Apostol, Tom M.
Overview
Works:  194 works in 1,026 publications in 8 languages and 12,697 library holdings 

Genres:  Educational films Nonfiction films Short films Animated films History Surveys Filmed lectures Nonfiction television programs Educational television programs Juvenile works 
Roles:  Author, Editor, Director, Creator, Scenarist 
Classifications:  QA300, 517 
Publication Timeline
.
Most widely held works about
Tom M Apostol
 Patras diary by Jane Apostol( Book )
 Apostol, Tom M. : Mathematics( )
 Interview with Tom Apostol by Tom M Apostol( Book )
 A treatise on problems in Apostol's mathematical analysis by Adam Y Wu( Book )
Most widely held works by
Tom M Apostol
Calculus by
Tom M Apostol(
Book
)
287 editions published between 1196 and 2014 in 6 languages and held by 2,252 WorldCat member libraries worldwide
Calculus / Tom M. Apostol.  v.1
287 editions published between 1196 and 2014 in 6 languages and held by 2,252 WorldCat member libraries worldwide
Calculus / Tom M. Apostol.  v.1
Mathematical analysis : a modern approach to advanced calculus by
Tom M Apostol(
Book
)
72 editions published between 1957 and 1974 in English and Undetermined and held by 1,132 WorldCat member libraries worldwide
Index
72 editions published between 1957 and 1974 in English and Undetermined and held by 1,132 WorldCat member libraries worldwide
Index
Introduction to analytic number theory by
Tom M Apostol(
Book
)
63 editions published between 1976 and 2010 in 6 languages and held by 1,093 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
63 editions published between 1976 and 2010 in 6 languages and held by 1,093 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
)
30 editions published between 1976 and 1997 in 4 languages and held by 831 WorldCat member libraries worldwide
This is the second volume of a 2volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their numbertheoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj(r), 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. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the SpringerVerlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory
30 editions published between 1976 and 1997 in 4 languages and held by 831 WorldCat member libraries worldwide
This is the second volume of a 2volume textbook* which evolved from a course (Mathematics 160) offered at the California Institute of Technology du ring the last 25 years. The second volume presupposes a background in number theory com parable to that provided in the first volume, together with a knowledge of the basic concepts of complex analysis. Most of the present volume is devoted to elliptic functions and modular functions with some of their numbertheoretic applications. Among the major topics treated are Rademacher's convergent series for the partition function, Lehner's congruences for the Fourier coefficients of the modular functionj(r), 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. Both volumes of this work emphasize classical aspects of a subject wh ich in recent years has undergone a great deal of modern development. It is hoped that these volumes will help the nonspecialist become acquainted with an important and fascinating part of mathematics and, at the same time, will provide some of the background that belongs to the repertory of every specialist in the field. This volume, like the first, is dedicated to the students who have taken this course and have gone on to make notable contributions to number theory and other parts of mathematics. T.M.A. January, 1976 * The first volume is in the SpringerVerlag series Undergraduate Texts in Mathematics under the title Introduction to Analytic Number Theory
Selected papers on calculus by
Tom M Apostol(
Book
)
23 editions published between 1969 and 1979 in English and Undetermined and held by 791 WorldCat member libraries worldwide
23 editions published between 1969 and 1979 in English and Undetermined and held by 791 WorldCat member libraries worldwide
Mathematical analysis by
Tom M Apostol(
Book
)
47 editions published between 1958 and 2008 in 3 languages and held by 703 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
47 editions published between 1958 and 2008 in 3 languages and held by 703 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
The mechanical universe : introduction to mechanics and heat by
Richard P Olenick(
Book
)
25 editions published between 1985 and 2012 in English and Chinese and held by 656 WorldCat member libraries worldwide
This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thoughtprovoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a telecourse to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lowerlevel edition to a greater degree
25 editions published between 1985 and 2012 in English and Chinese and held by 656 WorldCat member libraries worldwide
