Analytic geometry Books
Prometheus Books The Secrets of Triangles: A Mathematical Journey
Book SynopsisEveryone knows what a triangle is, yet very few people appreciate that the common three-sided figure holds many intriguing "secrets." For example, if a circle is inscribed in any random triangle and then three lines are drawn from the three points of tangency to the opposite vertices of the triangle, these lines will always meet at a common point - no matter what the shape of the triangle. This and many more interesting geometrical properties are revealed in this entertaining and illuminating book about geometry. Flying in the face of the common impression that mathematics is usually dry and intimidating, this book proves that this sometimes-daunting, abstract discipline can be both fun and intellectually stimulating. The authors, two veteran math educators, explore the multitude of surprising relationships connected with triangles and show some clever approaches to constructing triangles using a straightedge and a compass. Readers will learn how they can improve their problem-solving skills by performing these triangle constructions. The lines, points, and circles related to triangles harbor countless surprising relationships that are presented here in a very engaging fashion. Requiring no more than a knowledge of high school mathematics and written in clear and accessible language, this book will give all readers a new insight into some of the most enjoyable and fascinating aspects of geometry.
£16.99
O'Reilly Media Make - Trigonometry: Build your way from
Book SynopsisTrigonometry has 2000-year-old roots in everyday useful endeavors, like finding the size of an object too big or far away to measure directly, or navigating from Point A to Point B. However, it is often taught very theoretically, with an emphasis on abstractions. Make: Trigonometry uses 3D printable models and readily-available physical objects like wire and cardboard tubes to develop intuition about concepts in trigonometry and basic analytic geometry. Readers will imagine the thought process of the people who invented these mathematical concepts, and can try out "math experiments" to see for themselves how ingenious ancient navigators and surveyors really were. The analytic geometry part of the book links equations to many of these intuitive concepts, which we explore through in-depth explanations of manipulative models of conic sections. This book is aimed at high school students who might be in Algebra II or Pre-Calculus. It shows the geometrical and practical sides of these topics that otherwise can drown in their own algebra. Make: Trigonometry builds on the basics of the authors' earlier book, Make: Geometry, and is intended as a bridge from that book to their Make: Calculus book. The user can read this book and understand the concepts from the photographs of 3D printable models alone. However, since many models are puzzle-like, we encourage the reader to print the models on any consumer-grade filament based 3D printer. The models are available for download in a freely-available open source repository. They were created in the free program OpenSCAD, and can be 3D printed or modified by the student in OpenSCAD to learn a little coding along the way.
£19.19
Wooden Books Mathematical Functions
Book SynopsisWhat is a mathematical function? Why are they so important? How does plotting the graph of a function help us understand it? And where do gradients, differentials and calculus fit in? In this unique little book, packed with equations and their graphs, mathematics teacher Oliver Linton reveals the secrets of polynomial functions, polar functions, inverse functions, complex functions, vector functions and many more. Lines will never look the same again!Trade ReviewWooden Books are: "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST. "Stunning" NEW YORK TIMES. Small books, big ideas.
