The theory of integral operators constitutes a major branch of analysis, and transforms represent an important subdivision. This volume focuses on the Laplace and Stieltjes transforms. Highly theoretical in its emphasis, this classic treatment was derived from a series of lectures by a prominent Harvard mathematician.
Suitable for graduate-level mathematics majors, this introductory text explores fundamental formulas, the moment problem, monotonic functions, and Tauberian theorems. The" Bulletin of the American Mathematical Society "praised it as "extremely satisfactory," noting that "it will have a most valuable effect both on research and graduate study."

This textbook for the basic lecture course of the same name deals with selected topics of multidimensional analysis. It is also an introduction to the theory of ordinary differential equations and the Fourier theory, of importance in the application of image processing and acoustics.

Features an introduction to advanced calculus and highlights its inherent concepts from linear algebra

"Advanced Calculus" reflects the unifying role of linear algebra in an effort to smooth readers' transition to advanced mathematics. The book fosters the development of complete theorem-proving skills through abundant exercises while also promoting a sound approach to the study. The traditional theorems of elementary differential and integral calculus are rigorously established, presenting the foundations of calculus in a way that reorients thinking toward modern analysis.

Following an introduction dedicated to writing proofs, the book is divided into three parts:

Part One explores foundational one-variable calculus topics from the viewpoint of linear spaces, norms, completeness, and linear functionals.

Part Two covers Fourier series and Stieltjes integration, which are advanced one-variable topics.

Part Three is dedicated to multivariable advanced calculus, including inverse and implicit function theorems and Jacobian theorems for multiple integrals.

Numerous exercises guide readers through the creation of their own proofs, and they also put newly learned methods into practice. In addition, a "Test Yourself" section at the end of each chapter consists of short questions that reinforce the understanding of basic concepts and theorems. The answers to these questions and other selected exercises can be found at the end of the book along with an appendix that outlines key terms and symbols from set theory.

Guiding readers from the study of the topology of the real line to the beginning theorems and concepts of graduate analysis, "Advanced Calculus" is an ideal text for courses in advanced calculus and introductory analysis at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for engineers, scientists, and mathematicians.

This concise text offers an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, its subjects include practical direct methods for solution of variational problems. Each chapter features numerous illustrative problems, with solutions. 1961 edition.

Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Your INTEGRAL tool for mastering ADVANCED CALCULUS Interested in going further in calculus but don't where to begin? No problem! With Advanced Calculus Demystified, there's no limit to how much you will learn. Beginning with an overview of functions of multiple variables and their graphs, this book covers the fundamentals, without spending too much time on rigorous proofs. Then you will move through more complex topics including partial derivatives, multiple integrals, parameterizations, vectors, and gradients, so you'll be able to solve difficult problems with ease. And, you can test yourself at the end of every chapter for calculated proof that you're mastering this subject, which is the gateway to many exciting areas of mathematics, science, and engineering. This fast and easy guide offers: Numerous detailed examples to illustrate basic concepts Geometric interpretations of vector operations such as div, grad, and curl Coverage of key integration theorems including Green's, Stokes', and Gauss' Quizzes at the end of each chapter to reinforce learning A time-saving approach to performing better on an exam or at work Simple enough for a beginner, but challenging enough for a more advanced student, Advanced Calculus Demystified is one book you won't want to function without!

The power that analysis, topology and algebra bring to geometry has revolutionized the way geometers and physicists look at conceptual problems. Some of the key ingredients in this interplay are sheaves, cohomology, Lie groups, connections and differential operators. In Global Calculus, the appropriate formalism for these topics is laid out with numerous examples and applications by one of the experts in differential and algebraic geometry. Ramanan has chosen an uncommon but natural path through the subject. In this almost completely self-contained account, these topics are developed from scratch. The basics of Fourier transforms, Sobolev theory and interior regularity are proved at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex. Many new perspectives on traditional and modern questions of differential analysis and geometry are the hallmarks of the book. The book is suitable for a first year graduate course on global analysis.

Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The notion of convexity comes from geometry. Barvinok describes here its geometric aspects, yet he focuses on applications of convexity rather than on convexity for its own sake. Mathematical applications range from analysis and probability to algebra to combinatorics to number theory.Several important areas are covered, including topological vector spaces, linear programming, ellipsoids, and lattices. Specific topics of note are optimal control, sphere packings, rational approximations, numerical integration, graph theory, and more. And of course, there is much to say about applying convexity theory to the study of faces of polytopes, lattices and polyhedra, and lattices and convex bodies. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computer skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. Readers will find some new results. Also, many known results are discussed from a new perspective.

