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The World According to Wavelets
This best-selling book introduces a broad audience including scientists and engineers working in a variety of fields as well as mathematicians from other subspecialties to one of the most active new areas of applied mathematics and the story of its discovery and development. Organized in "hypertext fashion," the book tells a story of scientific dis
Multivariable Mathematics
Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. * Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. * Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. * Exercises are arranged in order of increasing difficulty.
Vector Calculus, Linear Algebra, and Differential Forms
This text covers most of the standard topics in multivariate calculus and part of a standard first course in linear algebra. It focuses on underlying ideas, integrates theory and applications, offers a host of pedagogical aids, and features coverage of differential forms and an emphasis on numerical methods to prepare students for modern applications of mathematics. *Covers important material that is usually omitted. *Presents more difficult and longer proofs (e.g. Proofs of the Kantorovitch theorem, the implicit function theorem) in an appendix. *Makes a careful distinction between vectors and points. *Features an innovative approach to the implicit function theorem and inverse function theorem using Newton's method. *Always emphasizes the underlying meaning - what is really going on (generally, with a geometric interpretation) - eg. The chain rule is a composition of linear transformations; the point of the implicit function theorem is to guarantee that under certain circumstances, non-linear equations have solutions. *Integrates theory and applications. *Begins most chapters with a treatment of a linear problem and then shows how the 7 methods apply to corresponding non-linear p
Differential Forms
This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student
Vector Calculus
This book gives a comprehensive and thorough introduction to ideas and major results of the theory of functions of several variables and of modern vector calculus in two and three dimensions. Clear and easy-to-follow writing style, carefully crafted examples, wide spectrum of applications and numerous illustrations, diagrams, and graphs invite students to use the textbook actively, helping them to both enforce their understanding of the material and to brush up on necessary technical and computational skills. Particular attention has been given to the material that some students find challenging, such as the chain rule, Implicit Function Theorem, parametrizations, or the Change of Variables Theorem.
Programming for Mathematicians
Aimed at teaching mathematics students how to program using their knowledge of mathematics, the entire books emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: manipulation and enrichment of existing code; use of recurrent sequences; deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed, and the text concludes with an explanation of how a compiler works and how to compile "by hand" little programs. Intended for anyone who thinks mathematically and wants to program and play with mathematics.
Childe Hassam, American Impressionist
"This illustrated publication accompanies a major exhibition at the Metropolitan Museum, the first retrospective presentation of Hassam's work in a museum since 1972. Unique to this volume are an account of Hassam's lifelong campaign to market his art, a study of the frames he selected and designed for his paintings, and an unprecedented lifetime exhibition record. Included in addition are a checklist of works in the exhibition and a chronology of Hassam's life. All works in the exhibition as well as comparative materials are reproduced."--BOOK JACKET.
Calculus On Manifolds
This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential.
