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A survey of some of the main-line developments in trigonometric series. It is an extension of a Presidential address to Section III of the Royal Society of Canada. Part I deals briefly, in chronological order, with the mathematical problems that arose out of trigonometric series and the interactions between these problems and general mathematical analysis. There is mention of the contributions of Euler, Daniel Bernoulli, d'Alembert, Fourier, Lagrange, Dirichlet. This is followed by a description of some of the problems still open at the end of the period covered by these men, and a description of the way these problems were later solved by Denjoy, by Zygmund and Marcinkiewicz, by Burkill and by James. Part II gives complete proofs of the results of the earlier period outlined in Part I, and concludes with the essential details of the approach of Denjoy and of James. Canadian Mathematical Congress Lecture Series, No. 2.

A survey of some of the main-line developments in trigonometric series. It is an extension of a Presidential address to Section III of the Royal Society of Canada. Part I deals briefly, in chronological order, with the mathematical problems that arose out of trigonometric series and the interactions between these problems and general mathematical analysis. There is mention of the contributions of Euler, Daniel Bernoulli, d'Alembert, Fourier, Lagrange, Dirichlet. This is followed by a description of some of the problems still open at the end of the period covered by these men, and a description of the way these problems were later solved by Denjoy, by Zygmund and Marcinkiewicz, by Burkill and by James. Part II gives complete proofs of the results of the earlier period outlined in Part I, and concludes with the essential details of the approach of Denjoy and of James. Canadian Mathematical Congress Lecture Series, No. 2.

*Price HAS BEEN REDUCED by 10% until Monday, Jan. 13 (sale item)* 2nd edition; 383, 364 pp., Paperback, very good. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

Professor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of developments in trigonometric series, Fourier series and related branches of pure mathematics since the publication of the original edition. The two volumes are here bound together. Volume I, containing the completely rewritten material of the original work, deals with trigonometric series and Fourier series. Volume II provides much material previously unpublished in book form

Professor Zygmund's Trigonometric Series, first published in Warsaw in 1935, established itself as a classic. It presented a concise account of the main results then known, but was on a scale which limited the amount of detailed discussion possible. A greatly enlarged second edition published by Cambridge in two volumes in 1959 took full account of developments in trigonometric series, Fourier series and related branches of pure mathematics since the publication of the original edition. The two volumes are here bound together. Volume I, containing the completely rewritten material of the original work, deals with trigonometric series and Fourier series. Volume II provides much material previously unpublished in book form

Provides 2500 solved problems in algebra and trigonometry for college students. Subjects covered include equations, graphs, polynomial and rational functions, exponential and logarithmic functions, trigonometric and linear functions and conic sections.

In this monograph, Ivan Niven provides a masterful exposition of some central results on irrational, transcendental, and normal numbers. He gives a complete treatment by elementary methods of the irrationality of the exponential, logarithmic, and trigonometric functions with rational arguments. The approximation of irrational numbers by rationals, up to such results as the best possible approximation of Hurwitz, is also given with elementary technique. The last third of the monograph treats normal and transcendental numbers, including the Lindemann theorem, and the Gelfond-Schneider theorem. The book is wholly self-contained. The results needed from analysis and algebra are central. Well-known theorems, and complete references to standard works are given to help the beginner. The chapters are for the most part independent. There are notes at the end of each chapter citing the main sources used by the author and suggesting further reading.

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author.

Functions, Graphs, Applications, Polynomial Functions, Inequalities, Exponents and Logarithms, Analytic Geometry, Trigonometry, Trigonometric Equations and Applications, Triangly Trigonometry, Trigonometric Addition Formulas, Polar Coordinates and Complex Numbers, Vectors and Determinants, Sequences and Series, Matrices, Combinatorics, Probability, Statistics, Curve Fitting and Models, Limits, Series and Iterated Functions, An Introduction to Calculus

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author.

This is a textbook for the second semester of calculus. The major topics are applications of integrals, methods of integration, the inverse trigonometric functions, elementary differential equations, calculus with polar coordinate functions and functions given by parametric equations, sequences and infinite series. The text has explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Topics are typically introduced by way of applications, and the text contains the usual theorems and techniques of a second semester of calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of calculus. The exposition and problem sets have been highly rated by reviewers.

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author.

Functions, Graphs, Applications, Polynomial Functions, Inequalities, Exponents and Logarithms, Analytic Geometry, Trigonometry, Trigonometric Equations and Applications, Triangly Trigonometry, Trigonometric Addition Formulas, Polar Coordinates and Complex Numbers, Vectors and Determinants, Sequences and Series, Matrices, Combinatorics, Probability, Statistics, Curve Fitting and Models, Limits, Series and Iterated Functions, An Introduction to Calculus

This is an expanded version of Calculus and its Applications, Tenth Edition, by the same authors. The additional coverage includes trigonometric functions, differential equations, sequences and series, and probability distributions. Chapters on Systems and Matrices and Discrete Probability are available as a custom option or online in MyMathLab.   Anticipating and meeting student needs Calculus and Its Applications remains a best-selling text due to its accessible presentation, which anticipates and addresses student needs. The writing style is ideal for today’s students, providing intuitive explanations with carefully crafted artwork to help them visualize calculus concepts. Additionally, the text’s numerous and up-to-date applications from business, economics, life sciences, and social sciences help to motivate students. Algebra diagnostic and review material is available for those who need to strengthen basic skills. Every aspect of this version is designed to motivate and help students to more readily understand and apply the mathematics.   Note: You are purchasing a standalone product; MyMathLab does not come packaged with this content. MyMathLab is not a self-paced technology and should only be purchased when required by an instructor. If you would like to purchase both the physical text and MyMathLab, search for:   0134123492 / 9780134123493 Calculus and Its Applications Expanded Version Media Update Plus MyMathLab -- Access Card Package   Package consists of 0134122585 / 9780134122588 Calculus and Its Applications Expanded Version Media Update 0321431308 / 9780321431301 MyMathLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker   Students, if interested in purchasing this title with MyMathLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.  

This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author.

The Expanded Eighth Edition of Applied Calculus for Business, Economics, and the Social and Life Sciences includes four additional chapters: - Chapter 8, Differential Equations - Chapter 9, Infinite Series and Taylor Approximations - Chapter 10, Probability and Calculus - Chapter 11, Trigonometric Functions The textbook meets the needs of instructors who cover topics in one or more of these four chapters together with material from the initial seven chapters. This is often a two-semester course. (The word "Applied" in this title distinguishes this volume from the shorter edition.)The book introduces calculus in real-world contexts; the primary goal is to provide a sound, intuitive understanding of basic concepts students need as they pursue careers in business, the life sciences and the social sciences.

This straightforward course based on the idea of a limit is intended for students who have acquired a working knowledge of the calculus and are ready for a more systematic treatment which also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series. Particular attention is given to clarity of exposition and the logical development of the subject matter. A large number of examples is included, with hints for the solution of many of them.