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.

  • Probabilistic Analysis and Related Topics

    Volume 1
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 1 focuses on the continuity, differentiability, and integrability of random functions, including functional analysis, operator theory, measure theory, and numerical analysis. The selection first offers information on stochastic partial differential equations in turbulence related problems and estimation and stochastic control for linear infinite-dimensional systems. Discussions focus on deterministic quadratic cost-control problem; partial differential equations in stochastic wave propagation; and theory of stochastic partial differential equations. The text then examines random integrodifferential equations, including small perturbations, existence and uniqueness of solutions, stochastic properties of solution processes, and vibration string. The manuscript ponders on equivalence and singularity of Gaussian measures and applications and stochastic Riemannian geometry. Concerns include semilocal properties, Brownian motion, reproducing kernel Hilbert spaces and Gaussian processes, equivalence and singularity of Gaussian processes, and general problem of equivalence and singularity. The selection is a vital source of information for mathematicians and researchers interested in the general theory of random functions.

  • Representations of Finite Groups

    • 1st Edition
    • Hirosi Nagao + 1 more
    • English
    Representations of Finite Groups provides an account of the fundamentals of ordinary and modular representations. This book discusses the fundamental theory of complex representations of finite groups. Organized into five chapters, this book begins with an overview of the basic facts about rings and modules. This text then provides the theory of algebras, including theories of simple algebras, Frobenius algebras, crossed products, and Schur indices with representation-theor... versions of them. Other chapters include a survey of the fundamental theory of modular representations, with emphasis on Brauer characters. This book discusses as well the module-theoretic representation theory due to Green and includes some topics such as Burry–Carlson's theorem and Scott modules. The final chapter deals with the fundamental results of Brauer on blocks and Fong's theory of covering, and includes some approaches to them. This book is a valuable resource for readers who are interested in the various approaches to the study of the representations of groups.

  • Waves on Fluid Interfaces

    Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin–Madison, October 18–20, 1982
    • 1st Edition
    • Richard E. Meyer
    • English
    Mathematics Research Center Symposium: Waves on Fluid Interfaces covers the proceedings of a symposium conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 18-20, 1982. The book focuses on nonlinear instabilities of classical interfaces, physical structure of real interfaces, and the challenges these reactions pose to the understanding of fluids. The selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Discussions focus on reformulation as an integro-differential equation, perturbation solutions, results for interfacial waves with current jump, wave of zero height, weakly nonlinear waves, and numerical methods. The text then takes a look at generalized vortex methods for free-surface flows; a review of solution methods for viscous flow in the presence of deformable boundaries; and existence criteria for fluid interfaces in the absence of gravity. The book ponders on the endothelial interface between tissue and blood, moving contact line, rupture of thin liquid films, film waves, and interfacial instabilities caused by air flow over a thin liquid layer. Topics include stability analysis of liquid film, interpretation of film instabilities, simple film, linear stability theory, inadequacy of the usual hydrodynamic model, and marcomolecule transport across the artery wall. The selection is a valuable source of data for researchers interested in the reactions of waves on fluid interfaces.

  • Calculus of One Variable

    • 2nd Edition
    • Stanley I. Grossman
    • English
    Calculus of One Variable, Second Edition presents the essential topics in the study of the techniques and theorems of calculus. The book provides a comprehensive introduction to calculus. It contains examples, exercises, the history and development of calculus, and various applications. Some of the topics discussed in the text include the concept of limits, one-variable theory, the derivatives of all six trigonometric functions, exponential and logarithmic functions, and infinite series. This textbook is intended for use by college students.

  • Numerical Solution of Partial Differential Equations—III, SYNSPADE 1975

    Proceedings of the Third Symposium on the Numerical Solution of Partial Differential Equations, SYNSPADE 1975, Held at the University of Maryland, College Park, Maryland, May 19-24, 1975
    • 1st Edition
    • Bert Hubbard
    • English
    Numerical Solution of Partial Differential Equations—III: Synspade 1975 provides information pertinent to those difficult problems in partial differential equations exhibiting some type of singular behavior. This book covers a variety of topics, including the mathematical models and their relation to experiment as well as the behavior of solutions of the partial differential equations involved. Organized into 16 chapters, this book begins with an overview of elastodynamic results for stress intensity factors of a bifurcating crack. This text then discusses the effects of nonlinearities, such as bifurcation, which occur in problems of nonlinear mechanics. Other chapters consider the equations of changing type and those with rapidly oscillating coefficients. This book discusses as well the effective computational methods for numerical solutions. The final chapter deals with the principal results on G-convergence, such as the convergence of the Green's operators for Dirichlet's and other boundary problems. This book is a valuable resource for engineers and mathematicians.

