Lectures on Functional Equations and Their Applications


Author: J. Aczel,Hansjorg Oser
Publisher: Courier Corporation
ISBN: 0486445232
Category: Mathematics
Page: 510
View: 6039

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Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

Elements of the Theory of Functions and Functional Analysis


Author: Andre? Nikolaevich Kolmogorov,Serge? Vasil?evich Fomin,S. V. Fomin
Publisher: Courier Corporation
ISBN: 9780486406831
Category: Mathematics
Page: 288
View: 6483

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Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.

Introduction to Functional Equations

Theory and Problem-solving Strategies for Mathematical Competitions and Beyond
Author: Costas Efthimiou
Publisher: American Mathematical Soc.
ISBN: 0821853147
Category: Mathematics
Page: 363
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Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

Partial Differential Equations of Mathematical Physics


Author: S. L. Sobolev
Publisher: Courier Corporation
ISBN: 9780486659640
Category: Science
Page: 427
View: 1540

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This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Lectures on Ordinary Differential Equations


Author: Witold Hurewicz
Publisher: Courier Corporation
ISBN: 9780486495101
Category: Mathematics
Page: 144
View: 8897

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"A rigorous and lively introduction . . . careful and lucid . . ."--The American Mathematical Monthly. Excellent hardcover edition. This concise and idea-rich introduction to a topic of perennial interest in mathematics is written so clearly and lucidly, it is well within the reach of senior mathematics students. It covers mainly existence theorems for first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Throughout, the emphasis is on geometric methods. Witold Hurewicz was a world-class mathematician whose untimely death in 1956 deprived the mathematics community of one of its leading lights. His contributions to dimension theory, homotopy and other topics are outlined by Professor Solomon Lefschetz in a prefatory article "Witold Hurewicz in Memoriam" included in this volume. Also included is a list of books on differential equations for those interested in further reading, and a bibliography of Hurewicz's published works. Unabridged Dover republication of the work originally published by MIT Press, 1958. Prefatory article "Witold Hurewicz in Memoriam" by Solomon Lefschetz. List of References. Index. 26 figures.

The Riemann Zeta-function

Theory and Applications
Author: A. Ivi?
Publisher: Courier Corporation
ISBN: 9780486428130
Category: Mathematics
Page: 517
View: 363

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Comprehensive and coherent, this text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, distribution of primes, Dirichlet and various other divisor problems, and more. 1985 edition.

Series Associated With the Zeta and Related Functions


Author: Hari M. Srivastava,Junesang Choi
Publisher: Springer Science & Business Media
ISBN: 9780792370543
Category: Mathematics
Page: 388
View: 2467

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In recent years there has been an increasing interest in problems involving closed form evaluations of (and representations of the Riemann Zeta function at positive integer arguments as) various families of series associated with the Riemann Zeta function ((s), the Hurwitz Zeta function ((s,a), and their such extensions and generalizations as (for example) Lerch's transcendent (or the Hurwitz-Lerch Zeta function) iI>(z, s, a). Some of these developments have apparently stemmed from an over two-century-old theorem of Christian Goldbach (1690-1764), which was stated in a letter dated 1729 from Goldbach to Daniel Bernoulli (1700-1782), from recent rediscoveries of a fairly rapidly convergent series representation for ((3), which is actually contained in a 1772 paper by Leonhard Euler (1707-1783), and from another known series representation for ((3), which was used by Roger Apery (1916-1994) in 1978 in his celebrated proof of the irrationality of ((3). This book is motivated essentially by the fact that the theories and applications of the various methods and techniques used in dealing with many different families of series associated with the Riemann Zeta function and its aforementioned relatives are to be found so far only"in widely scattered journal articles. Thus our systematic (and unified) presentation of these results on the evaluation and representation of the Zeta and related functions is expected to fill a conspicuous gap in the existing books dealing exclusively with these Zeta functions.

Zeta and Q-Zeta Functions and Associated Series and Integrals


Author: H. M. Srivastava,Choi Junesang
Publisher: Elsevier
ISBN: 0123852188
Category: Mathematics
Page: 657
View: 4813

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Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions

Harmonic Analysis on Symmetric Spaces and Applications I


Author: Audrey Terras
Publisher: Springer Science & Business Media
ISBN: 1461251281
Category: Mathematics
Page: 352
View: 5712

