Skip to main content
Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 3
    • Lev D. Beklemishev
    • English

  • Elementary Induction on Abstract Structures

    • 1st Edition
    • Volume 77
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 19
    • Lev D. Beklemishev
    • English

  • Provability, Computability and Reflection

    • 1st Edition
    • Volume 23
    • Lev D. Beklemishev
    • English

  • Logic Colloquium '77

    • 1st Edition
    • Volume 96
    • Lev D. Beklemishev
    • English

  • Differential Geometry and the Calculus of Variations by Robert Hermann

    • 1st Edition
    • Volume 49
    • English
    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.

  • Discrete Optimization I

    • 1st Edition
    • Volume 4
    • English

  • The Joy of Mathematica

    Instant Mathematica for Calculus, Differential Equations, and Linear Algebra
    • 2nd Edition
    • Alan Shuchat + 1 more
    • English
    Joy of Mathematica, Second Edition, is a book that makes Mathematica easier to use and learn. The software includes the most common Mathematica operations needed in the first two years of college and university courses. The book is a manual for the software and an introduction to using Mathematica for mathematics and its applications to other fields. It contains material for students in calculus, differential equations, and linear algebra courses. Students and professionals will benefit from this user-friendly, practical guide to Mathematica.

  • Introduction to Hilbert Spaces with Applications

    • 3rd Edition
    • Lokenath Debnath + 1 more
    • English
    Building on the success of the two previous editions, Introduction to Hilbert Spaces with Applications, Third Edition, offers an overview of the basic ideas and results of Hilbert space theory and functional analysis. It acquaints students with the Lebesgue integral, and includes an enhanced presentation of results and proofs. Students and researchers will benefit from the wealth of revised examples in new, diverse applications as they apply to optimization, variational and control problems, and problems in approximation theory, nonlinear instability, and bifurcation. The text also includes a popular chapter on wavelets that has been completely updated. Students and researchers agree that this is the definitive text on Hilbert Space theory.

  • Lie Algebras: Theory and Algorithms

    • 1st Edition
    • Volume 56
    • W.A. de Graaf
    • English
    The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Wi... theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

  • Linear Algebra with Mathematica

    An Introduction Using Mathematica
    • 1st Edition
    • Fred Szabo
    • English
    Linear Algebra: An Introduction With Mathematica uses a matrix-based presentation and covers the standard topics any mathematician will need to understand linear algebra while using Mathematica. Development of analytical and computational skills is emphasized, and worked examples provide step-by-step methods for solving basic problems using Mathematica. The subject's rich pertinence to problem solving across disciplines is illustrated with applications in engineering, the natural sciences, computer animation, and statistics.

  • Elsevier's Dictionary of Mathematics

    In English, German, French and Russian
    • 1st Edition
    • K. Peeva + 3 more
    • English
    Elsevier's Dictionary of Mathematics contains 11,652 entries with more than 4,750 cross-references. Selection of the terms was based either on their significance or on their frequency of use according to authoritative encyclopedias, dictionaries and textbooks. Included are both modern developments and contemporary changes in terminology as well as recently established terms.The terminology covers all the major branches from elementary to advanced subjects: arithmetic, algebra, geometry, set theory, discrete mathematics, logic, Boolean algebra, linear algebra, matrix algebra, calculus, differential equations, vector algebra, field theory, probability theory and statistics, optimization, numerical methods, mathematical programming, modern algebra, algebraic structures, computer algebra, category theory, applied mathematics, theory of automata and formal languages, theory of games, theory of graphs, as well as some commonly used entries in computer architecture, hardware, communications, system and application software, microprogramming, etc.This work will provide readers, writers and translators with a guide of the most widely used terms and collections in the area, and will prove to be a useful tool for all professionals exploring the multilingual scientific terminology.