  • Introduction to Discrete Linear Controls

    Theory and Application
    • 1st Edition
    • Albert B. Bishop
    • J. William Schmidt
    • English
    Introduction to Discrete Linear Controls: Theory and Applications focuses on the design, analysis, and operation of discrete-time decision processes. The publication first offers information on systems theory and discrete linear control systems, discrete control-system models, and the calculus of finite differences. Discussions focus on the calculus of finite differences and linear difference equations, summations, control of cylinder diameter, generalized discrete process controller with sampling, difference equations, control theory, and system models. The text then examines classical solution of linear difference equations with constant, inverse transformation, and measures and environmental effects of system performance. The manuscript takes a look at parameter selection in first-order systems considering sampling and instrumentation errors, second-order systems, and system instability, including responses of the generalized second-order process controller; criterion for stability of discrete linear systems; and proportional-plus-di... control. The publication is a valuable source of information for engineers, operations researchers, and systems analysts.

  • Nonlinear Analysis

    • 1st Edition
    • Erich H. Rothe
    • Lamberto Cesari + 2 more
    • English
    Nonlinear Analysis: A Collection of Papers in Honor of Erich H. Rothe is a collection of papers in honor of Erich H. Rothe, a mathematician who has made significant contributions to various aspects of nonlinear functional analysis. Topics covered range from periodic solutions of semilinear parabolic equations to nonlinear problems across a point of resonance for non-self-adjoint systems. Nonlinear boundary value problems for ordinary differential equations are also considered. Comprised of 14 chapters, this volume first discusses the use of fixed-point theorems in ordered Banach spaces to prove existence and multiplicity result for periodic solutions of semilinear parabolic differential equations of the second order. The reader is then introduced to linear maximal monotone operators and singular nonlinear integral equations of Hammerstein type. Subsequent chapters focus on the branching of periodic solutions of non-autonomous systems; restricted generic bifurcation; Tikhonov regularization and nonlinear problems at resonance; and minimax theorems and their applications to nonlinear partial differential equations. This monograph will be of interest to students and practitioners in the field of mathematics.

  • Optical Computing Hardware

    Optical Computing
    • 1st Edition
    • Jürgen Jahns + 1 more
    • Sing H. Lee
    • English
    Optical Computing Hardware provides information pertinent to the advances in the development of optical computing hardware. This book discusses the two application areas, namely, high-performance computing and high-throughput photonic switching. Organized into 11 chapters, this book begins with an overview of the requirements on hardware from s system perspective. This text then presents the self-electro-optic-e... devices (SPEED), the vertical-cavity-surf... emitting microlasers (VCSEL), and the vertical-to-surface transmission electrophotonic device (VSTEP). Other chapters consider the fundamental principles of the devices and their operation either as logic devices or for optical interconnection applications. This book discusses as well the planar optical microlens as an example of a refractive microlens of the gradient-index type and explains the diffractive optical elements. The final chapter describes a method for writing and reading optically in parallel from a three-dimensional matrix by means of two-photon interaction in photochromic organic materials. This book is a valuable resource for engineers, scientists, and researchers.

  • Introduction to Applied Probability

    • 1st Edition
    • Paul E. Pfeiffer + 1 more
    • English
    Introduction to Applied Probability provides a basis for an intelligent application of probability ideas to a wide variety of phenomena for which it is suitable. It is intended as a tool for learning and seeks to point out and emphasize significant facts and interpretations which are frequently overlooked or confused by the beginner. The book covers more than enough material for a one semester course, enhancing the value of the book as a reference for the student. Notable features of the book are: the systematic handling of combinations of events (Section 3-5); extensive use of the mass concept as an aid to visualization; an unusually careful treatment of conditional probability, independence, and conditional independence (Section 6-4); the resulting clarification facilitates the formulation of many applied problems; the emphasis on events determined by random variables, which gives unity and clarity to many topics important for interpretation; and the utilization of the indicator function, both as a tool for dealing with events and as a notational device in the handling of random variables. Students of mathematics, engineering, biological and physical sciences will find the text highly useful.

  • Recent Developments in Clustering and Data Analysis

    Développements Récents en Classification Automatique et Analyse des Données: Proceedings of the Japanese-French Scientific Seminar March 24–26, 1987
    • 1st Edition
    • Chikio Hayashi + 2 more
    • English
    Recent Developments in Clustering and Data Analysis presents the results of clustering and multidimensional data analysis research conducted primarily in Japan and France. This book focuses on the significance of the data itself and on the informatics of the data. Organized into four sections encompassing 35 chapters, this book begins with an overview of the quantification of qualitative data as a method of analyzing statistically multidimensional data. This text then examines the rules of interpretation of correspondence cluster analysis by selecting classes and explaining variables involved in the algorithm of hierarchical classification. Other chapters consider the bootstrap and cross-validation methods, which are applied to the logistic ad nonparametric regression analyses of ordered categorical responses. The final chapter deals with a simpler treatment to classify the sleep state. This book is a valuable resource for researchers and workers in the fields from the behavioral sciences, biological sciences, medicine, and industrial sciences.

Related subjects