editions published in 1987 in English and Undetermined and held by 162 WorldCat member libraries worldwide
17 editions published in 1987 in English and Undetermined and held by 162 WorldCat member libraries worldwide
Regularity of minimal surfaces by
Ulrich Dierkes(
Book
)
20 editions published between 2010 and 2013 in English and held by 133 WorldCat member libraries worldwide
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and Hsurfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general GaussBonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is t
20 editions published between 2010 and 2013 in English and held by 133 WorldCat member libraries worldwide
"Regularity of Minimal Surfaces" begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and Hsurfaces with fixed or free boundaries are studied. In particular, the asymptotic expansions at interior and boundary branch points are derived, leading to general GaussBonnet formulas. Furthermore, gradient estimates and asymptotic expansions for minimal surfaces with only piecewise smooth boundaries are obtained. One of the main features of free boundary value problems for minimal surfaces is t
Calculus of one variable by
Kenneth McAloon(
Book
)
5 editions published in 1972 in English and held by 130 WorldCat member libraries worldwide
5 editions published in 1972 in English and held by 130 WorldCat member libraries worldwide
Global analysis of minimal surfaces by
Ulrich Dierkes(
Book
)
21 editions published between 2010 and 2013 in English and held by 128 WorldCat member libraries worldwide
Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of 'edgecrawling' along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a 'global theory of minimal surfaces' as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmuller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau's problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented
21 editions published between 2010 and 2013 in English and held by 128 WorldCat member libraries worldwide
Many properties of minimal surfaces are of a global nature, and this is already true for the results treated in the first two volumes of the treatise. Part I of the present book can be viewed as an extension of these results. For instance, the first two chapters deal with existence, regularity and uniqueness theorems for minimal surfaces with partially free boundaries. Here one of the main features is the possibility of 'edgecrawling' along free parts of the boundary. The third chapter deals with a priori estimates for minimal surfaces in higher dimensions and for minimizers of singular integrals related to the area functional. In particular, far reaching Bernstein theorems are derived. The second part of the book contains what one might justly call a 'global theory of minimal surfaces' as envisioned by Smale. First, the Douglas problem is treated anew by using Teichmuller theory. Secondly, various index theorems for minimal theorems are derived, and their consequences for the space of solutions to Plateau's problem are discussed. Finally, a topological approach to minimal surfaces via Fredholm vector fields in the spirit of Smale is presented
A theory of branched minimal surfaces by
Anthony Tromba(
Book
)
15 editions published between 2012 and 2014 in English and held by 62 WorldCat member libraries worldwide
One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated.℗¡ The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
15 editions published between 2012 and 2014 in English and held by 62 WorldCat member libraries worldwide
One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere. The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use Dirichlet's energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of Dirichlet's energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated.℗¡ The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education
Minimal surfaces by
Ulrich Dierkes(
Book
)
in English and held by 53 WorldCat member libraries worldwide
"Minimal Surfaces" is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in threedimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently
in English and held by 53 WorldCat member libraries worldwide
"Minimal Surfaces" is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise is a substantially revised and extended version of the monograph Minimal Surfaces I, II (Grundlehren Nr. 295 & 296). The first volume begins with an exposition of basic ideas of the theory of surfaces in threedimensional Euclidean space, followed by an introduction of minimal surfaces as stationary points of area, or equivalently
Matemática y formas óptimas by
Stefan Hildebrandt(
Book
)
3 editions published in 1990 in Spanish and held by 16 WorldCat member libraries worldwide
3 editions published in 1990 in Spanish and held by 16 WorldCat member libraries worldwide
Lectures on integral equations by
Harold Widom(
Book
)
4 editions published in 1969 in English and held by 14 WorldCat member libraries worldwide
4 editions published in 1969 in English and held by 14 WorldCat member libraries worldwide
Lectures on measure and integration by
Harold Widom(
Book
)
3 editions published in 1969 in English and held by 10 WorldCat member libraries worldwide
3 editions published in 1969 in English and held by 10 WorldCat member libraries worldwide
Degree theory on Banach manifolds by
Anthony Tromba(
)
3 editions published in 1968 in English and held by 7 WorldCat member libraries worldwide
3 editions published in 1968 in English and held by 7 WorldCat member libraries worldwide
Cálculo vectorial : problemas resueltos : de Jerrold E. Marsden y Anthony J. Tromba by
Jerrold E Marsden(
Book
)
4 editions published in 1993 in Spanish and held by 7 WorldCat member libraries worldwide
4 editions published in 1993 in Spanish and held by 7 WorldCat member libraries worldwide
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Related Identities
 Hildebrandt, Stefan Author
 Marsden, Jerrold E. Author
 Dierkes, Ulrich Author
 Tomi, Friedrich Author
 McAloon, Kenneth Author
 Denzler, Jochen
 Weinstein, Alan 1943
 Sauvigny, Friedrich
 López Mateos, Manuel Translator
 Kortbeek, Tom (T. J.)
Useful Links
Associated Subjects
Boundary value problems Calculus Calculus of tensors Calculus of variations CalculusStudy and teaching Canada Critical point theory (Mathematical analysis) Differential equations, Nonlinear Differential equations, Partial Differential topology Engineering Existence theorems Form (Philosophy) Functional analysis Functions of complex variables Geometry, Differential Geometry, Riemannian Global analysis (Mathematics) Global differential geometry Index theorems Integral equations Integrals Integrals, Generalized Mathematics Mathematics in nature Measure theory Minimal surfaces Motion Nature (Aesthetics) Plateau's problem Scientists Sequences (Mathematics) Teichmüller spaces United States Vector algebra Vector analysis
Alternative Names
Anthony Tromba USamerikanischer Mathematiker
Tromba, A. 1943
Tromba, A. J.
Tromba, A. J. 1943
Tromba, A. J. (Anthony Joseph)
Tromba, A. J. (Anthony Joseph), 1943
Tromba, Anthony.
Tromba, Anthony 1943
Tromba, Anthony J.
Tromba, Anthony J. 1943...
Tromba, Anthony J. (Anthony Joseph)
Tromba, Anthony J. (Anthony Joseph), 1943
Tromba, Anthony Joseph 1943
أنتوني ترومبا، 1943
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