£6.95
McGraw-Hill Education - Europe Lsc Calif State U Northridge Math103l Aleks Prep
Book Synopsis
£32.13
McGraw-Hill Education - Europe Student Solutions Manual for Calculus
Book Synopsis
£99.97
McGraw-Hill Education - Europe VISUALIZING CALCULUS BY WAY OF MAPLE AN EMPHASIS
Book Synopsis
£58.32
Clarendon Press Analysis on Symmetric Cones Oxford Mathematical Monographs
Book SynopsisThis monograph treats the analysis of symmetric cones in a systematic way. It discusses harmonic analysis and special functions associated with symmetric cones; it also tries these results together with the study of holomorphic functions on bounded symmetric domains of tube type.Trade Review... the present book is more carefully directed at the graduate student level, includes numerous exercises, and has its emphasis more on the harmonic analysis side. Such a presentation is much needed. The detailed exposition, careful choice of organization and notation, and very helpful collection of exercises, mostly of medium difficulty, all attest to the effort put into this joint venture. As a highly readable and accessible presentation of Jordan algebras and their applications to Riemannian geometry and harmonic analysis, the book is strongly recommended to all analysts (starting at graduate level) working in the multi-variable setting of symmetric spaces and Lie groups. Bulletin of the London Mathematical SocietyTable of ContentsI. Convex cones ; II. Jordan algebras ; III. Symmetric cones and Euclidean Jordan algebras ; IV. The Peirce decomposition in a Jordan algebra ; V. Classification of Euclidean Jordan algebras ; VI. Polar decomposition and Gauss decomposition ; VII. The gamma function of a symmetric cone ; VIII. Complex Jordan algebras ; IX. Tube domains over convex cones ; X. Symmetric domains ; XI. Conical and spherical polynomials ; XII. Taylor and Laurent series ; XIII. Functions spaces on symmetric domains ; XIV. Invariant differential operators and spherical functions ; XV. Special functions ; XVI. Representations of Jordan algebras and Euclidean Fourier analysis ; Bibliography
£191.25
Dover Publications Inc. Coordinate Geometry Dover Books on Mathematics
Book SynopsisThis volume affords exceptional insights into coordinate geometry. Covers invariants of conic sections and quadric surfaces; algebraic equations on the 1st degree in 2 and 3 unknowns; and more. Over 500 exercises. 1939 edition.
£16.57
Dover Publications Inc. Analytical Conics Dover Books on Mathematics
Book SynopsisThis concise text introduces analytical geometry, covering basic ideas and methods. An invaluable preparation for more advanced treatments, it features solutions to many of its problems. 1957 edition.
£10.35
Cambridge University Press Minkowski Geometry 63 Encyclopedia of Mathematics and its Applications Series Number 63
Book SynopsisMinkowski geometry is a type of non-Euclidean geometry in a finite number of dimensions in which distance is not 'uniform' in all directions. This book presents the first comprehensive treatment of Minkowski geometry since the 1940s. The author begins by describing the fundamental metric properties and the topological properties of existence of Minkowski space. This is followed by a treatment of two-dimensional spaces and characterisations of Euclidean space among normed spaces. The central three chapters present the theory of area and volume in normed spaces, a fascinating geometrical interplay among the various roles of the ball in Euclidean space. Later chapters deal with trigonometry and differential geometry in Minkowski spaces. The book ends with a brief look at J. J. Schaffer's ideas on the intrinsic geometry of the unit sphere. Minkowski Geometry will appeal to students and researchers interested in geometry, convexity theory and functional analysis.Trade Review' … volume, isoperimetry, integral geometry and trigonometry … all are admirably treated here by an expert in the field.' Mathematika'This is a comprehensive monograph that will serve well both as an introduction and as a reference work.' Monatshefte für MathematikTable of Contents1. The algebraic properties of linear spaces and of convex sets; 2. Norms and norm topologies; 3. Convex bodies; 4. Comparisons and contrasts with Euclidean space; 5. Two dimensional Minkowski spaces; 6. The concept of area and content; 7. Special properties of the Holmes-Thompson definition; 8. Special properties of the Busemann definition; 9. Trigonometry; 10. Various numerical parameters.
£122.55
Cambridge University Press Complex Algebraic Curves 0023 London Mathematical Society Student Texts Series Number 23
Book SynopsisComplex algebraic curves were developed in the nineteenth century. They have many fascinating properties and crop up in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired by most undergraduate courses in mathematics, Dr Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis. This book grew from a lecture course given by Dr Kirwan at Oxford University and will be an excellent companion for final year undergraduates and graduates who are studying complex algebraic curves.Trade Review"Kirwan should succeed admirably with her goal of showing senior undergraduates who perhaps do not plan to study mathematics beyond the bachelor's degree 'how the basic ideas of pure mathematics they had studied in previous years could be brought together in one of the showpieces of mathematics.'" Choice"...worth serious consideration for those planning to teach such a course, and perhaps even more importantly, as an inspiration for mathematicians to offer such a course. The book offers us plenty to work with, and is an excellent contribution." S. Zdravkovska and Daniel M. Burns, Jr., Mathematical Reviews"At last an introduction to the theory of algebraic curves that is understandable by undergraduates, and that does not shy away from the various aspects of the theory: algebraic, topological, complex analytic, etc. Good bedside reading." Gian-Carlo Rota, The Bulletin of Mathematical BooksTable of Contents1. Introduction and background; 2. Foundations; 3. Algebraic properties; 4. Topological properties; 5. Riemann surfaces; 6. Differentials on Riemann surfaces; 7. Singular curves; Appendices.
