Calculus and mathematical analysis Books
MP-AMM American Mathematical Proceedings of the Conference on Banach Algebras
Book SynopsisContains papers presented at the conference on Banach Algebras and Several Complex Variables held June 21-24, 1983, to honor Professor Charles E Rickart upon his retirement from Yale University. This work includes articles that present advances in topics related to Banach algebras, function algebras and infinite dimensional holomorphy.Table of ContentsCapacities in $C^n$ by H. Alexander Holomorphic left-inverse functions by G. Allan Geometry of pseudoconvex open sets and distribution of values of analytic multivalued functions by B. Aupetit Some results on range transformations between function spaces by J. Bachar Recent results in the ideal theory of radical convolution algebras by W. Bade Module derivations from commutative Banach algebras by W. Bade and P. Curtis Criteria for boundedness and compactness of Hankel operators by F. Bonsall Algebra and topology in Banach algebras by H. Dales Mittag-Leffler methods in the theory of Banach algebras and a new approach to Michael's problem by J. Esterle Orthogonal and representing measures by I. Glicksberg Nuclearity (resp. Schwartzity) helps to embed holomorphic structure into spectra by B. Kramm Maximum modulus algebras and multi-dimensional analytic structure by D. Kumagai Central factorization in $C^*$-algebras and its use in automatic continuity by K. Laursen Nonstandard ideals and approximations in primary weighted $\ell^1$-algebras by J. McClure Holomorphic approximation in Lipschitz norms by A. O'Farrell, K. Preskenis, and D. Walsh Uses of $\beta S$ in invariant means and extremely left amenable semigroups by M. Rajagopalan and P. Ramakrishnan Deformation theory for uniform algebras: An introduction by R. Rochberg Nevanlinna's interpolation theorem revisited by W. Rudin Unbounded derivations in $C^*$-algebras and statistical mechanics by S. Sakai Remotely almost periodic functions by D. Sarason Analytic multifunctions, $q$-plurisubharmonic functions and uniform algebras by Z. Slodkowski Algebraic domains in Stein manifolds by E. Stout Sets of best approximations to elements in certain function spaces by J. Wada Green's functions and polynomial hulls by J. Wermer Continuous homomorphisms and derivations on Banach algebras by B. Yood The maximal ideal space of a commutative Banach algebra by W. Zame.
£97.20
MP-AMM American Mathematical Mathematical Aspects of Conformal and Topological
Book SynopsisContains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. This work deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations.Table of ContentsConnection coefficients for $A$-type Jackson integral and Yang-Baxter equation by K. Aomoto and Y. Kato Representations of the moonshine module vertex operator algebra by C. Dong The construction of the moonshine module as a $\mathbf Z_p$-orbifold by C. Dong and G. Mason Star products, quantum groups, cyclic cohomology, and pseudodifferential calculus by M. Flato and D. Sternheimer The universal $T$-matrix by C. Fronsdal and A. Galindo Fusion rings for modular representations of Chevalley groups by G. Georgiev and O. Mathieu Quantum groups and flag varieties by V. Ginzburg, N. Reshetikhin, and E. Vasserot Operadic formulation of the notion of vertex operator algebra by Y.-Z. Huang and J. Lepowsky Torus actions, moment maps, and the symplectic geometry of the moduli space of flat connections on a two-manifold by L. C. Jeffrey and J. Weitsman Vertex operator superalgebras and their representations by V. Kac and W. Wang Topological invariants for $3$-manifolds using representations of mapping class groups II: Estimating tunnel number of knots by T. Kohno Poisson Lie groups, quantum duality principle, and the quantum double by M. A. Semenov-Tian-Shansky Local $4$-point functions and the Knizhnik-Zamolodchikov equation by Y. S. Stanev and I. T. Todorov.
£102.60
MP-AMM American Mathematical Operators Functions and Systems An Easy Reading
Book SynopsisThis unique work combines four major topics of modern analysis and its applications: Hardy classes of holomorphic functions; Spectral theory of Hankel and Toeplitz operators; Function models for linear operators and free interpolations; and infinite-dimensional system theory and signal processing.
