Apostol, Tom M.Overview
Publication Timeline
Most widely held works about
Tom M Apostol
Most widely held works by
Tom M Apostol
Calculus
by Tom M Apostol
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Book
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59 editions published between 1196 and 1999 in 4 languages and held by 1,831 WorldCat member libraries worldwide
Selected papers on calculus
by Raymond W Brink
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Book
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20 editions published between 1969 and 1979 in English and Undetermined and held by 1,293 WorldCat member libraries worldwide
Mathematical analysis : a modern approach to advanced calculus
by Tom M Apostol
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Book
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57 editions published between 1957 and 2008 in English and Undetermined and held by 1,138 WorldCat member libraries worldwide Index
Introduction to analytic number theory
by Tom M Apostol
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Book
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42 editions published between 1976 and 2011 in 4 languages and held by 1,017 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
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Book
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19 editions published between 1976 and 1997 in 3 languages and held by 804 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
Mathematical analysis
by Tom M Apostol
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Book
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30 editions published between 1957 and 2007 in 3 languages and held by 665 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
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Book
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10 editions published between 1985 and 2008 in English and held by 591 WorldCat member libraries worldwide
Beyond the mechanical universe : from electricity to modern physics
by Richard P Olenick
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Book
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13 editions published between 1986 and 2008 in English and Italian and held by 493 WorldCat member libraries worldwide
New horizons in geometry
by Tom M Apostol
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Book
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8 editions published between 2012 and 2013 in English and held by 390 WorldCat member libraries worldwide Calculus problems solved by elementary geometrical methods  P. 4 of cover
A century of calculus
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Book
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8 editions published in 1992 in English and held by 361 WorldCat member libraries worldwide Selected papers reprinted from American mathematical monthly (Volumes 1  75) and Mathematics magazine (Volumes 1  40)
Linear algebra : a first course, with applications to differential equations
by Tom M Apostol
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Book
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11 editions published between 1997 and 2006 in English and held by 332 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
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Visual
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11 editions published between 1988 and 1989 in 3 languages and held by 311 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
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Visual
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7 editions published in 1989 in English and No Linguistic content and held by 274 WorldCat member libraries worldwide Math tutorial which defines pi, discusses its early history, and demonstrates its uses
Similarity
by California Institute of Technology
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Visual
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8 editions published in 1990 in English and held by 185 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
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Visual
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10 editions published between 1991 and 2005 in 3 languages and held by 173 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
Calculus. Calculus of several variables with applications to probability and vector analysis
by Tom M Apostol
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Book
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49 editions published between 1962 and 2004 in 3 languages and held by 110 WorldCat member libraries worldwide
Early history
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Visual
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1 edition published in 2000 in English and held by 110 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
by Apostol
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Visual
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2 editions published in 1992 in English and held by 108 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
by Apostol
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Visual
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1 edition published in 1993 in English and held by 82 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 Tunnel of Samos
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Visual
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4 editions published in 1995 in English and held by 75 WorldCat member libraries worldwide "This video describes a remarkable engineering work of ancient times: excavating a onekilometer tunnel straight through the heart of a mountain, using separate crews that dug from the two ends and met in the middle. How did they determine the direction for excavation? The program gives Hero's explanation (ca. 60 A.D.), using similar triangles, as well as alternative methods proposed in modern times."Www.projectmathematics.com more
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Associated Subjects
Algebra Algebraic number theory Algebras, Linear Apostol, Jane Apostol, Tom M Arithmetic functions Calculus California Institute of Technology Canada Circle Circlesquaring College teachers Differential equations Dirichlet series Elliptic functions Geometry GreecePatrai GreeceSamos (Municipality) Heat India Mathematical analysis Mathematics MathematicsStudy and teaching Mechanical universe (Television program) Mechanics Modular functions Numbers, Prime Number theory Numerals Physics PhysicsStudy and teaching (Higher)Audiovisual aids Pi Polynomials Precalculus Pythagoras Pythagorean theorem Ratio and proportion Research Similarity (Geometry) Soundwaves Surveying Triangle Triangulation Trigonometry Tunneling Tunnels United States Variables (Mathematics) Vibration Watersupply

Alternative Names
Apostol, T.M.
Apostol, T. M. 1923
Apostol, Tom Mike 1923
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