This innovative physics textbook intended for science and engineering majors develops classical mechanics from a historical perspective. The presentation of the standard course material includes a discussion of the thought processes of the discoverers and a description of the methods by which they arrived at their theories. However the presentation proceeds logically rather than strictly chronologically, so new concepts are introduced at the natural moment. The book assumes a familiarity with calculus, includes a discussion of rigid body motion, and contains numerous thoughtprovoking problems. It is largely based in content on The Mechanical Universe: Introduction to Mechanics and Heat, a book designed in conjunction with a telecourse to be offered by PBS in the Fall of 1985. The advanced edition, however, does not coincide exactly with the video lessons, contains additional material, and develops the fundamental ideas introduced in the lowerlevel edition to a greater degree
Beyond the mechanical universe : from electricity to modern physics by
Richard P Olenick(
Book
)
16 editions published between 1986 and 2008 in 3 languages and held by 504 WorldCat member libraries worldwide
16 editions published between 1986 and 2008 in 3 languages and held by 504 WorldCat member libraries worldwide
Selected papers on precalculus by
Tom M Apostol(
Book
)
15 editions published in 1977 in English and held by 483 WorldCat member libraries worldwide
15 editions published in 1977 in English and held by 483 WorldCat member libraries worldwide
A century of calculus(
Book
)
8 editions published in 1992 in English and held by 360 WorldCat member libraries worldwide
Selected papers reprinted from American mathematical monthly (Volumes 1  75) and Mathematics magazine (Volumes 1  40)
8 editions published in 1992 in English and held by 360 WorldCat member libraries worldwide
Selected papers reprinted from American mathematical monthly (Volumes 1  75) and Mathematics magazine (Volumes 1  40)
New horizons in geometry by
Tom M Apostol(
Book
)
16 editions published between 2012 and 2013 in English and Undetermined and held by 354 WorldCat member libraries worldwide
"Classical calculus problems generalized and solved by elementary geometrical methods, with 1000 color illustrations."Publisher's description
16 editions published between 2012 and 2013 in English and Undetermined and held by 354 WorldCat member libraries worldwide
"Classical calculus problems generalized and solved by elementary geometrical methods, with 1000 color illustrations."Publisher's description
Linear algebra : a first course, with applications to differential equations by
Tom M Apostol(
Book
)
19 editions published between 1997 and 2014 in 3 languages and held by 349 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
19 editions published between 1997 and 2014 in 3 languages and held by 349 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
The Theorem of Pythagoras by
Tom M Apostol(
Visual
)
13 editions published between 1988 and 1989 in 3 languages and held by 255 WorldCat member libraries worldwide
After posing problems from real life than can be solved by using the Pythagorean theorem, the videotape provides a historical perspective together with several different animated proofs. The theorem is extended to three dimensions. A dramatic view of the earth shows why the theorem fails on the surface of a sphere
13 editions published between 1988 and 1989 in 3 languages and held by 255 WorldCat member libraries worldwide
After posing problems from real life than can be solved by using the Pythagorean theorem, the videotape provides a historical perspective together with several different animated proofs. The theorem is extended to three dimensions. A dramatic view of the earth shows why the theorem fails on the surface of a sphere
The Story of pi by
California Institute of Technology(
Visual
)
5 editions published in 1989 in English and No Linguistic content and held by 226 WorldCat member libraries worldwide
Math tutorial which defines pi, discusses its early history, and demonstrates its uses
5 editions published in 1989 in English and No Linguistic content and held by 226 WorldCat member libraries worldwide
Math tutorial which defines pi, discusses its early history, and demonstrates its uses
Similarity by
California Institute of Technology(
Visual
)
7 editions published in 1990 in English and held by 157 WorldCat member libraries worldwide
Discusses the ratios of geometrical figures, their mathematical similarities, and the practical applications of using the mathematics
7 editions published in 1990 in English and held by 157 WorldCat member libraries worldwide
Discusses the ratios of geometrical figures, their mathematical similarities, and the practical applications of using the mathematics
Polynomials by
Tom M Apostol(
Visual
)
10 editions published between 1991 and 2005 in 3 languages and held by 137 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 137 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 92 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 92 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
Early history(
Visual
)
1 edition published in 2000 in English and held by 83 WorldCat member libraries worldwide