£101.70
MP-AMM American Mathematical SturmLiouville Theory
Book Synopsis
£103.50
MP-AMM American Mathematical An Introduction to Complex Analysis and Geometry
Book SynopsisTrade ReviewThe book provides the reader with a deep appreciation of complex analysis and how this subject fits into mathematics." - Mathematical Reviews"The book under review provides a refreshing presentation of both classical and modern topics in and relating to complex analysis, which will be appreciated by mature undergraduates, budding graduate students, and even research mathematicians . . . The book's strengths lie in the characteristics which distinguish it from other undergraduate complex analysis texts. Throughout the book, numerous uncommon topics and rich examples tie complex analysis to farther areas of math, giving the reader a glimpse of the power of this intriguing subject . . . Overall, the text provides a mature view of basic concepts from complex analysis and also succeeds in giving a succinct introduction to the more sophisticated topics covered. It furthermore makes its collection of advanced and fascinating special topics accessible to the undergraduate." - Kealy Dias, Zentralblatt MATHTable of Contents Preface From the real numbers to the complex numbers Complex numbers Complex numbers and geometry Power series expansions Complex differentiation Complex integration Applications of complex integration Additional topics Bibliography Index
£63.00
MP-AMM American Mathematical Introduction to Functional Equations
Book Synopsis
£44.06
MP-AMM American Mathematical Bernstein Polynomials
Book SynopsisBernstein polynomials are a remarkable family of polynomials associated to any given function on the unit interval. Their first notable appearance was in Bernstein's proof of the Weierstrass approximation theorem. This book gives an exhaustive exposition of the main facts about the Bernstein polynomials and discusses some of their applications in analysis.Table of ContentsIntroduction Bernstein Polynomials in Real Domain: 1.1 The theorem of Weierstrass; 1.2 Other proofs of the theorem of Weierstrass; 1.3 Generalizations of the theorem of Weierstrass; 1.4 Derivatives of the Bernstein polynomials; 1.5 Estimations and lemmas; 1.6 The degree of approximation by Bernstein polynomials; 1.6.1 Asymptotic formulae; 1.7 Monotone functions, convex functions, and functions of bounded variation; 1.8 Further theorems on derivatives; 1.9 Discontinuous functions Generalizations of Bernstein Polynomials: 2.1 Approximation of integrable functions; 2.2 Approximation of measurable functions; 2.3 Bernstein polynomials on an unbounded interval; 2.4 General methods of summation; 2.5 Euler methods of summation; 2.6 Degenerate Bernstein polynomials; 2.7 Divided differences and generalized $p_{n\nu}(x)$; 2.8 Approximation by linear aggregates of functions $x^{\alpha}$; 2.9 Some further generalizations Spaces of Functions and Moment Problems: 3.1 Banach spaces; 3.2 Functionals and moment problems; 3.3 Moment problems with Stieltjes integrals; 3.4 Rearrangements of functions; 3.5 Spaces $\Lambda$ and $M$. Other spaces of integrable functions; 3.6 Inequalities for spaces $\Lambda$; 3.7 Continuous linear functionals in spaces $\Lambda$ and $\Lambda^*$; 3.7.1 Spaces $M(\phi, p)$ as conjugate spaces; 3.8 Moment problems for integrable functions; 3.9 Hausdorff methods of summation Bernstein Polynomials of Analytic Functions: 4.1 Preliminary theorems; 4.2 Contour integrals and asymptotic formulae; 4.3 The loop $L_z$ and its properties; 4.3.1 Further properties of the loop; 4.4 The fundamental convergence theorem; 4.5 Sets of convergence and autonomous sets; 4.6 Examples of autonomous sets and sets of convergence; 4.7 Functions analytic on a part of the interval $[0, 1]$; 4.8 Summation of power series; 4.9 Degenerate Bernstein polynomials in the complex domain Bibliography Index
£55.80
MP-AMM American Mathematical Harmonic Analysis From Fourier to Wavelets
