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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.

  • Gait Analysis

    An Introduction
    • 1st Edition
    • Michael W. Whittle
    • English
    Gait Analysis: An Introduction focuses on the systematic study of human walking and its contributions in the medical management of diseases affecting the locomotor system. The book first covers normal gait and pathological gait. Discussions focus on common pathologies affecting gait, amputee gait, walking aids, particular gait abnormalities, gait in the elderly and the young, moments of force, energy consumption, gait cycle, muscular activity during gait, and optimization of energy usage. The manuscript then elaborates on the methods of gait analysis, including visual gait analysis, general gait parameters, timing the gait cycle, direct motion measurement systems, electrogoniometers, electromyography, accelerometers, gyroscopes, and force platforms. The publication tackles the applications of gait analysis, as well as clinical gait and scientific gait analysis, normal ranges for gait parameters, conversions between measurement units, and computer program for general gait parameters. The manuscript is a valuable source of data for students of physical therapy, bioengineering, orthopedics, rheumatology, neurology, and rehabilitation.

  • Teaching Machines and Programming

    • 1st Edition
    • K. Austwick
    • English
    Teaching Machines and Programming covers the significant developments in teaching machines and automated teaching, as well as the major theoretical issues and attributes involved in these procedures. After a brief introduction to teaching machine procedures, this six-chapter text goes on summarizing the industrial and military applications of teaching machines. The succeeding chapters consider the underlying theory, function, and schema of the adaptive teaching system, which are related to recognizable teaching functions performed by a human tutor. The last chapters discuss the development and features of linear programs and their application as new teaching aid. These chapters also look into some practical problems arising in programming for schools. This book will prove useful to computer programmers, school administrators, teachers, and students.

  • Fractal Attractionâ„¢

    a Fractal Design System for the Macintosh®
    • 1st Edition
    • Kevin D. Lee + 1 more
    • English
    Fractal Attraction™: A Fractal Design System for the Macintosh® provides information pertinent to fractal attraction, a Macintosh application. This book introduces the Iterated Function Systems (IFS). Organized into eight chapters, this book begins with an overview of the standard and enhanced versions of fractal attraction. This text then explains the ideas and basic principles behind generating fractals based on sets of equations. Other chapters explain an alternative algorithm, the random algorithm, and how to use it. This book discusses as well the Design window wherein the user can translate, rotate, shear, and re-size transformations all by pointing, clicking and dragging. The final chapter deals with an overview of the windows and the menu items are explained in detail. This book is a valuable resource for readers who are interested in using fractal attraction application.

  • Intermediate Algebra & Analytic Geometry

    • 1st Edition
    • William R. Gondin + 1 more
    • English
    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, systems involving quadratics, and determinants. Topics include determinants of higher order, application of Cramer's rule, second-order determinants, systems linear in quadratic terms, systems treatable by substitution, systems with a linear equation, and other systems treated by comparison. The manuscript ponders on trigonometric functions and equations, straight lines, and points, distances, and slopes, including intersection points of lines, perpendicular distances, angles between lines, positions of points, inverse trigonometric functions, and trigonometric equations. The publication is a valuable source of data for readers interested in intermediate algebra and analytic geometry.

  • Quadratic Forms and Matrices

    An Introductory Approach
    • 1st Edition
    • N. A. Yefimov
    • English
    Quadratic Forms and Matrices: An Introductory Approach focuses on the principles, processes, methodologies, and approaches involved in the study of quadratic forms and matrices. The publication first offers information on the general theory of quadratic curves, including reduction to canonical form of the general equation of a quadratic curve, invariants and classification, reduction to canonical form of the equation of a quadratic curve with center at the origin, and transformation of coordinates in the plane. The text then examines the general theory of quadratic surfaces. Topics include transformation of rectangular coordinates in space; general deductions based on the formulas for the transformation of coordinates; reduction to canonical form of the equation of a quadric with center at the origin; and reduction to canonical form of the general equation of a quadric surface. The manuscript ponders on linear transformations and matrices, including reduction of a quadratic form to canonical form; reduction to canonical form of the matrix of a symmetric linear transformation of space; change of the matrix of a linear transformation due to a change of basis; and geometric meaning of the determinant of a linear transformation. The publication is a vital reference for researchers interested in the study of quadratic forms and matrices.

  • Exploring Artificial Intelligence

    Survey Talks from the National Conferences on Artificial Intelligence
    • 1st Edition
    • Howard E. Shrobe
    • English
    Exploring Artificial Intelligence: Survey Talks from the National Conference on Artificial Intelligence provides information pertinent to the distinct subareas of artificial intelligence research. This book discusses developments in machine learning techniques. Organized into six parts encompassing 16 chapters, this book begins with an overview of intelligent tutoring systems, which describes how to guide a student to learn new concepts. This text then links closely with one of the concerns of intelligent tutoring systems, namely how to interact through the utilization of natural language. Other chapters consider the various aspects of natural language understanding and survey the huge body of work that tries to characterize heuristic search programs. This book discusses as well how computer programs can create plans to satisfy goals. The final chapter deals with computational facilities that support. This book is a valuable resource for cognitive scientists, psychologists, domain experts, computer scientists, instructional designers, expert teachers, and research workers.

  • NonEuclidean Geometry

    • 1st Edition
    • Herbert Meschkowski
    • D. Allan Bromley + 2 more
    • English
    Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics. The book first offers information on proofs and definitions and Hilbert's system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio. The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry. The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.

  • French's Index of Differential Diagnosis

    • 11th Edition
    • F. Dudley Hart
    • English
    French's Index of Differential Diagnosis, 11th Edition focuses on treatise on the application of differential diagnosis to all the main signs and symptoms of diseases. The book covers surgery, gynecology, ophthalmology, dermatology, and neurology. The manuscript first ponders on anemia, angioma, antisocial behavior, anxiety, ascites, ataxia, abnormal blood pressure, bradycardia, foulness of breath, and pain in breast. The book then discusses confabulation, cramps, cyanosis, cystinuria, delusions, dementia, diarrhea, diplopia, depression, erythema, and inflammation of eye. The publication takes a look at indigestion, impotence, insomnia, jaundice, keloid, marasmus, muscular atrophy, nasal obstruction, nausea, nasal discharge, swelling of neck, obesity, palpitations, and pelvic swelling. The manuscript also reviews loss of weight, vertigo, vomiting, defects of vision, vaginal discharge, vaginal swelling, sore throat, pain in tongue, trismus, grinding of teeth during sleep, and snoring. The book is a vital reference for researchers wanting to study differential diagnosis.

  • Matrix Calculus

    • 3rd Edition
    • E. Bodewig
    • English
    Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well as the decomposition of the matrix into two triangular matrices, choice of another pivotal element, Gauss-Doolittle process, Aitken's triple product, neighbor systems, errors and exactness of the solution, and complex systems. The publication also elaborates on the characteristic equation of the iteration processes, type of convergence of the iteration methods, speeding-up convergence by changing matrix, and methods for electronic computers. The determination of eigenvectors, pure methods, progressive algorithms, and deflation are also discussed. The manuscript is a helpful reference for researchers interested in matrix calculus.

  • Mathematical Logic and Formalized Theories

    A Survey of Basic Concepts and Results
    • 2nd Edition
    • Robert L. Rogers
    • English
    Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.

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