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This book proposes a new approach which is designed to serve as an introductory course in differential geometry for advanced undergraduate students. It is based on lectures given by the author at several universities, and discusses calculus, topology, and linear algebra.

Presents an introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. This work contains information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.

Suitable for a one-semester course in linear algebra for graduate or upper-level undergraduate students of mathematics and engineering, this title employs a matrix perspective, and emphasizes training in definitions, theorems, and proofs.

This book deals with solutions of second order, linear, parabolic partial differential equations on an infinite strip emphasizing their integral representation, their initial values in several senses, and the relations between these. It is useful for graduate students, analysts and specialists.

This book presents a theory of necessary conditions for an extremum, including formal conditions for an extremum and computational methods. It states the general results of the theory and shows how these results can be particularized to specific problems.

Exploring the qualitative aspects of periodic solutions of ODEs, this title presents the treatment of two-dimensional systems as well as periodic solutions in small parameter problems. It illustrates theorems with various examples, and provides an account of the Bendixson theory of solutions of two-dimensional autonomous systems.

This book presents original problems from graduate courses in pure and applied mathematics and even small research topics, significant theorems and information on recent results. It is helpful for specialists working in differential equations.

Presents the fundamental axioms of the real number system. This book also features the core of real analysis. It presents the essentials needed for analysis, including the concepts of sets, relations, and functions. It covers the theory of calculus on the real line, exploring limits, convergence tests.

This book introduces both the theory and applications of elementary analysis, with emphasis on the genesis and resolution of a variety of applied problems. It is helpful for the motivated student whose mathematical background consists of only a two-or three-semester calculus sequence.

A selection of some important topics in complex analysis, intended as a sequel to the author's Classical complex analysis (see preceding entry). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.

This work examines the mathematical aspects of nonlinear wave propagation, emphasizing nonlinear hyperbolic problems. It introduces the tools that are most effective for exploring the problems of local and global existence, singularity formation, and large-time behaviour of solutions, and for the study of perturbation methods.

Stressing the use of several software packages based on simplex method variations, this work teaches linear programming's four phases through actual practice. It shows how to decide whether LP models should be applied, set up appropriate models and use software to solve them.

This book presents to the reader a modern axiomatic construction of three-dimensional Euclidean geometry in a rigorous and accessible form. It is helpful for high school teachers who are interested in the modernization of the teaching of geometry.

This book represents the current (1985) state of knowledge about Zariski surfaces and related topics in differential equations in characteristic p > 0. It is aimed at research mathematicians and graduate and advanced undergraduate students of mathematics and computer science.

"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."

Uses complexes of differential forms to give a complete treatment of the Deligne theory of mixed Hodge structures on the cohomology of singular spaces. This book features an approach that employs recursive arguments on dimension and does not introduce spaces of higher dimension than the initial space.

Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. This book defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures.

Explores the analog of the theory of functions of a complex variable.

Research on number theory has produced a wealth of interesting and beautiful results yet topics are strewn throughout the literature, the notation is far from being standardized, and a unifying approach to the different aspects is lacking. Covering both classical and recent results, this book unifies the theory of continued fractions, quadratic orders, binary quadratic forms, and class groups based on the concept of a quadratic irrational. It highlights the connection between Gauss¿s theory of binary forms and the arithmetic of quadratic orders.

Presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. This book compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.

Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force

Combining both classical and current methods of analysis, this text present discussions on the application of functional analytic methods in partial differential equations. It furnishes a simplified, self-contained proof of Agmon-Douglis-Niremberg's Lp-estimates for boundary value problems, using the theory of singular integrals and the Hilbert transform.

A comprehensive presentation of abstract algebra and a treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.

Offers an introduction to differential geometry with applications to mechanics and physics. This title covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; and, tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms.

Presents hyperspace fundamentals, offering an overview and a foundation. This text contains topics such as the topology for hyperspaces, examples of geometric models for hyperspaces, 2x and C(X) for Peano continua X, arcs in hyperspaces, the shape and contractability of hyperspaces, hyperspaces and the fixed point property, and Whitney maps.

This work presents the principles of space and surface potential theory involving Euclidean and spherical concepts. It offers new insight on how to mathematically handle gravitation and geomagnetism for the relevant observables and how to solve the resulting potential problems in a systematic, mathematically rigorous framework. The authors build the foundation of potential theory in three-dimensional Euclidean space and its application to gravitation and geomagnetism. They then discuss surface potential theory on the unit sphere along with corresponding applications.

Beginning with an introduction to modeling and functional and numerical analysis, this title deals with the chapters to models involving adhesion and material damage, exploring a particular model. For various models, it provides a variational formulation and establishes the existence and uniqueness of a weak solution.

Offers a comprehensive listing of the various translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and sketches of the major relevant theorems.