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Since its beginnings with Fourier (and as far back as the Babylonian astron omers), harmonic analysis has been developed with the goal of unraveling the mysteries of the physical world of quasars, brain tumors, and so forth, as well as the mysteries of the nonphysical, but no less concrete, world of prime numbers, diophantine equations, and zeta functions. Quoting Courant and Hilbert, in the preface to the first German edition of Methods of Mathematical Physics: "Recent trends and fashions have, however, weakened the connection between mathematics and physics. " Such trends are still in evidence, harmful though they may be. My main motivation in writing these notes has been a desire to counteract this tendency towards specialization and describe appli cations of harmonic analysis in such diverse areas as number theory (which happens to be my specialty), statistics, medicine, geophysics, and quantum physics. I remember being quite surprised to learn that the subject is useful. My graduate eduation was that of the 1960s. The standard mathematics graduate course proceeded from Definition 1. 1. 1 to Corollary 14. 5. 59, with no room in between for applications, motivation, history, or references to related work. My aim has been to write a set of notes for a very different sort of course.

Calculus of Variations


Author: I. M. Gelfand,S. V. Fomin
Publisher: Courier Corporation
ISBN: 0486135012
Category: Mathematics
Page: 240
View: 8322

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Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.

Integral Equations


Author: Francesco Giacomo Tricomi
Publisher: Courier Corporation
ISBN: 9780486648286
Category: Mathematics
Page: 238
View: 7719

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Authoritative, well-written treatment of extremely useful mathematical tool with wide applications. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, more. Advanced undergraduate to graduate level. Exercises. Bibliography.

Das BUCH der Beweise


Author: Martin Aigner,Günter M. Ziegler
Publisher: Springer-Verlag
ISBN: 3662577674
Category: Mathematics
Page: 360
View: 6136

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Diese fünfte deutsche Auflage enthält ein ganz neues Kapitel über van der Waerdens Permanenten-Vermutung, sowie weitere neue, originelle und elegante Beweise in anderen Kapiteln. Aus den Rezensionen: “... es ist fast unmöglich, ein Mathematikbuch zu schreiben, das von jedermann gelesen und genossen werden kann, aber Aigner und Ziegler gelingt diese Meisterleistung in virtuosem Stil. [...] Dieses Buch erweist der Mathematik einen unschätzbaren Dienst, indem es Nicht-Mathematikern vorführt, was Mathematiker meinen, wenn sie über Schönheit sprechen.” Aus der Laudatio für den “Steele Prize for Mathematical Exposition” 2018 "Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdös immer wieder zitierte BUCH gehören, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Sätze enthält. Manchmal lässt der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, überraschenden Zusammenhängen und unerwarteten Volten." www.mathematik.de, Mai 2002 "Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdös, verständlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Lösungen mit Aha-Effekt, auch für Nicht-Mathematiker." www.vismath.de "Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999 "Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern." www.mathematik.de, Mai 2002

Lineare Algebra


Author: Gilbert Strang
Publisher: Springer-Verlag
ISBN: 3642556310
Category: Mathematics
Page: 656
View: 1368

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Diese Einführung in die lineare Algebra bietet einen sehr anschaulichen Zugang zum Thema. Die englische Originalausgabe wurde rasch zum Standardwerk in den Anfängerkursen des Massachusetts Institute of Technology sowie in vielen anderen nordamerikanischen Universitäten. Auch hierzulande ist dieses Buch als Grundstudiumsvorlesung für alle Studenten hervorragend lesbar. Darüber hinaus gibt es neue Impulse in der Mathematikausbildung und folgt dem Trend hin zu Anwendungen und Interdisziplinarität. Inhaltlich umfasst das Werk die Grundkenntnisse und die wichtigsten Anwendungen der linearen Algebra und eignet sich hervorragend für Studierende der Ingenieurwissenschaften, Naturwissenschaften, Mathematik und Informatik, die einen modernen Zugang zum Einsatz der linearen Algebra suchen. Ganz klar liegt hierbei der Schwerpunkt auf den Anwendungen, ohne dabei die mathematische Strenge zu vernachlässigen. Im Buch wird die jeweils zugrundeliegende Theorie mit zahlreichen Beispielen aus der Elektrotechnik, der Informatik, der Physik, Biologie und den Wirtschaftswissenschaften direkt verknüpft. Zahlreiche Aufgaben mit Lösungen runden das Werk ab.

Differentialgeometrie von Kurven und Flächen


Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 3322850722
Category: Technology & Engineering
Page: 263
View: 5217

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Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang

Lectures on Partial Differential Equations


Author: I. G. Petrovsky
Publisher: Courier Corporation
ISBN: 0486155080
Category: Mathematics
Page: 272
View: 5466

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Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.

Partial Differential Equations for Scientists and Engineers


Author: Stanley J. Farlow
Publisher: Courier Corporation
ISBN: 0486134733
Category: Mathematics
Page: 414
View: 8697

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Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.