In studies of general operators of the same nature, general convolution transforms are immediately encountered as the objects of inversion. The relation between differential operators and integral transforms is the basic theme of this work, which is geared toward upper-level undergraduates and graduate students. It may be read easily by anyone with a working knowledge of real and complex variable theory. Topics include the finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, and complex inversion theory.

This accessible introduction to Calculus is designed to demonstrate how calculus applies to various fields of study. The text is packed with real data and real-life applications to business, economics, social and life sciences. Applications using real data enhances student motivation. Many of these applications include source lines, to show how mathematics is used in the real world. * NEW! Conceptual problems ask students to put the concepts and results into their own words. These problems are marked with an icon to make them easier to assign. * More opportunities for the use of graphing calculator, including screen shots and instructions, and the use of icons that clearly identify each opportunity for the use of spreadsheets or graphing calculator. * Work problems appear throughout the text, giving the student the chance to immediately reinforce the concept or skill they have just learned. * Chapter Reviews contain a variety of features to help synthesize the ideas of the chapter, including: Objectives Check, Important Terms and Concepts, True-False Items, Fill in the Blanks and Review Exercises. * Includes Mathematical Questions from Professional Exams (CPA)

John C. Sparks is a senior staff engineer at Wright-Patterson Air Force Base in Dayton, Ohio with approximately thirty-one years of engineering and management experience. In addition to his Air Force career, Sparks has taught mathematics at Sinclair Community College for over twenty years. In late 2003, Sparks received the Ohio Association of Two-Year Colleges' 2002-2003 Adjunct Teacher of the Year award. He and his wife, Carolyn (photo), have celebrated thirty-five years of marriage and have two sons, Robert and Curtis, who are both married. Sparks is a lifelong resident of Xenia, Ohio. Sparks has written and published three volumes of poetry, Rhyme for All Seasons, Mixed Images, and Gold, Hay and Stubble: One Journeyman's Poetic Diary. Calculus without Limits is his first full-length mathematics work; and, with its publication, a thirty-year old dream is realized.

Originally published in 1997, An Introduction to Mathematical Analysis provides a rigorous approach to real analysis and the basic ideas of complex analysis. Although the approach is axiomatic, the language is evocative rather than formal, and the proofs are clear and well motivated. The author writes with the reader always in mind. The text includes a novel and simplified approach to the Lebesgue integral, a topic not usually found in books at this level. The problems are scattered throughout the text, and are designed to get the student actively involved in the development at every stage. "This Introduction to Mathematical Analysis is a very carefully written and well organized presentation of the major theorems in classical real and complex analysis. I can find no fault whatever pertaining to the level of rigor or mathematical precision of the manuscript. All in all I think this is a fine text." Reviewer from Portland State "To summarize I think this text is very good. Its strengths are many. The choices of the problems and examples are well made. The proofs are very to the point and the style makes the text very readable." Reviewer from Michigan State "H. S. Bear seems to be one of the best kept secrets around. His writing in general is superb. This book is a well organized first course in analysis broken into digestible chunks and surprisingly thorough. It covers the basic topics and then introduces the reader to complex analysis and later to Lebesgue integration." James M. Cargal Professor Bear obtained his degree at the University of California, Berkeley with a thesis in functional analysis. He has held permanent positions at several major western universities, as well as visiting appointments at Princeton, the University of California, San Diego, and Erlangen-Nurnberg, Germany. All of these venues involved a ridiculous amount of bad weather, so he went to the University of Hawaii as department chairman in 1969. He served as department chairman for five years, and later served a term as graduate chairman. He has numerous research and expository publications in the areas of functional analysis, real and complex analysis, and measure theory.

Originally published in the Soviet Union, this text is meant for students of higher schools and deals with the most important sections of mathematics - differential equations and the calculus of variations. The first part describes the theory of differential equations and reviews the methods for integrating these equations and investigating their solutions. The second part gives an idea of the calculus of variations and surveys the methods for solving variational problems. The book contains a large number of examples and problems with solutions involving applications of mathematics to physics and mechanics. Apart from its main purpose the textbook is of interest to expert mathematicians. Lev Elsgolts (deceased) was a Doctor of Physico-Mathematical Sciences, Professor at the Patrice Lumumba University of Friendship of Peoples. His research work was dedicated to the calculus of variations and differential equations. He worked out the theory of differential equations with deviating arguments and supplied methods for their solution. Lev Elsgolts was the author of many printed works. Among others, he wrote the well-known books Qualitative Methods in Mathematical Analysis and Introduction to the Theory of Differential Equations with Deviating Arguments. In addition to his research work Lev Elsgolts taught at higher schools for over twenty years.

Ideal for self-instruction as well as classroom use, this text helps students develop improved understanding and problem-solving skills in calculus. It features more than 1,200 problems, with concise explanations of the basic notions and theorems to be used in their solutions; complete answers appear in the text and at the end of the book. Unabridged republication of the edition published by Holden-Day, Inc., San Francisco, 1963.