Book SynopsisTrade ReviewThe presentation of the material is very clear and illustrated by a number of enlightening figures. Many motivating remarks and discussions are provided. A number of proofs in the more elementary chapters are omitted, but precise pointers to the literature are given. Also numerous exercises are posed as well as some more involved 'projects' which motivate the reader to get active herself." - R. Steinbauer, Monatshefte für Mathematik"This is a gentle introduction to Fourier analysis and wavelet theory that requires little background but still manages to explain some of the applications of Fourier and wavelet methods and touch on several current research topics. ... The authors have taken care to be accessible to undergraduate mathematicians. ... Compared to standard texts, this book is characterised by more personal and historical information, including footnotes. ... It comes with many projects for interested students, and lists a number of open-ended problems that suggest further developments and should engage interested students. ... In summary, this is a well-written and lively introduction to harmonic analysis that is accessible and stimulating for undergraduates and instructive and amusing for the more sophisticated reader. It could also be argued that the material herein should be part of the knowledge of most undergraduates in mathematics, given that the modern world relies more and more on data compression. It is therefore timely as well. It has certainly earned my enthusiastic recommendation." - Michael Cowling, Gazette of the Australian Mathematical Society"A wonderful introduction to harmonic analysis and applications. The book is intended for advanced undergraduate and beginning graduate students and it is right on target. Pereyra and Ward present in a captivating style a substantial amount of classical Fourier analysis as well as techniques and ideas leading to current research. ... It is a great achievement to be able to present material at this level with only a minimal prerequisite of advanced calculus and linear algebra and a set of Useful Tools included in the appendix. I recommend this excellent book with enthusiasm and I encourage every student majoring in math to take a look." - Florin Catrina, MAA Reviews"[T]he panorama of harmonic analysis presented in the book includes very recent achievements like the connection of the dyadic shift operator with the Hilbert transform. This gives to an interested reader a good chance to see concrete examples of contemporary research problems in harmonic analysis. I highly recommend this book as a good source for undergraduate and graduate courses as well as for individual studies." - Krzysztof Stempak, Zentralblatt MATHTable of Contents Contents List of figures List of tables IAS/Park City Mathematics Institute Preface Fourier series: Some motivation Interlude: Analysis concepts Pointwise convergence of Fourier series Summability methods Mean-square convergence of Fourier series A tour of discrete Fourier and Haar analysis The Fourier transform in paradise Beyond paradise From Fourier to wavelets, emphasizing Haar Zooming properties of wavelets Calculating with wavelets The Hilbert transform Useful tools Alexander’s dragon Bibliography Name index Subject index
£46.80
MP-AMM American Mathematical Numbers and Functions From a
Book SynopsisTrade ReviewOn the whole, this is an extraordinarily interesting book overflowing with (mostly) elementary non-routine mathematics. It's well-written and a pleasure to read. I've been keeping it on my desk for the ease of access; it's going to stay there for some while. I recommend it wholeheartedly to math instructors, teachers, and students, especially those who have only a slight interest in the subject. The book is bound to expand their horizons." - MAA ReviewsTable of Contents Preface The number systems Factorials and binomial coefficients The Fibonacci numbers Polynomials Binomial sums Catalan numbers The Stirling numbers of the second kind Rational functions Wallis’ formula Farey fractions The exponential function Trigonometric functions Bernoulli polynomials A sample of classical polynomials: Legendre, Chebyshev, and Hermite Landen transformations Three special functions: Γ,𝜓, and 𝜁 Bibliography Index
£50.40
MP-AMM American Mathematical A Course in Abstract Analysis
Book SynopsisTable of Contents Preface Chapter 1. Setting the stage Chapter 2. Elements of measure theory Chapter 3. A Hilbert space interlude Chapter 4. A return to measure theory Chapter 5. Linear transformations Chapter 6. Banach spaces Chapter 7. Locally convex spaces Chapter 8. Duality Chapter 9. Operators on a Banach space Chapter 10. Banach algebras and spectral theory Chapter 11. C*-algebras Appendix Bibliography List of symbols Index
£108.00
MP-AMM American Mathematical Analysis and Geometry of Metric Measure Spaces
Book SynopsisContains lecture notes from most of the courses presented at the 50th anniversary edition of the Seminaire de Mathematiques Superieure in Montreal. This 2011 summer school was devoted to the analysis and geometry of metric measure spaces, and featured much interplay between this subject and the emergent topic of optimal transportation.
