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Studies in Advanced Mathematics


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A Primer on Wavelets and Their Scientific Applications, Second Edition

A Primer on Wavelets and Their Scientific Applications, Second Edition

James S. Walker
January 29, 2008

In the first edition of his seminal introduction to wavelets, James S. Walker informed us that the potential applications for wavelets were virtually unlimited. Since that time thousands of published papers have proven him true, while also necessitating the creation of a new edition of his...

An Introduction to Quasigroups and Their Representations

An Introduction to Quasigroups and Their Representations

Jonathan D. H. Smith
November 15, 2006

Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this...

Separation of Variables for Partial Differential Equations: An Eigenfunction Approach

Separation of Variables for Partial Differential Equations: An Eigenfunction Approach

George Cain, Gunter H. Meyer
November 21, 2005

Separation of Variables for Partial Differential Equations: An Eigenfunction Approach includes many realistic applications beyond the usual model problems. The book concentrates on the method of separation of variables for partial differential equations, which remains an integral part of the...

Differential Geometry and Topology: With a View to Dynamical Systems

Differential Geometry and Topology: With a View to Dynamical Systems

Keith Burns, Marian Gidea
May 27, 2005

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the...

Higher-Order Finite Element Methods

Higher-Order Finite Element Methods

Pavel Solin, Karel Segeth, Ivo Dolezel
July 28, 2003

The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the...

Mathematical Quantization

Mathematical Quantization

Nik Weaver
May 31, 2001

With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with...

Wavelets and Other Orthogonal Systems, Second Edition

Wavelets and Other Orthogonal Systems, Second Edition

Gilbert G. Walter, Xiaoping Shen
December 20, 2000

A bestseller in its first edition, Wavelets and Other Orthogonal Systems: Second Edition has been fully updated to reflect the recent growth and development of this field, especially in the area of multiwavelets. The authors have incorporated more examples and numerous illustrations to help clarify...

Real Analysis: An Introduction to the Theory of Real Functions and Integration

Real Analysis: An Introduction to the Theory of Real Functions and Integration

Jewgeni H. Dshalalow
September 28, 2000

Designed for use in a two-semester course on abstract analysis, REAL ANALYSIS: An Introduction to the Theory of Real Functions and Integration illuminates the principle topics that constitute real analysis. Self-contained, with coverage of topology, measure theory, and integration, it offers a...

Handbook of Typography for the Mathematical Sciences

Handbook of Typography for the Mathematical Sciences

Steven G. Krantz
August 31, 2000

You know mathematics. You know how to write mathematics. But do you know how to produce clean, clear, well-formatted manuscripts for publication? Do you speak the language of publishers, typesetters, graphics designers, and copy editors?Your page design-the style and format of theorems and...

Algebra: A Computational Introduction

Algebra: A Computational Introduction

John Scherk
June 23, 2000

Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a...

Functional Analysis in Applied Mathematics and Engineering

Functional Analysis in Applied Mathematics and Engineering

Michael Pedersen
September 29, 1999

Presenting excellent material for a first course on functional analysis , Functional Analysis in Applied Mathematics and Engineering concentrates on material that will be useful to control engineers from the disciplines of electrical, mechanical, and aerospace engineering.This text/reference...

Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture

Spectral Geometry, Riemannian Submersions, and the Gromov-Lawson Conjecture

Peter B. Gilkey, John V Leahy, JeongHyeong Park
July 27, 1999

This cutting-edge, standard-setting text explores the spectral geometry of Riemannian submersions. Working for the most part with the form valued Laplacian in the class of smooth compact manifolds without boundary, the authors study the relationship-if any-between the spectrum of Dp on Y and Dp on...

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