£49.99
Cambridge University Press An Introduction to Twistor Theory Second Edition 4 London Mathematical Society Student Texts Series Number 4
Book SynopsisThis book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics which has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics.Trade Review' … the book is recommended to anyone seeking to get acquainted with the area.' American Scientist' … a certain amount of preliminary knowledge is assumed of the reader ... but anyone who has these prerequisites and who is interested in twistor theory could hardly do better than to start with this book.' Contemporary Physics'In all, the book provides a pleasant starting point for the study of this fascinating subject.' Dr F. E. Burstall, Contemporary PhysicsTable of Contents1. Introduction; 2. Review of tensor algebra; 3. Lorentzian spinors at a point; 4. Spinor fields; 5. Compactified Minkowski space; 6. The geometry of null congruences; 7. The geometry of twistor space; 8. Solving the zero rest mass equations I; 9. Sheaf cohomology; 10. Solving the zero rest mass equations II; 11. The twisted photon and Yang–Mills constructions; 12. The non-linear graviton; 13. Penrose's quasi-local momentum; 14. Cohomological functionals; 15. Further developments and conclusion; Appendix: The GHP equations.
£127.30
Cambridge University Press An Introduction to Twistor Theory Second Edition 0004 London Mathematical Society Student Texts Series Number 4
Book SynopsisThis text is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level.Trade Review' … the book is recommended to anyone seeking to get acquainted with the area.' American Scientist' … a certain amount of preliminary knowledge is assumed of the reader ... but anyone who has these prerequisites and who is interested in twistor theory could hardly do better than to start with this book.' Contemporary Physics'In all, the book provides a pleasant starting point for the study of this fascinating subject.' Dr F. E. Burstall, Contemporary PhysicsTable of Contents1. Introduction; 2. Review of tensor algebra; 3. Lorentzian spinors at a point; 4. Spinor fields; 5. Compactified Minkowski space; 6. The geometry of null congruences; 7. The geometry of twistor space; 8. Solving the zero rest mass equations I; 9. Sheaf cohomology; 10. Solving the zero rest mass equations II; 11. The twisted photon and Yang–Mills constructions; 12. The non-linear graviton; 13. Penrose's quasi-local momentum; 14. Cohomological functionals; 15. Further developments and conclusion; Appendix: The GHP equations.