  • Introductory Analysis

    The Theory of Calculus
    • 2nd Edition
    • John A. Fridy
    • English
    Introductory Analysis, Second Edition, is intended for the standard course on calculus limit theories that is taken after a problem solving first course in calculus (most often by junior/senior mathematics majors). Topics studied include sequences, function limits, derivatives, integrals, series, metric spaces, and calculus in n-dimensional Euclidean space

  • Handbook of Differential Geometry, Volume 1

    • 1st Edition
    • F.J.E. Dillen + 1 more
    • English
    In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

  • Handbook of Computational Geometry

    • 1st Edition
    • J.R. Sack + 1 more
    • English
    Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

  • Biomathematics

    Mathematics of Biostructures and Biodynamics
    • 1st Edition
    • S. Andersson + 3 more
    • English
    This book presents new mathematics for the description of structure and dynamics in molecular and cellular biology. On an exponential scale it is possible to combine functions describing inner organisation, including finite periodicity, with functions for outside morphology into a complete definition of structure. This mathematics is particularly fruitful to apply at molecular and atomic distances. The structure descriptions can then be related to atomic and molecular forces and provide information on structural mechanisms. The calculations have been focussed on lipid membranes forming the surface layers of cell organelles. Calculated surfaces represent the mid-surface of the lipid bilayer. Membrane dynamics such as vesicle transport are described in this new language. Periodic membrane assemblies exhibit conformations based on the standing wave oscillations of the bilayer, considered to reflect the true dynamic nature of periodic membrane structures. As an illustration the structure of an endoplasmatic reticulum has been calculated. The transformation of such cell membrane assemblies into cubosomes seems to reflect a transition into vegetative states. The organisation of the lipid bilayer of nerve cells is analyzed, taking into account an earlier observed lipid bilayer phase transition associated with the depolarisation of the membrane. Evidence is given for a new structure of the alveolar surface, relating the mathematical surface defining the bilayer organisation to new experimental data. The surface layer is proposed to consist of a coherent phase, consisting of a lipid-protein bilayer curved according to a classical surface - the CLP surface. Without employing this new mathematics it would not be possible to give an analytical description of this structure and its deformation during the respiration cycle. In more general terms this mathematics is applied to the description of the structure and dynamic properties of motor proteins, cytoskeleton proteins, and RNA/DNA. On a macroscopic scale the motions of cilia, sperm and flagella are modelled. This mathematical description of biological structure and dynamics, biomathematics, also provides significant new information in order to understand the mechanisms governing shape of living organisms.

  • Curves and Surfaces in Geometric Modeling

    Theory & Algorithms
    • 1st Edition
    • Jean Gallier
    • English
    Curves and Surfaces for Geometric Design offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work—whether you're a graduate student, scientist, or practitioner.Inside, the focus is on "blossoming"—the process of converting a polynomial to its polar form—as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for far more than its theoretical elegance, for the author proceeds to demonstrate the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more.The product of groundbreaking research by a noteworthy computer scientist and mathematician, this book is destined to emerge as a classic work on this complex subject. It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning.

  • Differential Equations with Maple V

    • 2nd Edition
    • Martha L. Abell + 1 more
    • English
    This book is an indespensable tool for anyone using Maple V in computing ordinary and partial differential equations.

  • Introduction to Applied Statistical Signal Analysis

    • 2nd Edition
    • Richard Shiavi
    • English
    This book provides a balanced perspective of the concept, mathematical bases, requirements for estimation, and detailed quantitative examples of the implementation of the techniques for classical signal analysis. The presentation integrates theory and implementation, practical examples, homework exercises which range from pencil and paper format to computer-based format problems, to instructional notebooks. The notebooks provide a mode of learning that is interactive and suited for self-pacing and independent learning.

  • Advances in Computers

    • 1st Edition
    • Volume 49
    • English
    Since its first volume in 1960, Advances in Computers has presented detailed coverage of innovations in hardware and software and in computer theory, design, and applications. It has also provided contributors with a medium in which they can examine their subjects in greater depth and breadth than that allowed by standard journal articles. As a result, many articles have become standard references that continue to be of significant, lasting value despite the rapid growth taking place in the field.

  • Classical Recursion Theory, Volume II

    • 1st Edition
    • Volume 143
    • P. Odifreddi
    • English
    Volume II of Classical Recursion Theory describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets.The first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexityclasses, ranging from small time and space bounds to the elementary functions,with a particular attention to polynomial time and space computability. It alsodeals with primitive recursive functions and larger classes, which are ofinterest to the proof theorist. The second half of the book starts with the classical theory of recursivelyenumerabl... sets and degrees, which constitutes the core of Recursion orComputability Theory. Unlike other texts, usually confined to the Turingdegrees, the book covers a variety of other strong reducibilities, studyingboth their individual structures and their mutual relationships. The lastchapters extend the theory to limit sets and arithmetical sets. The volumeends with the first textbook treatment of the enumeration degrees, whichadmit a number of applications from algebra to the Lambda Calculus.The book is a valuable source of information for anyone interested inComplexity and Computability Theory. The student will appreciate the detailedbut informal account of a wide variety of basic topics, while the specialistwill find a wealth of material sketched in exercises and asides. A massivebibliography of more than a thousand titles completes the treatment on thehistorical side.