'There were lots of young analysts who flocked to Chicago in those years, but virtually from the start it was clear that Tom had a special brilliance...Eventually, the mathematical door would open a crack as Tom discovered a new technique, usually of astonishing originality. The end would now be in sight, as [he] unleashed his tremendous technical abilities...Time after time, [Wolff] would pick a central problem in an area and solve it. After a few more results, the field would be changed forever...In the mathematical community, the common and rapid response to these breakthroughs was that they were seen, not just as watershed events, but as lightning strikes that permanently altered the landscape' - Peter W. Jones, Yale University.'Tom Wolff was not only a deep thinker in mathematics but also a technical master' - Barry Simon, California Institute of Technology. Thomas H. Wolff was a leading analyst and winner of the Salem and Bocher Prizes. He made significant contributions to several areas of harmonic analysis, in particular to geometrical and measure-theoretic questions related to the Kakeya needle problem. Wolff attacked the problem with awesome power and originality, using both geometric and combinatorial ideas.This book provides an inside look at the techniques used and developed by Wolff. It is based on a graduate course on Fourier analysis he taught at Caltech. The selection of the material is somewhat unconventional in that it leads the reader, in Wolff's unique and straightforward way, through the basics directly to current research topics. The book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The first few chapters cover the usual background material: the Fourier transform, convolution, the inversion theorem, the uncertainty principle, and the method of stationary phase.However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics, and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensure that both graduate students and research mathematicians will benefit from the book.

This book reproduces the doctoral thesis written by a remarkable mathematician, Sergei V. Kerov. His untimely death at age 54 left the mathematical community with an extensive body of work and this one-of-a-kind monograph. In it, he gives a clear and lucid account of results and methods of asymptotic representation theory. The book is a unique source of information on the important topic of current research. Asymptotic representation theory of symmetric groups deals with problems of two types: asymptotic properties of representations of symmetric groups of large order and representations of the limiting object, i.e., the infinite symmetric group.The author contributed significantly in the development of both directions. His book presents an account of these contributions, as well as those of other researchers. Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram. He also studies stochastic properties of the deviations of random diagrams from the limiting curve.Among the problems of the second type, Kerov studies an important problem of computing irreducible characters of the infinite symmetric group. This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams. In turn, this construction provides a completely new description of the relation between the classical moment problems of Hausdorff and Markov. The book is suitable for graduate students and research mathematicians interested in representation theory and combinatorics.

CALCULUS + PEPPERONI / FUN = MATH SUCCESS

Do you want to do well on your calculus exam? Are you looking for a quick refresher course? Or would you just like to get a taste of what calculus is all about? If so, you’ve selected the right book. Calculus and Pizza is a creative, surprisingly delicious overview of the essential rules and formulas of calculus, with tons of problems for the learner with a healthy appetite.

Setting up residence in a pizza parlor, Clifford Pickover focuses on procedures for solving problems, offering short, easy-to-digest chapters that allow you to quickly get the essence of a technique or question. From exponentials and logarithms to derivatives and multiple integrals, the book utilizes pepperoni, meatballs, and more to make complex topics fun to learn–emphasizing basic, practical principles to help you calculate the speed of tossed pizza dough or the rising cost of eggplant parmigiana. Plus, you’ll see how simple math–and a meal–can solve especially curious and even mind-shattering problems.

Authoritatively and humorously written, Calculus and Pizza provides a lively–and more tasteful–approach to calculus.

"Pickover has published nearly a book a year in which he stretches the limits of computers, art, and thought."
–Los Angeles Times

"A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today."
–Journal of Recreational Mathematics

Everything you need to know–basic essential concepts–about calculus

For anyone looking for a readable alternative to the usual unwieldy calculus text, here’s a concise, no-nonsense approach to learning calculus. Following up on the highly popular first edition of Understanding Calculus, Professor H. S. Bear offers an expanded, improved edition that will serve the needs of every mathematics and engineering student, or provide an easy-to-use refresher text for engineers.

Understanding Calculus, Second Edition provides in a condensed format all the material covered in the standard two-year calculus course. In addition to the first edition’s comprehensive treatment of one-variable calculus, it covers vectors, lines, and planes in space; partial derivatives; line integrals; Green’s theorem; and much more. More importantly, it teaches the material in a unique, easy-to-read style that makes calculus fun to learn. By explaining calculus concepts through simple geometric and physical examples rather than formal proofs, Understanding Calculus, Second Edition, makes it easy for anyone to master the essentials of calculus.

If the dry "theorem-and-proof" approach just doesn’t work, and the traditional twenty pound calculus textbook is just too much, this book is for you.