£43.99
Taylor & Francis Ltd Topological Circle Planes and Topological
Book SynopsisThis research note presents a complete treatment of the connection between topological circle planes and topological generalized quadrangles. The author uses this connection to provide a better understanding of the relationships between different types of circle planes and to solve a topological version of the problem of Apollonius. Topological Circle Planes and Topological Quadrangles begins with a foundation in classical circle planes and the real symmetric generalized quadrangle and the connection between them. This provides a solid base from which the author offers a more generalized exploration of the topological case. He also compares this treatment to the finite case. Subsequent chapters examine Laguerre, Möbius, and Minkowski planes and their respective relationships to antiregular quadrangles. The author addresses the Lie geometry of each and discuss the relationships of circle planes-the sisters of Möbius, Laguerre, and Minkowski planes - and concludes by solving a toTrade Review"This book is a must read for anyone interested in incidence geometry and especially anybody interested in topological incidence geometry."-Mathematical Reviews, Issue 97bTable of ContentsIntroductionCircle PlanesIntroductionDefinitions and NotationModels for Classical Circle PlanesDerived StructuresAntiregular QuadranglesIntroductionGeneralized QuadranglesSquare ProjectionsThe Twisting NumberAntiregular QuadranglesCharacterization of Antiregular QuadranglesLaguerre Planes and Antiregular QuadranglesIntroduction Laguerre Planes Constructed from Antiregular QuadranglesAntiregular Quadrangles Constructed from Laguerre PlanesConstructing Topologies on the Lie GeometryMöbius Planes and Antiregular QuadranglesIntroduction The Lie Geometry of a Möbius PlaneThe Lifted Lie Geometry of a Flat Möbius PlaneConstructing Topologies on the Lifted Lie GeometryCharacterizing Quadrangles Obtained from Flat Möbius PlanesMinkowski Planes and Antiregular QuadranglesIntroductionThe Point Space and Parallel ClassesThe Circle SpaceThe Other SpacesThe Derivation of a Minkowski PlaneThe Lie Geometry of a Minkowski PlaneThe Lifted Lie Geometry of a Minkowski PlaneThe Topology on the Lifted Lie GeometryCharacterizing Quadrangles Obtained from Minkowski PlanesRelationship of Circle PlanesIntroduction Sisters of Laguerre PlanesSisters of Möbius PlanesSisters of Minkowski PlanesThe Problem of ApolloniusIntroductionThe Problem of Apollonius in Laguerre PlanesThe Problem of Apollonius in Möbius Planes One Point and Two Circles Three CirclesThe Problem of Apollonius in Minkowski Planes Two Points and One Circle One Point and Two circles Three CirclesIndexGlossaryReferences
£109.25
Princeton University Press Meromorphic Functions and Analytic Curves
Book SynopsisThe description for this book, Meromorphic Functions and Analytic Curves. (AM-12), will be forthcoming.Table of Contents*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii*INTRODUCTION. EARLY HISTORY AND BIBLIOGRAPHY, pg. 1*CHAPTER I. GEOMETRIC AND FUNCTION-THEORETIC FOUNDATIONS, pg. 10*CHAPTER II. FIRST MAIN THEOREM FOR MEROMORPHIC CURVES, pg. 69*CHAPTER III. THE SECOND MAIN THEOREM FOR MEROMORPHIC CURVES, pg. 123*CHAPTER IV. FIRST AND SECOND MAIN THEOREMS FOR ANALYTIC CURVES, pg. 163*CHAPTER V. THE DEFECT RELATIONS, pg. 211*Backmatter, pg. 271
£70.40
Princeton University Press Topics in Algebraic and Analytic Geometry
Book SynopsisThis volume offers a systematic treatment of certain basic parts of algebraic geometry, presented from the analytic and algebraic points of view. The notes focus on comparison theorems between the algebraic, analytic, and continuous categories. Contents include: 1.1 sheaf theory, ringed spaces; 1.2 local structure of analytic and algebraic sets; 1Table of Contents*Frontmatter, pg. i*Introduction, pg. iii*Contents, pg. v*Chapter One, pg. 1*Chapter Two, pg. 23*Chapter Three, pg. 56*Chapter Four, pg. 73*Chapter Five, pg. 83*Chapter Six, pg. 136*Chapter Seven, pg. 154*Chapter Eight, pg. 196*Chapter Nine, pg. 215*Bibliography, pg. 217
£35.70
MP-AMM American Mathematical Nonlinear Analysis on Manifolds Sobolev Spaces
Book SynopsisOffers lectures given at the Courant Institute on the theory of Sobolev spaces on Riemannian manifolds. This volume includes a brief introduction to differential and Riemannian geometry. It deals with the general theory of Sobolev spaces for compact manifolds, and also presents special types of Sobolev inequalities under constraints.Table of ContentsElements of Riemannian geometry Sobolev spaces: The compact setting Sobolev spaces: The noncompact setting Best constants in the compact setting I Best constants in the compact setting II Optimal inequalities with constraints Best constants in the noncompact setting Euclidean-type Sobolev inequalities The influence of symmetries Manifolds with boundary Bibliography.
