Apostol, Tom M.
Overview
Works:  50 works in 191 publications in 5 languages and 2,959 library holdings 

Genres:  Surveys History 
Roles:  Author, Creator, Editor 
Classifications:  QA300, 517 
Publication Timeline
.
Most widely held works by
Tom M Apostol
Introduction to analytic number theory by
Tom M Apostol(
Book
)
45 editions published between 1976 and 2011 in 4 languages and held by 1,058 WorldCat member libraries worldwide
This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet Lfunctions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus
45 editions published between 1976 and 2011 in 4 languages and held by 1,058 WorldCat member libraries worldwide
This introductory textbook is designed to teach undergraduates the basic ideas and techniques of number theory, with special consideration to the principles of analytic number theory. The first five chapters treat elementary concepts such as divisibility, congruence and arithmetical functions. The topics in the next chapters include Dirichlet's theorem on primes in progressions, Gauss sums, quadratic residues, Dirichlet series, and Euler products with applications to the Riemann zeta function and Dirichlet Lfunctions. Also included is an introduction to partitions. Among the strong points of the book are its clarity of exposition and a collection of exercises at the end of each chapter. The first ten chapters, with the exception of one section, are accessible to anyone with knowledge of elementary calculus; the last four chapters require some knowledge of complex function theory including complex integration and residue calculus
Modular functions and Dirichlet series in number theory by
Tom M Apostol(
Book
)
20 editions published between 1976 and 1997 in 3 languages and held by 828 WorldCat member libraries worldwide
This volume is a sequel to the author's Introduction to Analytic Number Theory (UTM 1976, 3rd Printing 1986). It presupposes an undergraduate background in number theory comparable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of this book is devoted to a classical treatment of elliptic and modular functions with some of their numbertheoretic applications. Among the major topics covered are Rademacher's convergent series for the partition modular function, Lehner's congruences for the Fourier coefficients of the modular function j, and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. In addition to the correction of misprints, minor changes in the exercises and an updated bibliography, this new edition includes an alternative treatment of the transformation formula for the Dedekind eta function, which appears as a fivepage supplement to Chapter 3
20 editions published between 1976 and 1997 in 3 languages and held by 828 WorldCat member libraries worldwide
This volume is a sequel to the author's Introduction to Analytic Number Theory (UTM 1976, 3rd Printing 1986). It presupposes an undergraduate background in number theory comparable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of this book is devoted to a classical treatment of elliptic and modular functions with some of their numbertheoretic applications. Among the major topics covered are Rademacher's convergent series for the partition modular function, Lehner's congruences for the Fourier coefficients of the modular function j, and Hecke's theory of entire forms with multiplicative Fourier coefficients. The last chapter gives an account of Bohr's theory of equivalence of general Dirichlet series. In addition to the correction of misprints, minor changes in the exercises and an updated bibliography, this new edition includes an alternative treatment of the transformation formula for the Dedekind eta function, which appears as a fivepage supplement to Chapter 3
Linear algebra : a first course, with applications to differential equations by
Tom M Apostol(
Book
)
12 editions published between 1997 and 2006 in English and held by 337 WorldCat member libraries worldwide
"This text provides ample coverage of major topics traditionally taught in a first course on linear algebra: linear spaces, independence, orthogonality, linear transformations, matrices, eigenvalues, and quadratic forms. The last three chapters describe applications to differential equations. Although much of the material has been extracted from the author's twovolume Calculus, the present text is designed to be independent of the Calculus volumes."Jacket
12 editions published between 1997 and 2006 in English and held by 337 WorldCat member libraries worldwide
"This text provides ample coverage of major topics traditionally taught in a first course on linear algebra: linear spaces, independence, orthogonality, linear transformations, matrices, eigenvalues, and quadratic forms. The last three chapters describe applications to differential equations. Although much of the material has been extracted from the author's twovolume Calculus, the present text is designed to be independent of the Calculus volumes."Jacket
Polynomials by
Tom M Apostol(
Visual
)
10 editions published between 1991 and 2005 in 3 languages and held by 156 WorldCat member libraries worldwide