  • A Wavelet Tour of Signal Processing

    • 2nd Edition
    • Stephane Mallat
    • English
    This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris.

  • History of Topology

    • 1st Edition
    • I.M. James
    • English
    Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.

  • Handbook of Analysis

    CD-ROM Version
    • 1st Edition
    • Eric Schechter
    • English
    This version of Handbook of Analysis provides convenient access to reference material on the foundations of mathematical analysis. It is appropriate for advanced undergraduates and beginning graduate students in mathematics, as well as practitioners. The CD-ROM is a unified presentation of the foundation of virtually all of mathematics, with the exception of geometry.

  • Kohonen Maps

    • 1st Edition
    • E. Oja + 1 more
    • English
    The Self-Organizing Map, or Kohonen Map, is one of the most widely used neural network algorithms, with thousands of applications covered in the literature. It was one of the strong underlying factors in the popularity of neural networks starting in the early 80's. Currently this method has been included in a large number of commercial and public domain software packages. In this book, top experts on the SOM method take a look at the state of the art and the future of this computing paradigm.The 30 chapters of this book cover the current status of SOM theory, such as connections of SOM to clustering, classification, probabilistic models, and energy functions. Many applications of the SOM are given, with data mining and exploratory data analysis the central topic, applied to large databases of financial data, medical data, free-form text documents, digital images, speech, and process measurements. Biological models related to the SOM are also discussed.

  • Tools and Techniques in Modal Logic

    • 1st Edition
    • Volume 142
    • M. Kracht
    • English
    This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.

  • Computer Solution of Large Linear Systems

    • 1st Edition
    • Volume 28
    • Gerard Meurant
    • English
    This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

  • Mathematical Modeling

    A Chemical Engineer's Perspective
    • 1st Edition
    • Volume 1
    • Rutherford Aris
    • English
    Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners. Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities.

  • Fourier Acoustics

    Sound Radiation and Nearfield Acoustical Holography
    • 1st Edition
    • Earl G. Williams
    • English
    Intended a both a textbook and a reference, Fourier Acoustics develops the theory of sound radiation uniquely from the viewpoint of Fourier Analysis. This powerful perspective of sound radiation provides the reader with a comprehensive and practical understanding which will enable him or her to diagnose and solve sound and vibration problems in the 21st Century. As a result of this perspective, Fourier Acoustics is able to present thoroughly and simply, for the first time in book form, the theory of nearfield acoustical holography, an important technique which has revolutionised the measurement of sound. Relying little on material outside the book, Fourier Acoustics will be invaluable as a graduate level text as well as a reference for researchers in academia and industry.

  • Ordinary Differential Equations and Applications

    Mathematical Methods for Applied Mathematicians, Physicists, Engineers and Bioscientists
    • 1st Edition
    • W S Weiglhofer + 1 more
    • English
    This introductory text presents ordinary differential equations with a modern approach to mathematical modelling in a one semester module of 20–25 lectures.

  • Mathematics for Physical Chemistry

    • 2nd Edition
    • Robert G. Mortimer
    • English
    Mathematics for Physical Chemistry is the ideal textbook for upper-level undergraduates or graduate students who want to sharpen their mathematics skills while they are enrolled in a physical chemistry course. Solved examples and problems, interspersed throughout the presentation and intended to be worked when met in the text, encourage self-study by students new to the material. The author provides readers with a review of calculus and differential equations that will enable them to succeed in a physical chemistry course. An ideal reference text for practicing chemists as well.

  • Geometry and Its Applications

    • 1st Edition
    • Walter A. Meyer
    • English
    Geometry and Its Applications combines traditional geometry with ideas of recent decades to present a new approach for the 21st century. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidian geometry, non-Euclidian geometry, and transformational geometry. The text integrates realistic applications throughout, includes historical notes in many chapters, and contains student and instructor's guides that support Geometer's Sketchpad. Includes a free instructor's manual to professors of adopting universities.