£36.05
Cengage Learning, Inc Algebra and Trigonometry with Analytic Geometry
Book SynopsisTable of ContentsEvery chapter ends with Review Exercises, Discussion Exercises, and a Chapter Test. 1. FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Fractional Expressions. 2. EQUATIONS AND INEQUALITIES. Equations. Applied Problems. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. 5. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 6. THE TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 7. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Addition and Subtraction Formulas. Multiple-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. The Inverse Trigonometric Functions. 8. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 10. SEQUENCES, SERIES AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. 11. TOPICS FROM ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle.
£315.77
Read Books Plane And Solid Analytic Geometry
£28.49
American Mathematical Society Geometric Function Theory and Related Topics
£104.40
ACTAR D Lines of Development
Book Synopsis
£45.00
Imperial College Press Mesh Enhancement: Selected Elliptic Methods,
Book SynopsisThis book focuses on mesh (grid) enhancement techniques — specifically, the use of selected elliptic methods for both structured and unstructured meshes associated with computational physics applications. Mesh enhancement is the process in which an existing mesh is modified to better meet the requirements of the physics application. To provide the reader with sufficient background information, seven of the nine chapters contain a summary of the numerical simulation process, basic background on mesh terminology and generation approaches, computational geometry, discretization of differential equations, methods of solving linear and nonlinear algebraic systems, geometry of surfaces in Euclidean space, and general elliptic methods for mesh enhancement. Furthermore, these chapters use the concept of harmonic coordinates to develop a unifying framework, the Laplace-Beltrami system, which is the governing principle of the book. The final two chapters apply this scheme, along with other selected elliptic methods, to various structured and unstructured example problems.Table of ContentsBasic Concepts; Computational Geometry and Geometric Data Structures; Discretization Methods for Differential Equations; Solving the Mesh Enhancement Algebraic Equation System; The Geometry of Surfaces in Euclidean Space; Special Coordinate Systems; Elliptic Mesh Enhancement Equation Systems; Structured Mesh Smoothing and Enhancement; Mesh Enhancement Methods for Unstructured Meshes
£168.30
Springer International Publishing AG Linear Algebra and Analytic Geometry for Physical Sciences
Book SynopsisA self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises.Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number.The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.Trade Review“There are over 230 exercises integrated into the text, most with several parts and explained in detail. These exercises also serve as examples. The book contains about 20 figures and several additional examples. This text will interest both beginning and advanced undergraduates studying physics. … Summing Up: Recommended. Undergraduates through faculty and professionals.” (D. P. Turner, Choice, Vol. 56 (04), December, 2018)Table of ContentsIntroduction.- Vectors and coordinate systems.- Vector spaces.- Euclidean vector spaces.- Matrices.- The determinant.- Systems of linear equations.- Linear transformations.- Dual spaces.- Endomorphisms and diagonalization.- Spectral theorems on euclidean spaces.- Rotations.- Spectral theorems on hermitian spaces.- Quadratic forms.- Affine linear geometry.- Euclidean affine linear geometry.- Conic sections.- A Algebraic Structures.- A.1 A few notions of Set Theory.- A.2 Groups.- A.3 Rings and Fields.- A.4 Maps between algebraic structures.- A5 Complex numbers.- A.6 Integers modulo a prime number.
£49.49
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Mesh: Eine Reise Durch Die Diskrete Geometrie
Book Synopsis
£7.51
Mathematical Society of Japan Cone And Contraction Theorem For Projective
Book Synopsis
£19.00
World Scientific Publishing Co Pte Ltd Geometric Properties Of Natural Operators Defined
Book SynopsisA central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold. The full curvature tensor is in general quite difficult to deal with. This book presents results about the geometric consequences that follow if various natural operators defined in terms of the Riemann curvature tensor (the Jacobi operator, the skew-symmetric curvature operator, the Szabo operator, and higher order generalizations) are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition.The book presents algebraic preliminaries and various Schur type problems; deals with the skew-symmetric curvature operator in the real and complex settings and provides the classification of algebraic curvature tensors whose skew-symmetric curvature has constant rank 2 and constant eigenvalues; discusses the Jacobi operator and a higher order generalization and gives a unified treatment of the Osserman conjecture and related questions; and establishes the results from algebraic topology that are necessary for controlling the eigenvalue structures. An extensive bibliography is provided. Results are described in the Riemannian, Lorentzian, and higher signature settings, and many families of examples are displayed.Table of ContentsAlgebraic curvature tensors; the skew-symmetric curvature operator; the Jacobi operator; controlling the eigenvalue structure.
