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.

Books Journals

Solution of Equations and Systems of Equations

2nd Edition
June 3, 2016
A. M. Ostrowski
Paul A. Smith + 1 more
English
eBook
9 7 8 1 4 8 3 2 2 3 6 4 3

Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions. This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

Comparison and Oscillation Theory of Linear Differential Equations

1st Edition
June 3, 2016
C. A. Swanson
Richard Bellman
English
eBook
9 7 8 1 4 8 3 2 6 6 6 7 1

Mathematics in Science and Engineering, Volume 48: Comparison and Oscillation Theory of Linear Differential Equations deals primarily with the zeros of solutions of linear differential equations. This volume contains five chapters. Chapter 1 focuses on comparison theorems for second order equations, while Chapter 2 treats oscillation and nonoscillation theorems for second order equations. Separation, comparison, and oscillation theorems for fourth order equations are covered in Chapter 3. In Chapter 4, ordinary equations and systems of differential equations are reviewed. The last chapter discusses the result of the first analog of a Sturm-type comparison theorem for an elliptic partial differential equation. This publication is intended for college seniors or beginning graduate students who are well-acquainted with advanced calculus, complex analysis, linear algebra, and linear differential equations.

Adaptive Processes in Economic Systems

1st Edition
June 3, 2016
Roy E. Murphy
Richard Bellman
English
eBook
9 7 8 1 4 8 3 2 6 4 0 7 3

Mathematics in Science and Engineering, Volume 20, Adaptive Processes in Economic Systems demonstrates the usefulness of communications theory, self-adaptive control theory, and thermodynamic theory to certain economic processes. This book discusses the common properties of adaptive processes, role of the decision maker, and mixed adaptive processes of the first and second kind. The economic environmental processes, concept of entropy time, and stochastic dynamic economic process are also elaborated. This text likewise covers the investment model with full liquidity, adaptive capital allocation process, and concept of an economic state space. Other topics include the stochastic equilibrium in the market and individual adaptive behavior. This volume is suitable for engineers, economists, and specialists of disciplines related to economic systems.

Concepts from Tensor Analysis and Differential Geometry

1st Edition
June 3, 2016
Tracy Y. Thomas
Richard Bellman
English
eBook
9 7 8 1 4 8 3 2 6 3 7 1 7

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

Algebra of Proofs

1st Edition
June 3, 2016
M. E. Szabo
K. J. Barwise + 2 more
English
eBook
9 7 8 1 4 8 3 2 7 5 4 2 0

Algebra of Proofs deals with algebraic properties of the proof theory of intuitionist first-order logic in a categorical setting. The presentation is based on the confluence of ideas and techniques from proof theory, category theory, and combinatory logic. The conceptual basis for the text is the Lindenbaum-Tarski algebras of formulas taken as categories. The formal proofs of the associated deductive systems determine structured categories as their canonical algebras (which are of the same type as the Lindenbaum-Tarski algebras of the formulas of underlying languages). Gentzen's theorem, which asserts that provable formulas code their own proofs, links the algebras of formulas and the corresponding algebras of formal proofs. The book utilizes the Gentzen's theorem and the reducibility relations with the Church-Rosser property as syntactic tools. The text explains two main types of theories with varying linguistic complexity and deductive strength: the monoidal type and the Cartesian type. It also shows that quantifiers fit smoothly into the calculus of adjoints and describe the topos-theoretical setting in which the proof theory of intuitionist first-order logic possesses a natural semantics. The text can benefit mathematicians, students, or professors of algebra and advanced mathematics.

Semihypergroup Theory

1st Edition
June 2, 2016
Bijan Davvaz
English
Paperback
9 7 8 0 1 2 8 0 9 8 1 5 8
eBook
9 7 8 0 1 2 8 0 9 9 2 5 4

Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject.

Theory and Methods of Statistics

1st Edition
May 26, 2016
P.K. Bhattacharya + 1 more
English
Paperback
9 7 8 0 1 2 8 0 2 4 4 0 9
eBook
9 7 8 0 1 2 8 0 4 1 2 3 9

Theory and Methods of Statistics covers essential topics for advanced graduate students and professional research statisticians. This comprehensive resource covers many important areas in one manageable volume, including core subjects such as probability theory, mathematical statistics, and linear models, and various special topics, including nonparametrics, curve estimation, multivariate analysis, time series, and resampling. The book presents subjects such as "maximum likelihood and sufficiency," and is written with an intuitive, heuristic approach to build reader comprehension. It also includes many probability inequalities that are not only useful in the context of this text, but also as a resource for investigating convergence of statistical procedures.

Poincaré-Andronov-Melnikov Analysis for Non-Smooth Systems

1st Edition
May 17, 2016
Michal Feckan + 1 more
English
Hardback
9 7 8 0 1 2 8 0 4 2 9 4 6
eBook
9 7 8 0 1 2 8 0 4 3 6 4 6

Poincaré-Andronov-Me... Analysis for Non-Smooth Systems is devoted to the study of bifurcations of periodic solutions for general n-dimensional discontinuous systems. The authors study these systems under assumptions of transversal intersections with discontinuity-switch... boundaries. Furthermore, bifurcations of periodic sliding solutions are studied from sliding periodic solutions of unperturbed discontinuous equations, and bifurcations of forced periodic solutions are also investigated for impact systems from single periodic solutions of unperturbed impact equations. In addition, the book presents studies for weakly coupled discontinuous systems, and also the local asymptotic properties of derived perturbed periodic solutions. The relationship between non-smooth systems and their continuous approximations is investigated as well. Examples of 2-, 3- and 4-dimensional discontinuous ordinary differential equations and impact systems are given to illustrate the theoretical results. The authors use so-called discontinuous Poincaré mapping which maps a point to its position after one period of the periodic solution. This approach is rather technical, but it does produce results for general dimensions of spatial variables and parameters as well as the asymptotical results such as stability, instability, and hyperbolicity.

Newnes Circuit Calculations Pocket Book

1st Edition
April 20, 2016
Thomas J. Davies
English
eBook
9 7 8 1 4 8 3 1 0 1 1 3 2

Newnes Circuit Calculations Pocket Book: With Computer Programs presents equations, examples, and problems in circuit calculations. The text includes 300 computer programs that help solve the problems presented. The book is comprised of 20 chapters that tackle different aspects of circuit calculation. The coverage of the text includes dc voltage, dc circuits, and network theorems. The book also covers oscillators, phasors, and transformers. The text will be useful to electrical engineers and other professionals whose work involves electronic circuitry.

Data Gathering, Analysis and Protection of Privacy Through Randomized Response Techniques: Qualitative and Quantitative Human Traits

1st Edition
Volume 34
April 13, 2016
Arijit Chaudhuri + 2 more
English
Hardback
9 7 8 0 4 4 4 6 3 5 7 0 9
eBook
9 7 8 0 4 4 4 6 3 5 7 1 6

Data Gathering, Analysis and Protection of Privacy through Randomized Response Techniques: Qualitative and Quantitative Human Traits tackles how to gather and analyze data relating to stigmatizing human traits. S.L. Warner invented RRT and published it in JASA, 1965. In the 50 years since, the subject has grown tremendously, with continued growth. This book comprehensively consolidates the literature to commemorate the inception of RR.

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