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Elsevier

Books in Mathematics and applied mathematics

This portfolio offers comprehensive coverage of pure and applied mathematics, including algebra, calculus, differential equations, and computational techniques. It supports researchers, educators, and students in advancing theoretical understanding and practical problem-solving across engineering, physics, and data science. Featuring innovative methodologies, real-world case studies, and emerging trends, these resources enable breakthroughs in modelling, simulation, and analytical skills critical for technological progress and scientific discovery.

  • Computational Methods and Production Engineering

    Research and Development
    • 1st Edition
    • J. Paulo Davim + 1 more
    • English
    Computational Methods and Production Engineering: Research and Development is an original book publishing refereed, high quality articles with a special emphasis on research and development in production engineering and production organization for modern industry. Innovation and the relationship between computational methods and production engineering are presented. Contents include: Finite Element method (FEM) modeling/simulation; Artificial neural networks (ANNs); Genetic algorithms; Evolutionary computation; Fuzzy logic; neuro-fuzzy systems; Particle swarm optimization (PSO); Tabu search and simulation annealing; and optimization techniques for complex systems. As computational methods currently have several applications, including modeling manufacturing processes, monitoring and control, parameters optimization and computer-aided process planning, this book is an ideal resource for practitioners.

  • Exterior Algebras

    Elementary Tribute to Grassmann's Ideas
    • 1st Edition
    • Vincent Pavan
    • English
    Exterior Algebras: Elementary Tribute to Grassmann's Ideas provides the theoretical basis for exterior computations. It first addresses the important question of constructing (pseudo)-Euclidian Grassmmann's algebras. Then, it shows how the latter can be used to treat a few basic, though significant, questions of linear algebra, such as co-linearity, determinant calculus, linear systems analyzing, volumes computations, invariant endomorphism considerations, skew-symmetric operator studies and decompositions, and Hodge conjugation, amongst others.

  • Mathematics Applied to Engineering

    • 1st Edition
    • Mangey Ram + 1 more
    • English
    Mathematics Applied in Engineering presents a wide array of applied mathematical techniques for an equally wide range of engineering applications, covering areas such as acoustics, system engineering, optimization, mechanical engineering, and reliability engineering. Mathematics acts as a foundation for new advances, as engineering evolves and develops. This book will be of great interest to postgraduate and senior undergraduate students, and researchers, in engineering and mathematics, as well as to engineers, policy makers, and scientists involved in the application of mathematics in engineering.

  • Complementarity and Variational Inequalities in Electronics

    • 1st Edition
    • Daniel Goeleven
    • English
    Complementarity and Variational Inequalities in Electronics evaluates the main mathematical models relevant to the study of electrical network problems involving devices. The book focuses on complementarity problems, variational inequalities and non-regular dynamical systems which are well-known for their applications in mechanics and economics, but rarely target electrical applications. The book uses these tools to review the qualitative properties of devices, including slicers, amplitude selectors, sampling gates, operational amplifiers, and four-diode bridge full-wave rectifiers. Users will find demonstrations on how to compute optimized output signal relevant to potentially superior applications. In addition, the book describes how to determine the stationary points of dynamical circuits and to determine the corresponding Lyapunov stability and attractivity properties, topics of major importance for further dynamical analysis and control. Hemivariational inequalities are also covered in some depth relevant to application in thyristor devices.

  • Modeling and Analysis of Modern Fluid Problems

    • 1st Edition
    • Liancun Zheng + 1 more
    • English
    Modeling and Analysis of Modern Fluids helps researchers solve physical problems observed in fluid dynamics and related fields, such as heat and mass transfer, boundary layer phenomena, and numerical heat transfer. These problems are characterized by nonlinearity and large system dimensionality, and ‘exact’ solutions are impossible to provide using the conventional mixture of theoretical and analytical analysis with purely numerical methods. To solve these complex problems, this work provides a toolkit of established and novel methods drawn from the literature across nonlinear approximation theory. It covers Padé approximation theory, embedded-parameters perturbation, Adomian decomposition, homotopy analysis, modified differential transformation, fractal theory, fractional calculus, fractional differential equations, as well as classical numerical techniques for solving nonlinear partial differential equations. In addition, 3D modeling and analysis are also covered in-depth.