£90.00
World Scientific Publishing Co Pte Ltd Introduction To Finsler Geometry, An
Book SynopsisThis introductory book uses the moving frame as a tool and develops Finsler geometry on the basis of the Chern connection and the projective sphere bundle. It systematically introduces three classes of geometrical invariants on Finsler manifolds and their intrinsic relations, analyzes local and global results from classic and modern Finsler geometry, and gives non-trivial examples of Finsler manifolds satisfying different curvature conditions.Table of ContentsFinsler Manifolds; Geometric Quantities on a Minkowski Space; Chern Connection; Covariant Differentiation and Second Class of Geometric Invariants; Riemann Invariants and Variations of Arc Length; Geometry of Projective Sphere Bundle; Relation Among Three Classes of Invariants; Finsler Manifolds with Scalar Curvature; Harmonic Maps from Finsler Manifolds.
£77.90
World Scientific Publishing Co Pte Ltd Lectures On The Geometry Of Manifolds (2nd
Book SynopsisThe goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that “in learning the sciences examples are of more use than precepts”. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a “global and analytical bias”. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincaré duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hölder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.Table of ContentsManifolds; Natural Constructions on Manifolds; Calculus on Manifolds; Riemannian Geometry; Elements of the Calculus of Variations; The Fundamental Group and Covering Spaces; Cohomology; Characteristic Classes; Classical Integral Geometry Elliptic Equations on Manifolds; Dirac Operators.
£175.50
World Scientific Publishing Co Pte Ltd Relative Index Theory, Determinants And Torsion
Book SynopsisFor closed manifolds, there is a highly elaborated theory of number-valued invariants, attached to the underlying manifold, structures and differential operators. On open manifolds, nearly all of this fails, with the exception of some special classes. The goal of this monograph is to establish for open manifolds, structures and differential operators an applicable theory of number-valued relative invariants. This is of great use in the theory of moduli spaces for nonlinear partial differential equations and mathematical physics. The book is self-contained: in particular, it contains an outline of the necessary tools from nonlinear Sobolev analysis.Table of ContentsAbsolute Invariants for Open Manifolds and Bundles: Absolute Characteristic Numbers; Index Theorems for Open Manifolds; Non-linear Sobolev Structures; Generalized Dirac Operators: Generalized Dirac Operators, Their Heat Kernel and Spectral Properties; Duhamels Principle, Trace Class Conditions and Scattering Theory; Trace Class Properties; Relative Index Theory: Relative Index Theorems; The Spectral Shift Function and the Scattering Index; Relative Zeta Functions, Eta Functions, Determinants, Partition Functions of QFT and Torsion.
£100.80
World Scientific Publishing Co Pte Ltd Lectures On The Geometry Of Manifolds (2nd
Book SynopsisThe goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that “in learning the sciences examples are of more use than precepts”. We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a “global and analytical bias”. We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincaré duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand Hölder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.Table of ContentsManifolds; Natural Constructions on Manifolds; Calculus on Manifolds; Riemannian Geometry; Elements of the Calculus of Variations; The Fundamental Group and Covering Spaces; Cohomology; Characteristic Classes; Classical Integral Geometry Elliptic Equations on Manifolds; Dirac Operators.