In the academic year 1994/95 I lectured on semigroups in the Scuola Normale Superiore and in the Politecnico di Torino. The purpose of the lectures was to present to an audience of graduate students a self-contained introduction to the theory of strongly continuous semigroups of linear operators acting on a Banach space. The main trust was concentrated on laying down the basic geometrical aspects of the theory as a background for applications to concrete problems in the analysis of differential operators.

Aimed at readers who may be more familiar with statistics than calculus and mathematics, this carefully written volume gives an overview of the central ideas in calculus. Author Gudmund R. Iversen shows examples of how calculus is used to translate many real-world phenomena into mathematical functions. Beginning with an explanation of the two major parts of calculus, differentiation and integration, Iversen illustrates how calculus is used in statistics to distinguish between the mean and the median, to derive the least squares formulas for regression coefficients, to find values of parameters from theoretical distributions, and to find a statistical p value when we using one of the continuous test variables like the t variable. Social scientists who either never took a calculus course or who want to "brush up" on their understanding of calculus will find this book a necessity.

This book walks students through the basic concepts and techniques of differential and integral calculus, particularly as these relate to the theory and problem-solving required in the disciplines of business, economics and the sciences today. Simple calculations and examples, and more then a thousand problems with detailed solutions, help make it easy to understand how calculus works.

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.

"Kiss My Math" meets "A Tour of the Calculus"
Jennifer Ouellette never took math in college, mostly because she-like most people-assumed that she wouldn't need it in real life. But then the English-major-turned-award-winning-science-writer had a change of heart and decided to revisit the equations and formulas that had haunted her for years. "The Calculus Diaries" is the fun and fascinating account of her year spent confronting her math phobia head on. With wit and verve, Ouellette shows how she learned to apply calculus to everything from gas mileage to dieting, from the rides at Disneyland to shooting craps in Vegas-proving that even the mathematically challenged can learn the fundamentals of the universal language.

The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this book, Dr Burn follows a route that proved successful with A Pathway to Number Theory and Groups: A Path to Geometry. He invites the student reader to tackle each of the key concepts in turn, progressing from experience (using computers for graph drawing where appropriate) through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed by historical insight and complemented by historical discussion. The sequence also takes into account recent research which has shown how intuitive ideas about numbers, limits, functions and infinity may be at odds with the standard definitions. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.

This book is an in-depth and broad text on the subject of chaos in dynamical systems. It is intended to serve both as a graduate course text for science and engineering students, and as a reference and introduction to the subject for researchers in science and engineering needing to understand this important new subject.

Books a la Carte are unbound, three-hole-punch versions of the textbook. This lower cost option is easy to transport and comes with same access code or media that would be packaged with the bound book.
This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students' geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows. 0321977300/9780321977304 - Calculus, Books a la Carte Plus MyMathLab/MyStatLab Student Access Kit, 2/ePackage consists of: 0321431308 / 9780321431301 MyMathLab -- Glue-in Access Card 0321654064 / 9780321654069 MyMathLab Inside Star Sticker 0321954351 / 9780321954350 Calculus

The book addresses the compelling demand for quantitative training in plant biology, including comparisons of the rate of processes, the size of structures and interactions among different processes, approached at different levels from molecules to the environment. Attention is paid to aspects of modern molecular biology and to modern biophysical treatments of classical transport and circulatory problems. This will allow the reader to become familiar with calculus as a tool to understand plant science. The book discusses specific problems covering six specific topics, and includes an additional section devoted to miscellaneous issues. It is also complemented by appendices describing units, conversion factors, formulae and data relevant to plant biology and to the relationship of plants with the environment.

Renowned authors William Briggs and Lyle Cochran have built from the ground up a new AP(R) calculus program that draws on their decades of teaching experience and carries the teacher's voice beyond the classroom. That voice is evident in the lively narrative, the intuitive figures, and the integrated questions that check for comprehension. The result is a master AP(R) teacher leading AP(R) students to deeper levels of understanding. The authors appeal to readers' geometric intuition to introduce fundamental concepts and lay the foundation for success on the AB and BC Calculus exams. Briggs/Cochran AP(R) Calculus: *AP(R) Aligned: AP-specific chapter content clearly correlates to the AP Curriculum Framework and prepares students for the AB or BC exam.*Geometric Intuition: The authors appeal to students' intuition and geometric instincts to make calculus natural and believable. They introduce new ideas through concrete examples, figures, applications, or analogies.*Ground breaking Technology & Interactive Figures: Interactive figures within the eBook enable teachers and students to manipulate figures and bring hard-to-convey concepts to life.* A Balanced Approach: The authors purposely teach from examples that provide in depth explanations and build students' conceptual understanding and computational fluency.