  • Techniques of Functional Analysis for Differential and Integral Equations

    • 1st Edition
    • Paul Sacks
    • English
    Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature.

  • Transcendental Curves in the Leibnizian Calculus

    • 1st Edition
    • Viktor Blasjo
    • English
    Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it.

  • Optimal Sports Math, Statistics, and Fantasy

    • 1st Edition
    • Robert Kissell + 1 more
    • English
    Optimal Sports Math, Statistics, and Fantasy provides the sports community—students, professionals, and casual sports fans—with the essential mathematics and statistics required to objectively analyze sports teams, evaluate player performance, and predict game outcomes. These techniques can also be applied to fantasy sports competitions. Readers will learn how to: Accurately rank sports teams Compute winning probability Calculate expected victory margin Determine the set of factors that are most predictive of team and player performance Optimal Sports Math, Statistics, and Fantasy also illustrates modeling techniques that can be used to decode and demystify the mysterious computer ranking schemes that are often employed by post-season tournament selection committees in college and professional sports. These methods offer readers a verifiable and unbiased approach to evaluate and rank teams, and the proper statistical procedures to test and evaluate the accuracy of different models. Optimal Sports Math, Statistics, and Fantasy delivers a proven best-in-class quantitative modeling framework with numerous applications throughout the sports world.

  • Cryptographic Boolean Functions and Applications

    • 2nd Edition
    • Thomas W. Cusick + 1 more
    • English
    Cryptographic Boolean Functions and Applications, Second Edition is designed to be a comprehensive reference for the use of Boolean functions in modern cryptography. While the vast majority of research on cryptographic Boolean functions has been achieved since the 1970s, when cryptography began to be widely used in everyday transactions, in particular banking, relevant material is scattered over hundreds of journal articles, conference proceedings, books, reports and notes, some of them only available online. This book follows the previous edition in sifting through this compendium and gathering the most significant information in one concise reference book. The work therefore encompasses over 600 citations, covering every aspect of the applications of cryptographic Boolean functions. Since 2008, the subject has seen a very large number of new results, and in response, the authors have prepared a new chapter on special functions. The new edition brings 100 completely new references and an expansion of 50 new pages, along with heavy revision throughout the text.

  • Existence Theory for Generalized Newtonian Fluids

    • 1st Edition
    • Dominic Breit
    • English
    Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs.

  • Quantitative Techniques for the Analysis of Sediments

    An International Symposium
    • 1st Edition
    • Daniel F Merriam
    • English
    Quantitative Techniques for the Analysis of Sediments: An International Symposium is a compilation of studies about the integration and application of statistics, mathematics, and computers in the field of sedimentology. The book includes 13 studies from different experts in the field of sedimentology. These studies discuss topics such as the analysis and management of systems suitable for sedimentological data; the different methods of analysis and the numerical classification of different sedimentological data; and the assessment of quantitative methods in comparing lithological succession data. Also included is the trend analysis of sedimentary thickness data; numerical classification of multi-variate petrographic presence-absence data by association analysis; and the mathematical modeling and statistical recognition of terrestrial and marine sediments. The text will interest those in the field of sedimentology and geology, especially those who are engaged in research and wish to be aided by the different techniques included.

  • Mathematica by Example

    • 5th Edition
    • Martha L. Abell + 1 more
    • English
    Mathematica by Example, Fifth Edition is an essential desk reference for the beginning Mathematica user, providing step-by-step instructions on achieving results from this powerful software tool. The book fully accounts for the dramatic changes to functionality and visualization capabilities in the most recent version of Mathematica (10.4). It accommodates the full array of new extensions in the types of data and problems that Mathematica can immediately handle, including cloud services and systems, geographic and geometric computation, dynamic visualization, interactive applications and other improvements. It is an ideal text for scientific students, researchers and aspiring programmers seeking further understanding of Mathematica. Written by seasoned practitioners with a view to practical implementation and problem-solving, the book's pedagogy is delivered clearly and without jargon using representative biological, physical and engineering problems. Code is provided on an ancillary website to support the use of Mathematica across diverse applications.

  • Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications

    • 1st Edition
    • Bayram Sahin
    • English
    Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore’s classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps.