  • Theory of Rank Tests

    • 2nd Edition
    • Zbynek Sidak + 2 more
    • English
    The first edition of Theory of Rank Tests (1967) has been the precursor to a unified and theoretically motivated treatise of the basic theory of tests based on ranks of the sample observations. For more than 25 years, it helped raise a generation of statisticians in cultivating their theoretical research in this fertile area, as well as in using these tools in their application oriented research. The present edition not only aims to revive this classical text by updating the findings but also by incorporating several other important areas which were either not properly developed before 1965 or have gone through an evolutionary development during the past 30 years. This edition therefore aims to fulfill the needs of academic as well as professional statisticians who want to pursue nonparametrics in their academic projects, consultation, and applied research works.

  • Categorical Logic and Type Theory

    • 1st Edition
    • Volume 141
    • B. Jacobs
    • English
    This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

  • A Course in Real Analysis

    • 1st Edition
    • John N. McDonald + 1 more
    • English
    A Course in Real Analysis provides a firm foundation in real analysis concepts and principles while presenting a broad range of topics in a clear and concise manner. This student-oriented text balances theory and applications, and contains a wealth of examples and exercises. Throughout the text, the authors adhere to the idea that most students learn more efficiently by progressing from the concrete to the abstract. McDonald and Weiss have also created real application chapters on probability theory, harmonic analysis, and dynamical systems theory. The text offers considerable flexibility in the choice of material to cover.

  • Recursive Algebra, Analysis and Combinatorics

    • 1st Edition
    • Volume 2
    • English

  • Recursive Model Theory

    • 1st Edition
    • Volume 1
    • English

  • Handbook of Coding Theory

    Part 2: Connections, Part 3: Applications
    • 1st Edition
    • Volume II
    • Bozzano G Luisa
    • English
    The second volume of this work contains Parts 2 and 3 of the "Handbook of Coding Theory". Part 2, "Connections", is devoted to connections between coding theory and other branches of mathematics and computer science. Part 3, "Applications", deals with a variety of applications for coding.

  • Projects for Calculus

    The Language of Change
    • 2nd Edition
    • Keith D. Stroyan
    • English
    Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.

  • Asymptotic Methods in Probability and Statistics

    A Volume in Honour of Miklós Csörgő
    • 1st Edition
    • B. Szyszkowicz
    • English
    One of the aims of the conference on which this book is based, was to provide a platform for the exchange of recent findings and new ideas inspired by the so-called Hungarian construction and other approximate methodologies. This volume of 55 papers is dedicated to Miklós Csörgő a co-founder of the Hungarian construction school by the invited speakers and contributors to ICAMPS'97.This excellent treatize reflects the many developments in this field, while pointing to new directions to be explored. An unequalled contribution to research in probability and statistics.

  • Handbook of Fourier Transform Raman and Infrared Spectra of Polymers

    • 1st Edition
    • Volume 45
    • A.H. Kuptsov + 1 more
    • English
    A collection of infrared and Raman spectra of 500 natural and synthetic polymers of industrial importance is presented in this book. A large variety of compounds are included, starting with linear polyolefins and finishing with complex biopolymers and related compounds. The spectra were registered using Infrared Fourier Transform Spectrometers in the laboratory of the All-Russia Institute of Forensic Sciences. The IR and Raman spectra are presented together on the same sheet. The accompanying data include general and structure formulae, CAS register numbers, and sample preparation conditions.Features of this book:• Continues the long tradition of publishing specific and standard data of new chemical compounds.• For low-molecular weight substances, complementary IR and Raman spectra are featured on the same sample and printed on the same page. This "fingerprint" data allows the substance of the sample to be identified without doubt.• An important feature of this unique collection of data is the increase in the identification precision of unknown substances.• Peak tables are available in digital (ASCII) format, on a diskette delivered with the book. This allows the user to search for unknowns.• All the spectra in the collection are base-line corrected.This book will be of interest to scientists involved in the synthesis of new polymeric materials, polymer identification, and quality control. Libraries of scientific institutes, research centers, and universities involved in vibrational spectroscopy will also find this collection invaluable.

  • Fractional Differential Equations

    An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications
    • 1st Edition
    • Volume 198
    • Igor Podlubny
    • English
    This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.