£77.90
World Scientific Publishing Co Pte Ltd Classical Complex Analysis: A Geometric Approach
Book SynopsisClassical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 1 begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described in detail, and various applications of residues are included; analytic continuation is also introduced.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.Table of ContentsComplex Numbers; Complex-Valued Functions of a Complex Variable; Fundamental Theory: Differentiation, Integration and Analytic Functions; Fundamental Theory: Integration (Continued).
£171.00
World Scientific Publishing Co Pte Ltd Classical Complex Analysis: A Geometric Approach
Book SynopsisClassical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 1 begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described in detail, and various applications of residues are included; analytic continuation is also introduced.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.Table of ContentsComplex Numbers; Complex-Valued Functions of a Complex Variable; Fundamental Theory: Differentiation, Integration and Analytic Functions; Fundamental Theory: Integration (Continued).
£73.15
World Scientific Publishing Co Pte Ltd Classical Complex Analysis: A Geometric Approach
Book SynopsisClassical Complex Analysis, available in two volumes, provides a clear, broad and solid introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. Volume 2 begins with analytic continuation. The Riemann mapping theorem is proved and used in solving Dirichlet's problem for an open disk and, hence, a class of general domains via Perron's method. Finally, proof of the uniformization theorem of Riemann surfaces is given.The book is rich in contents, figures, examples and exercises. It is self-contained and is designed for a variety of usages and motivations concerning advanced studies. It can be used both as a textbook for undergraduate and graduate students, and as a reference book in general.
£80.75
World Scientific Publishing Company Complex Analytic Geometry From The Localization
Book Synopsis
£162.00
World Scientific Publishing Co Pte Ltd Differential Manifolds: A Basic Approach For
Book SynopsisDifferential Manifold is the framework of particle physics and astrophysics nowadays. It is important for all research physicists to be well accustomed to it and even experimental physicists should be able to manipulate equations and expressions in that framework.This book gives a comprehensive description of the basics of differential manifold with a full proof of any element. A large part of the book is devoted to the basic mathematical concepts in which all necessary for the development of the differential manifold is expounded and fully proved.This book is self-consistent: it starts from first principles. The mathematical framework is the set theory with its axioms and its formal logic. No special knowledge is needed.Table of ContentsManifold: Differentiable Manifold; Smooth Maps; Vector Fields on a Differentiable Manifold; Conventions; Tangent Spaces and Tangent Vectors; Coordinate Changes; Metric on a Differentiable Manifold; One-Form Field and Differential; Tensorial Field; Wedge Product of 1-Linear Forms (versus Vector Fields); Exterior Differential; Volume and Integral in Differential Manifold, Stokes Kelvin - Thomson Theorem; Lie Bracket; Bundles and Differentiable Manifold; Parallel Transport; Curvature; Lagrangian of the Electro-Weak Interactions (Left Handed); General Relativity; Notations; Some Basic Mathematics Needed for Manifolds: General Concepts; Real Numbers, Set ℛ; Euclidean Metric; Metric and Topology on ℛ; Behavior at a Point; Some Properties of Continuous Maps from ℛ to ℛ; Continuous Maps from Topological Sets to ℛ; Derivable Function; Group; Module Over a Commutative Ring; Vector Spaces; Complex Numbers; ℛn; Convex Subset; Topology on ℛn; Continuous Map on ℛn to ℛp; Sequence; Sequence in ℛ∞; Sequence of Maps; Partial Derivative; Topology on Convex Subsets; Path Connected Sets; Riemann Integral of Maps with Compact Support; Volume in ℛn; Integral of a Continuous Map; Differential Equations; Lebesgue Integral; Taylor Expansion of Functions with Derivatives; Exponentials; Polynomials; Useful Smooth Maps Built with Exponentials; Eigenvectors of a Linear Transformation; Conventions, Basic Relations and Symbols: Logical Theory; Specifics Terms; Quantificators; Specifics Relations; Sets; Relations and Operations on Sets; Zermolo Theorem; Cardinals; Integers; Rational Numbers; Conventions.
£67.45
World Scientific Publishing Co Pte Ltd Analysis And Beyond An Introduction With Examples
Book Synopsis
£42.75