£87.30
MP-AMM American Mathematical Fundamentals of the Theory of Operator Algebras
Book SynopsisThe goal of this text is to teach the subject and lead readers to where the vast literature - in the subject specifically and in its many applications - becomes accessible. The choice of material was made from among the fundamentals of what may be called the ""classical'' theory of operator algebras.Trade ReviewA fitting companion to the existing volumes and a welcome addition to the literature on functional analysis. The exercises ... were carefully designed by the authors to illustrate the results of the text and to expand its scope ... the authors' solutions ... are models of clarity and efficiency, reflecting their vast experience and insight into the subject. -- Mathematical Reviews The organization (exercise groupings), extra index of Volumes III and IV and the special bibliography will be very helpful in finding material for seminar or private projects. -- Monatshefte fur MathematikTable of ContentsLinear spaces--exercises and solutions Basics of Hilbert space and linear operators--exercises and solutions Banach algebras--exercises and solutions Elementary $C^*$-algebra theory--exercises and solutions Elementary von Neumann algebra theory--exercises and solutions Bibliography Index
£46.50
MP-AMM American Mathematical A Course in Complex Analysis and Riemann Surfaces
Book SynopsisTrade Review[T]his is an extremely valuable textbook for graduate classical complex analysis in one variable both for lecturers and students not following the increasing standardization trends of student's curricula... The presentation style is excellent, a very well contemplated pleasant reading throughout, rich in interesting outlooks. I recommend this work to all the mathematical libraries at universities as an extremely helpful material in teaching or studying complex analysis." - László L. Stachó, ACTA Sci. Math.Table of Contents From i to z: the basics of complex analysis From z to the Riemann mapping theorem: some finer points of basic complex analysis Harmonic functions Riemann surfaces: definitions, examples, basic properties Analytic continuation, covering surfaces, and algebraic functions Differential forms on Riemann surfaces The theorems of Riemann-Roch, Abel, and Jacobi Uniformization Review of some basic background material Bibliography Index
£108.00
Taylor & Francis Inc Partial Differential Equations On Multistructures
Book SynopsisThis text is based on lectures presented at the International Conference on Partial Differential Equations (PDEs) on Multistructures, held in Luminy, France. It contains advances in the field, compiling research on the analyses and applications of multistructures - including treatments of classical theories, specific characterizations and modellings of multistructures, and discussions on uses in physics, electronics, and biology.Table of ContentsTransient vibrations of planar networks of beams - interaction of flexion, transversal and longitudinal waves; can one hear the shape of a network?; sensitivity analysis of 2D interface cracks; on the asymptotic expansion of the solution of a Dirichlet-Ventcel problem with a small parameter; on instantaneous control of singularly perturbed hyperbolic systems on graphs; Hadamard formula in non-smooth domains and applications; singular stress field at the tip of a closed interface crack; on the geometric and algebraic multiplicities for eigenvalue problems on graphs; the asymptotic Laplace transform - new results and relation to Komatsu's Laplace transform of hyperfunctions; some systems of PDE on polygonal networks; about a geometrical approach to multistructures and some qualitative properties of solutions; study of a vibration problem for a perforated plate with Fourier boundary conditions; singular perturbations with non-smooth limit and finite element approximation of layers for model problems of shells; modelling of a thin piezoelectric shell coupled with a distributed electronic circuit by piezoelectric transducers.
£228.00
Taylor & Francis Inc Continuum Theory
Book SynopsisCelebrating the work of world-renowned mathematician Sam B. Nadler, Jr., this reference examines the most recent advances in the analysis of continua. The book offers articles on the contributions of Professor Nadler, theorems on the structure and uniqueness of hyperspaces, results on the dynamics of solenoids, examples involving inverse limits of maps of the interval conditions on embeddability of hyperspaces and symmetric products, open problems on a number of topics. It examines boundary bumping theorems, fixed point theorems for nonseparating plane continua, Whitney maps and Whitney properties, topological entropy for arc-like continua, a variety of mapping properties, and more.Table of ContentsIntroduction 1. The Life and Times of Sam B. Nadler, Jr. 2. The Work of Sam B. Nadler, Jr. on Hyperspaces 3. Continua with Unique Hyperspace 4. Ordered Embeddings of Hyperspaces 5. Embedding Symmetric Products in Euclidean Spaces 6. On Strongly Monotone Mappings 7. On Semi-Universal Mappings 8. Problems on Hyperspace Retractions 9. The Dynamics of Maps of Solenoids Homotopic to the Identity 10. The Buckethandle Continuum Admits No Mean 11. Inverse Limits on [0,1] Using