  • Statistics with Mathematica

    • 1st Edition
    • Martha L. Abell + 2 more
    • English
    Mathematica's diverse capabilities make it particularly well suited to perform the many calculations encountered in statistics. This book introduces Mathematica for various types of statistical computations. It covers a broad range of topics, and should appeal to both students and professional statisticians.

  • The Nature of Mathematics and the Mathematics of Nature

    • 1st Edition
    • S. Andersson + 1 more
    • English
    Chemistry, physics and biology are by their nature genuinely difficult. Mathematics, however, is man-made, and therefore not as complicated. Two ideas form the basis for this book: 1) to use ordinary mathematics to describe the simplicity in the structure of mathematics and 2) to develop new branches of mathematics to describe natural sciences.Mathematics can be described as the addition, subtraction or multiplication of planes. Using the exponential scale the authors show that the addition of planes gives the polyhedra, or any solid. The substraction of planes gives saddles. The multiplication of planes gives the general saddle equations and the multispirals. The equation of symmetry is derived, which contains the exponential scale with its functions for solids, the complex exponentials with the nodal surfaces, and the GD (Gauss Distribution) mathematics with finite periodicity.Piece by piece, the authors have found mathematical functions for the geometrical descriptions of chemical structures and the structure building operations. Using the mathematics for dilatation; twins, trillings, fourlings and sixlings are made, and using GD mathematics these are made periodic. This description of a structure is the nature of mathematics itself. Crystal structures and 3D mathematics are synonyms. Mathematics are used to describe rod packings, Olympic rings and defects in solids. Giant molecules such as cubosomes, the DNA double helix, and certain building blocks in protein structures are also described mathematically.

  • Problems in Real Analysis

    • 2nd Edition
    • Charalambos D. Aliprantis + 1 more
    • English
    A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods. Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.

  • Time-Frequency/Time-Scale Analysis

    • 1st Edition
    • Volume 10
    • Patrick Flandrin
    • English
    This highly acclaimed work has so far been available only in French. It is a detailed survey of a variety of techniques for time-frequency/time-... analysis (the essence of "Wavelet Analysis"). This book has broad and comprehensive coverage of a topic of keen interest to a variety of engineers, especially those concerned with signal and image processing. Flandrin provides a discussion of numerous issues and problems that arise from a mixed description in time and frequency, as well as problems in interpretation inherent in signal theory.

  • Advanced Applied Finite Element Methods

    • 1st Edition
    • Carl T. F. Ross
    • English
    This book is aimed at senior undergraduates, graduates and engineers. It fills the gap between the numerous textbooks on traditional Applied Mechanics and postgraduate books on Finite Element Methods.

  • Practical Time-Frequency Analysis

    Gabor and Wavelet Transforms, with an Implementation in S
    • 1st Edition
    • Volume 9
    • Rene Carmona + 2 more
    • English
    Time frequency analysis has been the object of intense research activity in the last decade. This book gives a self-contained account of methods recently introduced to analyze mathematical functions and signals simultaneously in terms of time and frequency variables. The book gives a detailed presentation of the applications of these transforms to signal processing, emphasizing the continuous transforms and their applications to signal analysis problems, including estimation, denoising, detection, and synthesis. To help the reader perform these analyses, Practical Time-Frequency Analysis provides a set of useful tools in the form of a library of S functions, downloadable from the authors' Web sites in the United States and France.

  • Principles of Real Analysis

    • 3rd Edition
    • Charalambos D. Aliprantis
    • Owen Burkinshaw
    • English
    With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

  • Wavelets in a Box

    • 1st Edition
    • Andrew K. Chan + 1 more
    • English
    Wavelets are considered by many to be the most powerful mathematical tool for signal and image processing. This unique CD-ROM boxed set contains three useful items: a copy of the text An Introduction to Wavelets by Charles Chui, a CD containing well-designed wavelets and signal processing software by computer scientist Steve Liu, and a booklet that serves both as the manual for the software and a quick reference guide to wavelet basics by electrical engineer Andrew Chan. The software supports all essential wavelets and allows users to put in additional wavelets of their choice and delete the ones they don't need. It also includes custom computation routines (in C-language) for wavelet signal processing. A flexible programming interface through the DLL standard allows the user to plug in new and original processing routines easily. This self-learning package provides the tools for the user to compare short time fourier transform and wavelet transform as well as the trade-off between time/spatial and frequency domain signal analysis.

Related subjects