Lectures on Functional Equations and Their Applications


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

Functional Equations and How to Solve Them


Author: Christopher G. Small
Publisher: Springer Science & Business Media
ISBN: 0387489010
Category: Mathematics
Page: 131
View: 8136

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Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.

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
View: 5671

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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.

An Introduction to the Theory of Functional Equations and Inequalities

Cauchy's Equation and Jensen's Inequality
Author: Marek Kuczma
Publisher: Springer Science & Business Media
ISBN: 3764387491
Category: Mathematics
Page: 595
View: 1842

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Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)

Lecture Notes on Functional Analysis

With Applications to Linear Partial Differential Equations
Author: Alberto Bressan
Publisher: American Mathematical Soc.
ISBN: 0821887718
Category: Mathematics
Page: 250
View: 9965

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This textbook is addressed to graduate students in mathematics or other disciplines who wish to understand the essential concepts of functional analysis and their applications to partial differential equations. The book is intentionally concise, presenting all the fundamental concepts and results but omitting the more specialized topics. Enough of the theory of Sobolev spaces and semigroups of linear operators is included as needed to develop significant applications to elliptic, parabolic, and hyperbolic PDEs. Throughout the book, care has been taken to explain the connections between theorems in functional analysis and familiar results of finite-dimensional linear algebra. The main concepts and ideas used in the proofs are illustrated with a large number of figures. A rich collection of homework problems is included at the end of most chapters. The book is suitable as a text for a one-semester graduate course.

The Functions of Mathematical Physics


Author: Harry Hochstadt
Publisher: Courier Corporation
ISBN: 0486168786
Category: Science
Page: 352
View: 1609

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Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.

An Introduction to Differential Equations and Their Applications


Author: Stanley J. Farlow
Publisher: Courier Corporation
ISBN: 0486135136
Category: Mathematics
Page: 640
View: 2447

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This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

Distribution Theory and Transform Analysis

An Introduction to Generalized Functions, with Applications
Author: A.H. Zemanian
Publisher: Courier Corporation
ISBN: 0486151948
Category: Mathematics
Page: 400
View: 3098

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Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.

Lectures on Ordinary Differential Equations


Author: Witold Hurewicz
Publisher: Courier Corporation
ISBN: 9780486495101
Category: Mathematics
Page: 144
View: 2688

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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.

Singular Integral Equations

Boundary Problems of Function Theory and Their Application to Mathematical Physics
Author: N. I. Muskhelishvili
Publisher: Courier Corporation
ISBN: 0486145069
Category: Mathematics
Page: 464
View: 7973

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DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div

Partial Differential Equations of Mathematical Physics


Author: S. L. Sobolev
Publisher: Courier Corporation
ISBN: 9780486659640
Category: Science
Page: 427
View: 5532

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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.

Calculus of Variations


Author: I. M. Gelfand,S. V. Fomin
Publisher: Courier Corporation
ISBN: 0486135012
Category: Mathematics
Page: 240
View: 7868

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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.

Elementary Functional Analysis


Author: Georgi E. Shilov
Publisher: Courier Corporation
ISBN: 0486318680
Category: Mathematics
Page: 352
View: 5916

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Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 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: 4260

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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.

Lectures on Integral Equations


Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486810275
Category: Mathematics
Page: 128
View: 9864

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This concise and classic volume presents the main results of integral equation theory as consequences of the theory of operators on Banach and Hilbert spaces. In addition, it offers a brief account of Fredholm's original approach. The self-contained treatment requires only some familiarity with elementary real variable theory, including the elements of Lebesgue integration, and is suitable for advanced undergraduates and graduate students of mathematics. Other material discusses applications to second order linear differential equations, and a final chapter uses Fourier integral techniques to investigate certain singular integral equations of interest for physical applications as well as for their own sake. A helpful index concludes the text.

Applied Functional Analysis


Author: D.H. Griffel
Publisher: Courier Corporation
ISBN: 0486141322
Category: Mathematics
Page: 390
View: 6575

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This introductory text examines applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Covers distribution theory, Banach spaces, Hilbert space, spectral theory, Frechet calculus, Sobolev spaces, more. 1985 edition.

Lectures on Measure and Integration


Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486810283
Category: Mathematics
Page: 176
View: 6992

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These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

Galois Theory

Lectures Delivered at the University of Notre Dame by Emil Artin (Notre Dame Mathematical Lectures,
Author: Emil Artin
Publisher: Courier Corporation
ISBN: 048615825X
Category: Mathematics
Page: 86
View: 7841

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Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.

Mathematics of Classical and Quantum Physics


Author: Frederick W. Byron,Robert W. Fuller
Publisher: Courier Corporation
ISBN: 0486135063
Category: Science
Page: 672
View: 6060

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Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.