Piecewise Linear Unimodal Bonding Maps, II 12. A Tale of Six Atriodic Tree-Like Continua 13. Hyperspaces Locally 2-Cell at the Top 14. Cantor Sets of Ray Composants in Local Siegel Disk Boundaries 15. The RNT Property of Compactifications of the Ray 16. Non-Confluence of the Natural Map of Products onto Symmetric Products 17. Boundary Bumping in Connected Topological Spaces 18. The Selection Space of a Dendroid, I 19. On Period Three and Topological Entropy in Hereditarily Decomposable Arc-Like Continua 20. A Fixed Point Theorem for Certain Maps on Certain Nonseparating Plane Continua 21. Dendroids, Digraphs, and Posets 22. Sequential Decreasing Whitney Properties 23. More on Products of Effros Spaces 24. Continua Irreducible About n Points 25. A Note on Computation of Span 26. Spans of Spaces Contained in a Convex Disc Cross an Arc
£999.99
CRC Press Evolution Equations
Book SynopsisCelebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani. Table of ContentsPreface, Contributors, Biography, The Hille-Yoshida Cantata, 1. Matrix-Valued Generalizations of the Theorems of Borg and Hochstadt, 2. Local and Global Well-Posedness Results for Generalized BBM-type Equations, 3. Variable Coefficient KdV Equations and Waves in Elastic Tubes, 4. Infinitely Many Solutions for a Superlinear Neumann Problem in Tileable Regions, 5. On Applications of Maximal Regularity to Inverse Problems for Integrodifferential Equations of Parabolic Type, 6. A Semilinear Integrodifferential Inverse Problem, 7. Gearhart-Priiss Theorem in Stability for Wave Equations. A Survey, 8. A Note on Generalized Maximum Principles for Elliptic and Parabolic PDE, 9. Finite Dimensional Convex Gradient Systems Perturbed by Noise, 10. Differentiability of the Solution Semigroup for Delay Differential Equations, 11. Second Order Differential Operators on C[0,1] with Wentzell–Robin Boundary Conditions, 12. A New Approach to the Regularity of Solutions for Parabolic Equations, 13. The Regulator Problem for a Singular Control System, 14. Criteria for R-Boundedness of Operator Families, 15. One Dimensional Hyperbolic Systems and Hille-Yosida Operators, 16. On the Wave Equation Subjected to Coulomb Friction, 17. Asymptotics of Perturbations to the Wave Equation, 18. A Class of Ordinary Differential Operators with Jump Boundary Conditions, 19. An Alternate Proof of Kato’s Inequality, 20. On a Continuous Coagulation and Fragmentation Equation with a Singular Fragmentation Kernel, 21. Almost Periodicity of Inhomogeneous Parabolic Evolution Equations, 22. Linear Delay Equations in the Lp-context, 23. Integrated Form of Continuous Newton’s Method, 24. Effects of a Variable Step-Size in Some Abstract Product Formulas, 25. Evolution Operators in Stochastic Processes and Inference, 26. Competition between Diffusion and Inhomogeneous Reaction, 27. Global Bifurcations of Concave Semipositone Problems, 28. An Obstruction to Prescribing Positive Scalar Curvature on Complete Manifolds with Ricci ≥ 0
£237.50
Taylor & Francis Inc Real And Complex Singularities 232 Lecture Notes
Book SynopsisThis text offers a selection of papers on singularity theory presented at the Sixth Workshop on Real and Complex Singularities held at ICMC-USP, Brazil. It should help students and specialists to understand results that illustrate the connections between singularity theory and related fields. The authors discuss irreducible plane curve singularities, openness and multitransversality, the distribution Afs and the real asymptotic spectrum, deformations of boundary singularities and non-crystallographic coxeter groups, transversal Whitney topology and singularities of Haefliger foliations, the topology of hypersurface singularities, polar multiplicities and equisingularity of map germs from C3 to C4, and topological invariants of stable maps from a surface to the plane from a global viewpoint.Table of ContentsIrreducible plane curve singularities, Abramo Hefez; openness and multitransversality, C.T.C. wall; the distribution A and the real asymptotic spectrum, Daniel Barlet and Ahmed Jeddi; deformations of boundary singularities and non-crystallographic Coxeter Groups, Ina Scherbak; transversal Whitney topology and singularities of Haefliger Foliations, Shyuchi Izumiya and Kunihide Maruyama; on a Conjecture of Chisini for coverings of the Plane with A-D-E-singularities, Valentine S. Kulikov; not all codimension 1 germs have good real pictures, David Mond and Roberta G. Wik Atique; on the topology of hypersurface singularities, Jose Seade; polar multiplicities and equisingularity of map germs from C3 to C4, Victor Hugo Jorge Perez; topological invariants of stable maps from a surface to the plane from a global viewpoint, D. Hacon, C. Mendez de Jesus, and M.C. Romero Fuster; cubics in R and C, Radmila Bulajich, Leon Kushner, and Santiago Lopez de Medrano; indices of Newton non-degenerate vector fields and a conjecture of Loewner for surfaces in R4, Carlo Gutierrez and Maria Aparecida Soares Ruas; generic singularities of H-directions, Luis Fernando O. Mello; vertices of curves on constant curvature manifolds, Claudia C. Pasonato and Sueli I.R. Costa; projections of hypersurfaces in R4 to planes, Ana Claudia Nabarro; Frobenius manifolds and hypersurface singularities, Claus Hertling.