This text is designed for first courses in financial calculus aimed at students with a good background in mathematics. Key concepts such as martingales and change of measure are introduced in the discrete time framework, allowing an accessible account of Brownian motion and stochastic calculus. The Black-Scholes pricing formula is first derived in the simplest financial context. Subsequent chapters are devoted to increasing the financial sophistication of the models and instruments. The final chapter introduces more advanced topics including stock price models with jumps, and stochastic volatility. A large number of exercises and examples illustrate how the methods and concepts can be applied to realistic financial questions.

Computable Calculus treats the fundamental topic of calculus in a novel way that is more in tune with today's computer age. Comprising 11 chapters and an accompanying CD-ROM, the book presents mathematical analysis that has been created to deal with constructively defined concepts. The book's "show your work" approach makes it easier to understand the pitfalls of various computations and, more importantly, how to avoid these pitfalls.
The accompanying CD-ROM has self-contained programs that interact with the text, providing for easy grasp of the new concepts and enabling readers to write their own demonstration programs.
Contains software on CD ROM:
The accompanying software demonstrates, through simulation and exercises, how each concept of calculus can be associated with a program for the 'ideal computer'
Using this software readers will be able to write their own demonstration programs

Although much has happened in the field since the publication of this book, as demonstrated by Helgason's own three-volume expansion of the original work, this single volume on Riemannian geometry and for the analysis and geometry of symmetric spaces still offers a clear overview of the subjects. The text includes a well-developed treatment of Cartan's classification and structure theory of symmetric spaces, and the last chapter, on functions on symmetric spaces, remains a comprehensive introduction to the study of spherical functions, the theory of invariant differential operators, and other topics in harmonic analysis.

For a Riemannian manifold $M$, the geometry, topology and analysis are interrelated in ways that are widely explored in modern mathematics. Bounds on the curvature can have significant implications for the topology of the manifold. The eigenvalues of the Laplacian are naturally linked to the geometry of the manifold. For manifolds that admit spin (or $\textrm {spin}^\mathbb{C}$) structures, one obtains further information from equations involving Dirac operators and spinor fields. In the case of four-manifolds, for example, one has the remarkable Seiberg-Witten invariants.In this text, Friedrich examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and $\textrm {spin}^\mathbb{C}$ structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature.Considerations of Killing spinors and solutions of the twistor equation on $M$ lead to results about whether $M$ is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections. This detailed book with elegant proofs is suitable as a text for courses in advanced differential geometry and global analysis, and can serve as an introduction for further study in these areas. This edition is translated from the German edition published by Vieweg Verlag.

The "Ausdehnungslehre" of 1862 is Grassmann's most mature presentation of his "extension theory" and captured the full sweep of his mathematical achievements. Compared with Grassmann's first book, "Lineale Ausdehnungslehre", this book contains new material, including a detailed development of the inner product and its relation to the concept of angle, the "theory of functions" from the point of view of extension theory, and Grassmann's contribution to the Pfaff problem. In many ways, this book is the version of Grassmann's system most accessible to contemporary readers. This translation is based on the material in Grassmann's "Gesammelte Werke", published by B.G. Teubner (Stuttgart and Leipzig, Germany). It includes nearly all the editorial notes from that edition, but the "improved" proofs are relocated, and Grassmann's original proofs are restored to their proper places. The original editorial notes are augmented by supplementary notes, elucidating Grassmann's achievement in modern terms.

This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of $C^*$-algebras and von Neumann algebras, together with recent work on the classification of $C^*$-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.

Written by three gifted--and funny--teachers, How to Ace Calculus provides humorous and readable explanations of the key topics of calculus without the technical details and fine print that would be found in a more formal text. Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on exams--all the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun.

This substantially illustrated manual describes how to use Maple as an investigative tool to explore calculus concepts numerically, graphically, symbolically and verbally. Every chapter begins with Maple commands employed in the chapter, an introduction to the mathematical concepts being covered, worked examples in Maple worksheet format, followed by thought-provoking exercises and extensive discovery projects to encourage readers to investigate ideas on their own.

This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, invariant differential operators, and invariant integral operators play an important role in the exposition. The author treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator. Also explored are the classical results for spheres and complex projective spaces and the relation between spherical functions and harmonic polynomials. This book is suitable as a graduate textbook.

The notion of uniform rectifiability of sets (in a Euclidean space), which emerged only recently, can be viewed in several different ways. It can be viewed as a quantitative and scale-invariant substitute for the classical notion of rectifiability; as the answer (sometimes only conjecturally) to certain geometric questions in complex and harmonic analysis; as a condition which ensures the parametrizability of a given set, with estimates, but with some holes and self-intersections allowed; and as an achievable baseline for information about the structure of a set. This book is about understanding uniform rectifiability of a given set in terms of the approximate behaviour of the set at most locations and scales. In addition to being a general reference on uniform rectifiability, the book also poses many open problems, some of which are quite basic.