  • The Partition Method for a Power Series Expansion

    Theory and Applications
    • 1st Edition
    • Victor Kowalenko
    • English
    The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics. In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established. Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics.

  • Uncertainties in GPS Positioning

    A Mathematical Discourse
    • 1st Edition
    • Alan Oxley
    • English
    Uncertainties in GPS Positioning: A Mathematical Discourse describes the calculations performed by a GPS receiver and the problems associated with ensuring that the derived location is a close match to the actual location. Inaccuracies in calculating a location can have serious repercussions, so this book is a timely source for information on this rapidly evolving technology.

  • Handbook of Numerical Methods for Hyperbolic Problems

    Applied and Modern Issues
    • 1st Edition
    • Volume 18
    • Remi Abgrall + 1 more
    • English
    Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations.

  • A Generalized Framework of Linear Multivariable Control

    • 1st Edition
    • Liansheng Tan
    • English
    A Generalized Framework of Linear Multivariable Control proposes a number of generalized models by using the generalized inverse of matrix, while the usual linear multivariable control theory relies on some regular models. The book supports that in H-infinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the H-infinity control does not apply any more in the normal framework. Therefore, it is very important to relax those restrictions to generalize the classical notions and models to include some non-regular cases. This book is ideal for scholars, academics, professional engineer and students who are interested in control system theory.

  • New Approaches of Protein Function Prediction from Protein Interaction Networks

    • 1st Edition
    • Jingyu Hou
    • English
    New Approaches of Protein Function Prediction from Protein Interaction Networks contains the critical aspects of PPI network based protein function prediction, including semantically assessing the reliability of PPI data, measuring the functional similarity between proteins, dynamically selecting prediction domains, predicting functions, and establishing corresponding prediction frameworks. Functional annotation of proteins is vital to biological and clinical research and other applications due to the important roles proteins play in various biological processes. Although the functions of some proteins have been annotated via biological experiments, there are still many proteins whose functions are yet to be annotated due to the limitations of existing methods and the high cost of experiments. To overcome experimental limitations, this book helps users understand the computational approaches that have been rapidly developed for protein function prediction.

  • Handbook of Numerical Methods for Hyperbolic Problems

    Basic and Fundamental Issues
    • 1st Edition
    • Volume 17
    • Remi Abgrall + 1 more
    • English
    Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.

  • Stress Testing and Risk Integration in Banks

    A Statistical Framework and Practical Software Guide (in Matlab and R)
    • 1st Edition
    • Tiziano Bellini
    • English
    Stress Testing and Risk Integration in Banks provides a comprehensive view of the risk management activity by means of the stress testing process. An introduction to multivariate time series modeling paves the way to scenario analysis in order to assess a bank resilience against adverse macroeconomic conditions. Assets and liabilities are jointly studied to highlight the key issues that a risk manager needs to face. A multi-national bank prototype is used all over the book for diving into market, credit, and operational stress testing. Interest rate, liquidity and other major risks are also studied together with the former to outline how to implement a fully integrated risk management toolkit. Examples, business cases, and exercises worked in Matlab and R facilitate readers to develop their own models and methodologies.

  • Mathematical Models for Neglected Tropical Diseases: Essential Tools for Control and Elimination, Part B

    • 1st Edition
    • Volume 94
    • English
    Mathematic Modelling: Improving the Implementation, Monitoring and Evaluation of Interventions, Part B, the latest volume in the Advances in Parasitology series contains comprehensive and up-to-date reviews in the field of mathematic modeling and its implementation within parasitology. The series includes medical studies of parasites of major influence, such as Plasmodium falciparum and trypanosomes, along with reviews of more traditional areas, such as zoology, taxonomy, and life history, all of which shape current thinking and applications.

  • Factorization of Boundary Value Problems Using the Invariant Embedding Method

    • 1st Edition
    • Jacques Henry + 1 more
    • English
    Factorization Method for Boundary Value Problems by Invariant Embedding presents a new theory for linear elliptic boundary value problems. The authors provide a transformation of the problem in two initial value problems that are uncoupled, enabling you to solve these successively. This method appears similar to the Gauss block factorization of the matrix, obtained in finite dimension after discretization of the problem. This proposed method is comparable to the computation of optimal feedbacks for linear quadratic control problems.