"Two introductory segments give an overview of the program. The first outlines some of the important developments in the period from 3000 B.C. to 300 B.C., which culminated with the publication of Euclid's Elements. The second gives an outline of some of the landmark achievements from 300 B.C. up to the events that led to the development of calculus. The remaining segments describe in more detail some of the important highlights on the road to calculus. They discuss number systems developed in different cultures; numerology or number mysticism as practiced by the Pythagoreans; the origin of number theory as an outgrowth of numerology; the Pythagorean Theorem for right triangles and how it led to the discovery of irrational numbers; the golden age of Hellenistic mathematics as it flourished in the ancient city of Alexandria; the multicultural search for an understanding of the number pi and the landmark contributions to this effort by Archimedes; how astronomy gave birth to trigonometry; and other developments such as algebra and analytic geometry that eventually led to the calculus."Www.projectmathematics.com
1 edition published in 2000 in English and held by 83 WorldCat member libraries worldwide
"Two introductory segments give an overview of the program. The first outlines some of the important developments in the period from 3000 B.C. to 300 B.C., which culminated with the publication of Euclid's Elements. The second gives an outline of some of the landmark achievements from 300 B.C. up to the events that led to the development of calculus. The remaining segments describe in more detail some of the important highlights on the road to calculus. They discuss number systems developed in different cultures; numerology or number mysticism as practiced by the Pythagoreans; the origin of number theory as an outgrowth of numerology; the Pythagorean Theorem for right triangles and how it led to the discovery of irrational numbers; the golden age of Hellenistic mathematics as it flourished in the ancient city of Alexandria; the multicultural search for an understanding of the number pi and the landmark contributions to this effort by Archimedes; how astronomy gave birth to trigonometry; and other developments such as algebra and analytic geometry that eventually led to the calculus."Www.projectmathematics.com
Sines and cosines(
Visual
)
3 editions published in 1993 in English and held by 70 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
3 editions published in 1993 in English and held by 70 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
The Mechanical universe ... and beyond by
David L Goodstein(
Visual
)
1 edition published in 1989 in English and held by 64 WorldCat member libraries worldwide
"A visually splendid introductory physics course, [this series] combines computer graphics and reenactments of the history of science with introductory lectures by David L. Goodstein of Caltech. This adventure of the mind traces the interaction of ideas from Aristotle to Einstein to explain the theories of Copernicus, Kepler, and Newton."Container
1 edition published in 1989 in English and held by 64 WorldCat member libraries worldwide
"A visually splendid introductory physics course, [this series] combines computer graphics and reenactments of the history of science with introductory lectures by David L. Goodstein of Caltech. This adventure of the mind traces the interaction of ideas from Aristotle to Einstein to explain the theories of Copernicus, Kepler, and Newton."Container
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Related Identities
 California Institute of Technology Producer
 Goodstein, David L. 1939
 Mathematical Association of America Publisher
 Project Mathematics!
 Olenick, Richard P. Author
 Mnatsakanian, Mamikon A. Illustrator Author
 Freedman, Benedict
 Hibbs, Al Narrator
 Davis, Susan G. 1953 Narrator
 Mnatsakanian, Mamikon A.
Useful Links
Associated Subjects
Algebras, Linear Arithmetic functions Atoms Calculus Circle Circlesquaring Copernicus, Nicolaus, Differential equations Dirichlet series Einstein, Albert, Electric fields Elliptic functions Force and energy Geometry Gravity Heat India Kepler, Johannes, Mathematical analysis Mathematics Mechanical universe (Television program) Mechanics MechanicsAudiovisual aids MechanicsStudy and teaching (Higher) Modular functions Momentum (Mechanics) Newton, Isaac, Numbers, Prime Number theory Numerals Physics PhysicsAudiovisual aids PhysicsStudy and teaching PhysicsStudy and teaching (Higher) PhysicsStudy and teaching (Higher)Audiovisual aids Pi Polynomials Precalculus Pythagorean theorem Ratio and proportion Similarity (Geometry) Soundwaves Space and time Surveying Triangle Triangulation Trigonometry TrigonometryStudy and teaching (Higher) United States Vibration
Alternative Names
Apostol, T.M.
Apostol, T. M. 1923
Apostol, Tom Mike 1923
Tom Apostol Amerikaans wiskundige
Tom Apostol USamerikanischer Mathematiker
Tom M. Apostol amerikansk matematikar
Tom M. Apostol amerikansk matematiker
Tom M. Apostol matematico statunitense
Tom M. Apostol mathématicien américain
Tom Mike Apostol
トム・アポストル
湯姆·麥克·阿波斯托
Languages
English
(504)
Spanish (121)
Portuguese (5)
Chinese (4)
Greek, Modern (4)
German (3)
Persian (3)
Italian (3)
Spanish (121)
Portuguese (5)
Chinese (4)
Greek, Modern (4)
German (3)
Persian (3)
Italian (3)
Covers