Animations show how the Cartesian equation changes if the graph of a polynomial is translated or subjected to a vertical change of scale. Zeros, local extrema, and points of inflection are discussed. Reallife examples include parabolic trajectories and the use of cubic splines in designing sailboats and computergenerated teapots
10 editions published between 1991 and 2005 in 3 languages and held by 156 WorldCat member libraries worldwide
Animations show how the Cartesian equation changes if the graph of a polynomial is translated or subjected to a vertical change of scale. Zeros, local extrema, and points of inflection are discussed. Reallife examples include parabolic trajectories and the use of cubic splines in designing sailboats and computergenerated teapots
Sines and cosines(
Visual
)
3 editions published in 1992 in English and held by 101 WorldCat member libraries worldwide
"Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related to vibrating motion, and as ratios of sides of right triangles. They are related by reflection or translation of their graphs. Animation demonstrates the Gibbs phenomenon of Fourier series."Www.projectmathematics.com
3 editions published in 1992 in English and held by 101 WorldCat member libraries worldwide
"Sines and cosines occur as rectangular coordinates of a point moving on a unit circle, as graphs related to vibrating motion, and as ratios of sides of right triangles. They are related by reflection or translation of their graphs. Animation demonstrates the Gibbs phenomenon of Fourier series."Www.projectmathematics.com
Sines and cosines(
Visual
)
2 editions published in 1993 in English and held by 78 WorldCat member libraries worldwide
"This video focuses on trigonometry, with special emphasis on the law of cosines and the law of sines, together with applications to The Great Survey of India. The history of surveying instruments is outlined, from Hero's dioptra to modern orbiting satellites."Www.projectmathematics.com
2 editions published in 1993 in English and held by 78 WorldCat member libraries worldwide
"This video focuses on trigonometry, with special emphasis on the law of cosines and the law of sines, together with applications to The Great Survey of India. The history of surveying instruments is outlined, from Hero's dioptra to modern orbiting satellites."Www.projectmathematics.com
Mathematical analysis : a modern approach to advanced calculus by
Tom M Apostol(
Book
)
11 editions published between 1957 and 1977 in English and Spanish and held by 58 WorldCat member libraries worldwide
The real and complex number systems. Some basic notions of set theory. Elements of point set topology. Limits and continuity. Derivatives. Functions of bounded variation and rectifiable curves. The Riemannstieltjes integral. Infinite series and infinite products. Sequences of functions. The lebesgue integral. Fourier series and fourier integrals. Multivariable differential calculus. Implicit functions and extremum problems. Multiple Riemann integrals. Multiple lebesgue integrals. Cauchy's theorem and the residue calculus
11 editions published between 1957 and 1977 in English and Spanish and held by 58 WorldCat member libraries worldwide
The real and complex number systems. Some basic notions of set theory. Elements of point set topology. Limits and continuity. Derivatives. Functions of bounded variation and rectifiable curves. The Riemannstieltjes integral. Infinite series and infinite products. Sequences of functions. The lebesgue integral. Fourier series and fourier integrals. Multivariable differential calculus. Implicit functions and extremum problems. Multiple Riemann integrals. Multiple lebesgue integrals. Cauchy's theorem and the residue calculus
Calculus by
Tom M Apostol(
Book
)
15 editions published between 1196 and 2003 in English and Spanish and held by 56 WorldCat member libraries worldwide
V.1. Calculo con funciones de una introduccion al algebra lineal. v.2.Calculo con funciones de varias variables y algebra lineal, con aplicaciones e las ecuaciones diferenciales y a las probabilidades
15 editions published between 1196 and 2003 in English and Spanish and held by 56 WorldCat member libraries worldwide
V.1. Calculo con funciones de una introduccion al algebra lineal. v.2.Calculo con funciones de varias variables y algebra lineal, con aplicaciones e las ecuaciones diferenciales y a las probabilidades
Project mathematics(
Visual
)
3 editions published in 2005 in English and held by 40 WorldCat member libraries worldwide
Explores basic topics in high school mathematics using computer animation, live action, music, special effects and humor
3 editions published in 2005 in English and held by 40 WorldCat member libraries worldwide
Explores basic topics in high school mathematics using computer animation, live action, music, special effects and humor
Sines and cosines(
Visual
)
1 edition published in 1994 in English and held by 39 WorldCat member libraries worldwide
"Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy's Almagest. This leads to elegant derivations of addition formulas, with applications to simple harmonic motion."Www.projectmathematics.com
1 edition published in 1994 in English and held by 39 WorldCat member libraries worldwide
"Animation relates the sine and cosine of an angle with chord lengths of a circle, as explained in Ptolemy's Almagest. This leads to elegant derivations of addition formulas, with applications to simple harmonic motion."Www.projectmathematics.com
Sines and cosines by
Tom M Apostol(
Visual
)
6 editions published in 2005 in English and No Linguistic content and held by 34 WorldCat member libraries worldwide
Part I's program opens with examples of circular motion in real life, and then introduces the sine in connection with a point moving counterclockwise on a circle of unit radius. Shows that a sine wave is generated by recording change in air pressure caused by a vibrating tuning fork. Also gives historical background and shows how sines and cosines occur in trigonometry as ratios of lengths of sides of right triangles
6 editions published in 2005 in English and No Linguistic content and held by 34 WorldCat member libraries worldwide
Part I's program opens with examples of circular motion in real life, and then introduces the sine in connection with a point moving counterclockwise on a circle of unit radius. Shows that a sine wave is generated by recording change in air pressure caused by a vibrating tuning fork. Also gives historical background and shows how sines and cosines occur in trigonometry as ratios of lengths of sides of right triangles
Introducción a la teoría analítica de números by
Tom M Apostol(
Book
)
7 editions published between 1980 and 1984 in Spanish and held by 27 WorldCat member libraries worldwide
7 editions published between 1980 and 1984 in Spanish and held by 27 WorldCat member libraries worldwide
Klassieke mechanica by
Niek de Kort(
Book
)
1 edition published in 1989 in Dutch and held by 24 WorldCat member libraries worldwide
Ontwikkeling van het denken van Aristoteles tot Einstein
1 edition published in 1989 in Dutch and held by 24 WorldCat member libraries worldwide
Ontwikkeling van het denken van Aristoteles tot Einstein
Klassieke mechanica by
Niek de Kort(
Book
)
1 edition published in 1990 in Dutch and held by 19 WorldCat member libraries worldwide
1 edition published in 1990 in Dutch and held by 19 WorldCat member libraries worldwide
Calculus by
Tom M Apostol(
Book
)
4 editions published between 1967 and 1976 in English and held by 14 WorldCat member libraries worldwide
4 editions published between 1967 and 1976 in English and held by 14 WorldCat member libraries worldwide
Selected papers on calculus by
Tom M Apostol(
Book
)
3 editions published between 1969 and 1977 in English and held by 10 WorldCat member libraries worldwide
3 editions published between 1969 and 1977 in English and held by 10 WorldCat member libraries worldwide
Calculus by
Tom M Apostol(
Book
)
4 editions published between 1961 and 1965 in English and held by 9 WorldCat member libraries worldwide
4 editions published between 1961 and 1965 in English and held by 9 WorldCat member libraries worldwide
Beyond the mechanical universe : from electricity to modern physics by
Richard P Olenick(
Book
)
2 editions published between 1986 and 2007 in English and held by 6 WorldCat member libraries worldwide
2 editions published between 1986 and 2007 in English and held by 6 WorldCat member libraries worldwide
Program guide and workbook to accompany the videotape on Similarity by
Tom M Apostol(
Book
)
4 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
4 editions published in 1990 in English and held by 6 WorldCat member libraries worldwide
New horizons in geometry by
Tom M Apostol(
Book
)
3 editions published in 2012 in English and held by 5 WorldCat member libraries worldwide
Calculus problems solved by elementary geometrical methods  P. 4 of cover
3 editions published in 2012 in English and held by 5 WorldCat member libraries worldwide
Calculus problems solved by elementary geometrical methods  P. 4 of cover
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Associated Subjects
Addition Algebra Algebraic number theory Algebras, Linear Almagest (Ptolemy) Arithmetic functions Calculus Canada College administrators College teachers Differential equations Dirichlet series EgyptAlexandria Elliptic functions Geometry GeometryStudy and teaching Harmonic motion India Lecturers Mathematical analysis Mathematics MathematicsStudy and teaching MathematicsStudy and teaching (Secondary) Modular functions Numbers, Prime Number theory Physics Pi Polynomials Precalculus Probabilities Ratio and proportion Ratio and proportionStudy and teaching Research Resemblance (Philosophy) Scaling laws (Statistical physics) Scientists Set theory Similarity (Geometry) Soundwaves Surveying Teachers Triangle Triangulation Trigonometrical functions Trigonometry United States Variables (Mathematics) Vector analysis Vibration
Alternative Names
Apostol, T.M.
Apostol, T. M. 1923
Apostol, Tom Mike 1923
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