  • Stochastic Models of Financial Mathematics

    • 1st Edition
    • Vigirdas Mackevicius
    • English
    This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black–Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox−Ingersoll−Ross, and Heath–Jarrow–Morton interest rate models are also explored.The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided.

  • An Invitation to Applied Mathematics

    Differential Equations, Modeling, and Computation
    • 1st Edition
    • Carmen Chicone
    • English
    An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics.

  • Fractional Calculus and Fractional Processes with Applications to Financial Economics

    Theory and Application
    • 1st Edition
    • Hasan Fallahgoul + 2 more
    • English
    Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.

  • Tools For Chemical Product Design

    From Consumer Products to Biomedicine
    • 1st Edition
    • Volume 39
    • Mariano Martín Martín + 2 more
    • English
    Tools for Chemical Product Design: From Consumer Products to Biomedicine describes the challenges involved in systematic product design across a variety of industries and provides a comprehensive overview of mathematical tools aimed at the design of chemical products, from molecular design to customer products. Chemical product design has become increasingly important over the past decade and includes a wide range of sectors including gasoline additives and blends in the petroleum industry, active ingredients and excipients in the pharmaceutical industry, and a variety of consumer products and specialty chemicals. Traditionally, such products have been designed through trial and error methods, which not only are time-consuming, but more importantly only provide limited knowledge that can be translated into next generation products.

  • Differential Equations with Mathematica

    • 4th Edition
    • Martha L. Abell + 1 more
    • English
    Differential Equations with Mathematica, Fourth Edition is a supplementing reference which uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities.

  • Cognitive Computing: Theory and Applications

    • 1st Edition
    • Volume 35
    • Vijay V Raghavan + 3 more
    • English
    Cognitive Computing: Theory and Applications, written by internationally renowned experts, focuses on cognitive computing and its theory and applications, including the use of cognitive computing to manage renewable energy, the environment, and other scarce resources, machine learning models and algorithms, biometrics, Kernel Based Models for transductive learning, neural networks, graph analytics in cyber security, neural networks, data driven speech recognition, and analytical platforms to study the brain-computer interface.

  • Theory and Computation of Tensors

    Multi-Dimensional Arrays
    • 1st Edition
    • Yimin Wei + 1 more
    • English
    Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships.

  • Fractal Functions, Fractal Surfaces, and Wavelets

    • 2nd Edition
    • Peter R. Massopust
    • English
    Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content.

  • Random Operator Theory

    • 1st Edition
    • Reza Saadati
    • English
    Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications.

  • Annual Review in Automatic Programming

    International Tracts in Computer Science and Technology and Their Application, Vol. 2
    • 1st Edition
    • Richard Goodman
    • English
    Annual Review in Automatic Programming, Volume 2 is a collection of papers that discusses the controversy about the suitability of COBOL as a common business oriented language, and the development of different common languages for scientific computation. A couple of papers describes the use of the Genie system in numerical calculation and analyzes Mercury autocode in terms of a phrase structure language, such as in the source language, target language, the order structure of ATLAS, and the meta-syntactical language of the assembly program. Other papers explain interference or an "intermediate return" using ALGOL, the National-Elliot 803 Computer, and the MADCAP II. MADCAP II is A version of the automatic programming compiler for MANIAC II. One paper discusses the APT which serves as a common computer language for computational problems. Another paper explains SAKO which can bypass machine language almost entirely in the field of numerical and logical problems, particularly in programs using XYZ and ZAM II. A report of the Working Committee of the British Computer Society Discussion Group No. 5 concludes that COBOL is unnecessarily complex due to its close machine orientation. Computer engineers, computer instructors, programmers, and students of computer science will find the collection highly valuable.

  • Analytical Solution Methods for Boundary Value Problems

    • 1st Edition
    • A.S. Yakimov
    • English
    Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods.

  • Fixed Point Theory and Graph Theory

    Foundations and Integrative Approaches
    • 1st Edition
    • Monther Alfuraidan + 1 more
    • English
    Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets.

  • A Collection of Problems on a Course of Mathematical Analysis

    International Series of Monographs in Pure and Applied Mathematics
    • 1st Edition
    • G. N. Berman
    • I. N. Sneddon + 2 more
    • English
    A Collection of Problems on a Course of Mathematical Analysis is a collection of systematically selected problems and exercises (with corresponding solutions) in mathematical analysis. A common instruction precedes a group of problems of the same type. Problems with a physics content are preceded by the necessary physical laws. In the case of more or less difficult problems, hints are given in the answers. This book is comprised of 15 chapters and begins with an overview of functions and methods of specifying them; notation for and classification of functions; elementary investigation of functions; and trigonometric and inverse trigonometric functions. The following chapters deal with limits and tests for their existence; differential calculus, with emphasis on derivatives and differentials; functions and curves; definite and indefinite integrals; and methods of evaluating definite integrals. Some applications of the integral in geometry, statics, and physics are also considered; along with functions of several variables; multiple integrals and iterated integration; line and surface integrals; and differential equations. The final chapter is devoted to trigonometric series. This monograph is intended for students studying mathematical analysis within the framework of a technical college course.

  • A Collection of Problems in Analytical Geometry

    Three-Dimensional Analytical Geometry
    • 1st Edition
    • D. V. Kletenik
    • W. J. Langford + 1 more
    • English
    A Collection of Problems in Analytical Geometry, Part II: Three-Dimensional Analytical Geometry is a collection of problems dealing with analytical geometry in the field of theoretical mechanics. The book discusses rectangular Cartesian coordinates in three-dimensional space and the division of an interval in a given ratio. The sample questions concern problems dealing with isosceles triangles, vertices, and center of gravity of equal masses. The book defines the concept of a vector and then lists problems concerning the triangle law and the scalar product of two vectors. Other problems focus on the equations of a surface and a curve and on questions related to the intersection of three surfaces. The text lists other problems such as the equation of a plane, the direction-vector of a straight line, and miscellaneous problems pertaining to the equations of a plane, of a straight line, and of a sphere in a direction-vector. The selection is useful for professors in analytical geometry and for other courses in physic-mathematics and general engineering.

  • Exploring University Mathematics

    Lectures Given at Bedford College, London
    • 1st Edition
    • Mary Bradburn + 2 more
    • N. J. Hardiman
    • English
    Exploring University Mathematics, Volume 3 provides information pertinent to pure and applied mathematics. This book discusses the close relationship between mathematics and physics. Organized into seven chapters, this volume begins with an overview of the concept of mapping in mathematics, which provides a correspondence between elements of one set with elements of another. This text then examines the theory of inflatable structures in the study of the hovercrafs in two dimensions. Other chapters consider the explicit investigation of logic by mathematicians whereby mathematics has been conceived as pre-eminently a deductive science. This book discusses as well how Taylor's formula is used in various aspects, including integration, approximating functions, finding roots of algebraic equations, and solving differential equations in forms suitable for computer calculations. This book is intended to be suitable for students on a degree course in mathematics. Mathematicians, teachers, and research workers will also find this book extremely useful.

  • Introduction to Dynamic Programming

    International Series in Modern Applied Mathematics and Computer Science, Volume 1
    • 1st Edition
    • Leon Cooper + 1 more
    • E. Y. Rodin
    • English
    Introduction to Dynamic Programming introduces the reader to dynamic programming and presents the underlying mathematical ideas and results, as well as the application of these ideas to various problem areas. A large number of solved practical problems and computational examples are included to clarify the way dynamic programming is used to solve problems. A consistent notation is applied throughout the text for the expression of quantities such as state variables and decision variables. This monograph consists of 10 chapters and opens with an overview of dynamic programming as a particular approach to optimization, along with the basic components of any mathematical optimization model. The following chapters discuss the application of dynamic programming to variational problems; functional equations and the principle of optimality; reduction of state dimensionality and approximations; and stochastic processes and the calculus of variations. The final chapter looks at several actual applications of dynamic programming to practical problems, such as animal feedlot optimization and optimal scheduling of excess cash investment. This book should be suitable for self-study or for use as a text in a one-semester course on dynamic programming at the senior or first-year, graduate level for students of mathematics, statistics, operations research, economics, business, industrial engineering, or other engineering fields.

  • An Introduction to Mathematical Analysis

    International Series of Monographs on Pure and Applied Mathematics
    • 1st Edition
    • Robert A. Rankin
    • I. N. Sneddon + 2 more
    • English
    An Introduction to Mathematical Analysis is an introductory text to mathematical analysis, with emphasis on functions of a single real variable. Topics covered include limits and continuity, differentiability, integration, and convergence of infinite series, along with double series and infinite products. This book is comprised of seven chapters and begins with an overview of fundamental ideas and assumptions relating to the field operations and the ordering of the real numbers, together with mathematical induction and upper and lower bounds of sets of real numbers. The following chapters deal with limits of real functions; differentiability and maxima, minima, and convexity; elementary properties of infinite series; and functions defined by power series. Integration is also considered, paying particular attention to the indefinite integral; interval functions and functions of bounded variation; the Riemann-Stieltjes integral; the Riemann integral; and area and curves. The final chapter is devoted to convergence and uniformity. This monograph is intended for mathematics students.

  • A Collection of Contributions in Honour of Jack van Lint

    • 1st Edition
    • P.J. Cameron + 1 more
    • English
    This collection of contributions is offered to Jack van Lint on the occasion of his sixtieth birthday and appears simultaneously in the series Topics in Discrete Mathematics and as a special double volume of Discrete Mathematics (Volumes 106/107). It is hoped that the papers selected, all written by experts in their own fields, represent the many interesting areas that together constitute the discipline of Discrete Mathematics. It is in this sphere that van Lint has become the acknowledged master and this expansive volume serves to demonstrate the enormous significance he has had on the development of Discrete Mathematics during the last 30 years.

  • Newnes Amateur Radio Computing Handbook

    • 1st Edition
    • Joe Pritchard
    • English
    Newnes Amateur Radio Computing Handbook discusses the applications of computers in amateur radio and short wave listening. The book is comprised of 16 chapters that deal with the various concerns in amateur radio computing. The coverage of the text includes equipment, such as packet slow scan television (SSTV) and facsimile (FAX), packet radio, and commercial decoding equipment. The book also discusses the software used in amateur radio, such as satellite and geographical software, logkeeping and QSL software, and software for electronic design. The text will be of great use to individuals who want to utilize their computer in short wave radio listening.

  • A Course of Higher Mathematics

    International Series of Monographs In: Pure and Applied Mathematics, Volume 3, Part 1
    • 1st Edition
    • V. I. Smirnov
    • I. N. Sneddon + 2 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 59: A Course of Higher Mathematics, III/I: Linear Algebra focuses on algebraic methods. The book first ponders on the properties of determinants and solution of systems of equations. The text then gives emphasis to linear transformations and quadratic forms. Topics include coordinate transformations in three-dimensional space; covariant and contravariant affine vectors; unitary and orthogonal transformations; and basic matrix calculus. The selection also focuses on basic theory of groups and linear representations of groups. Representation of a group by linear transformations; linear representations of the unitary group in two variables; linear representations of the rotation group; and Abelian groups and representations of the first degree are discussed. Other considerations include integration over groups, Lorentz transformations, permutations, and classes and normal subgroups. The text is a vital source of information for students, mathematicians, and physicists.

  • Programming in GW-BASIC

    • 1st Edition
    • P. K. McBride
    • English
    Programming in GW-BASIC provides a reference guide on GW-Basic along with a range of extra commands and functions. The book discusses starting a program, program planning and the essentials of GW-Basic, including the most commonly used commands; how data is stored in memory; how a program fits together; and the use of the keyboard and screen in editing. The text also describes graphics and color and the string-handling functions. The principles and concepts of program structures, such as the Paintbox program and chaining, and the use of the Turtle graphics, such as Logo and DRAW, are also considered. The book covers two of the key techniques for handling data in quantity (sorting into order and searching for specific items), statistical analysis, and display program. The text then tackles PEEK and POKE, which examine sections of memory and serve as alternative to PRINT for creating screen displays, and advanced graphics, which enables one to analyze the screen, develop first a double-size print utility, then a sprite designer and some movement routines. The selection is useful to computer programmers and students taking computer courses.

  • MSX Made Simple

    Made Simple Computerbooks
    • 1st Edition
    • Margaret Norman
    • English

  • Directions in Infinite Graph Theory and Combinatorics

    With an introduction by C.St.J.A. Nash-Williams
    • 1st Edition
    • Volume 3
    • R. Diestel
    • English
    This book has arisen from a colloquium held at St. John's College, Cambridge, in July 1989, which brought together most of today's leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.

  • The Process of Learning Mathematics

    The Commonwealth and International Library: Mathematical Topics
    • 1st Edition
    • L. R. Chapman
    • English
    The Process of Learning Mathematics is a collection of essays from a two-term course of intercollegiate lectures for students of B.Ed. degree. This collection starts with two different views on the nature of mathematics. One essay discusses the role of intuition in understanding mathematics, while another paper expounds on the role of logic. This book then discusses the generalization, structure, and approximations used in teaching mathematics, and emphasizes the problems of applied mathematics and technology pertaining to equations of motion, mathematical representation of physical phenomena, or in relations such as conservation of matter. One paper reviews Piaget's studies on the development of children's thinking process, noting that teachers should consider the level of thinking the pupil uses when designing his teaching material. Another essay deals with how the existing knowledge in a student can affect new kinds of learning through assimilation and accommodation. This book then describes the use of symbols and "reflective intelligence," addressing reflective activities, communication, and the contribution of symbols. This text then discusses computer-assisted education and several mathematical teaching or learning experiments. This compendium can prove useful for mathematics majors, educators, school administrators, and math teachers.

  • Mathematical Analysis

    A Special Course
    • 1st Edition
    • G. Ye. Shilov
    • I.N. Sneddon + 2 more
    • English
    Mathematical Analysis: A Special Course focuses on the study of mathematical analysis. The book first discusses set theory, including operations on sets, countable sets, equivalence of sets, and sets of the power of the continuum. The text also discusses the elements of the theory of metric and normed linear spaces. Topics include convergent sequences and closed sets; theorem of the fixed point; normed linear spaces; and continuous functions and compact spaces. The selection also discusses the calculus of variations; the theory of the integral; and geometry of Hilbert space. The text also covers differentiation and integration, including functions of bounded variation, derivative of a non-decreasing function, differentiation of functions of sets, and the Stieltjes integral. The book also looks at the Fourier transform. Topics include convergence of Fourier series; Laplace transform; Fourier transform in the case of various independent variables; and quasi-analytic classes of functions. The text is a valuable source of data for readers interested in the study of mathematical analysis.

  • Students' Guide to Programming Languages

    • 1st Edition
    • Malcolm Bull
    • English
    Students' Guide to Programming Languages introduces programming languages, emphasizing why they are needed, how they are defined and constructed, and where and how they are used. With greater access to computers at work, at school, and in the home, more and more people are now able to write programs. Only a small number of these people recognize the underlying features of the programming languages they are using, and even fewer people appreciate the features that are common to most programming languages. This book demonstrates how most programming languages are based upon the same concepts and how knowledge of these concepts can benefit the analyst and the programmer. When specifying computer solutions to real problems, the systems analyst and the programmer must be able to stand back from the particular problem in hand and visualize a solution that is independent of the constraints and limitations imposed by the programming language itself. The text helps in achieving these goals. The book as well is suitable for college students following BTEC and City and Guilds courses in computer studies and IT topics, including professional commercial and end-users.

  • Real Time Programming 1981

    Proceedings of the IFAC/IFIP Workshop, Kyoto, Japan, 31 August - 2 September 1981
    • 1st Edition
    • T. Hasegawa
    • English
    Annual Review in Automatic Programming, Volume 11: Real Time Programming 1981 contains the proceedings of the IFAC/IFIP Workshop held in Kyoto, Japan on August 31 - September 2, 1981. Organized into 18 chapters, this book begins with a discussion on advances and trends in distributed control systems. Subsequent chapters explore the application and technology of industrial computers in Japan; on-line system changeover using a virtual machine system; a debugging tool for real time software; and program fall-back method in real time systems. Some other chapters address file design of small real time computer system; development of a distributed operating system kernel for real time applications; and evaluation of pipelined common processor in distributed processing system.

  • Proceedings of the Ninth Power Systems Computation Conference

    • 1st Edition
    • Cascais Portugal
    • English

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