£247.00
Taylor & Francis Inc Stochastic Processes and Functional Analysis
Book SynopsisShows the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes.Trade Review"More than 20 original papers reflect Rao's broad scientific interests in probability, stochastic processes, Banach space theory, measure theory and (stochastic) differential equations. …The volume is completed with a biography and bibliography of M. M. Rao, a remarkable collection of personal reminiscences (written by his former students) adds a human dimension to this fine book."-EMS Newsletter, June 2005Table of ContentsBiography of M. M. Rao, Published Writings of M. M. Rao, Ph.D. Theses Completed Under the Direction of M. M. Rao, Contributors, For M. M. Rao, An Appreciation of My Teacher, M. M. Rao, 1001 Words About Rao, A Guide to Life, Mathematical and Otherwise, Rao and the Early Riverside Years, On M. M. Rao, Reflections on M. M. Rao, 1: Stochastic Analysis and Function Spaces, 2: Applications of Sinkhorn Balancing to Counting Problems, 3: Zakai Equation of Nonlinear Filtering with Ornstein-Uhlenbeck Noise: Existence and Uniqueness, 4: Hyperfunctionals and Generalized Distributions, 5: Process-Measures and Their Stochastic Integral, 6: Invariant Sets for Nonlinear Operators, 7: The Immigration-Emigration with Catastrophe Model, 8: Approximating Scale Mixtures, 9: Cyclostationary Arrays: Their Unitary Operators and Representations, 10: Operator Theoretic Review for Information Channels, 11: Pseudoergodicity in Information Channels, 12: Connections Between Birth-Death Processes, 13: Integrated Gaussian Processes and Their Reproducing Kernel Hilbert Spaces, 14: Moving Average Representation and Prediction for Multidimensional Harmonizable Processes, 15: Double-Level Averaging on a Stratified Space, 16: The Problem of Optimal Asset Allocation with Stable Distributed Returns, 17: Computations for Nonsquare Constants of Orlicz Spaces, 18: Asymptotically Stationary and Related Processes, 19: Superlinearity and Weighted Sobolev Spaces, 20: Doubly Stochastic Operators and the History of Birkhoff s Problem 111, 21: Classes of Harmonizable Isotropic Random Fields, 22: On Geographically-Uniform Coevolution: Local Adaptation in Non-fluctuating Spatial Patterns, 23: Approximating the Time Delay in Coupled van der Pol Oscillators with Delay Coupling
£266.00
MP-AMM American Mathematical Grundzuge der Mengenlehre German Edition
Book SynopsisContains such topics as Symmetric Sets, Principle of Duality, most of the 'Algebra' of Sets, Partially Ordered Sets, Arbitrary Sets of Complexes, Normal Types, Initial and Final Ordering, Complexes of Real Numbers, General Topological Spaces, Euclidean Spaces, and the Special Methods Applicable in the Euclidean Plane.Table of ContentsMengen und ihre Verknupfungen: Summe, Durchschnitt, Differenz Mengen und ihre Verknupfungen: Funktion, Produkt, Potenz Kardinalzahlen oder Machtigkeiten Geordnete Mengen. Ordnungstypen Wohlgeordnete Mengen. Ordnungszahlen Beziehungen zwischen geordneten und wohlgeordneten Mengen Punktmengen in allgemeinen Raumen Punktmengen in speziellen Raumen Abbildungen oder Funktionen Inhalte von Punktmengen Nachtrage und Anmerkungen.
£48.45
MP-AMM American Mathematical Theorie des Operations Lineaires
Book SynopsisTable of ContentsL'integrale de Lebesgue-Stieltjes Ensembles et operations mesurables $(B)$ dans les espaces metriques Groupes Espaces vectoriels generaux Espaces du type $(F)$ Espaces normes Espaces du type $(B)$ Operations totalement continues et associees Suites biorthogonales Fonctionnelles lineaires dans les espaces du type $(B)$ Suites faiblement convergentes d'elements Equations fonctionnelles lineaires Isometrie, equivalence, isomorphie Dimension lineaire Convergence faible dans les espaces du type $(B)$ Remarques Note. Sur la mesure de Haar Auteurs Cites Index Terminologique.
£55.80
MP-AMM American Mathematical Iterative Methods for the Solution of Equations
Book SynopsisPresents a general theory of iteration algorithms for the numerical solution of equations and systems of equations. This book investigates the relationship between the quantity and the quality of information that is used by an algorithm.Table of ContentsGeneral Preliminaries: 1.1 Introduction 1.2 Basic concepts and notations General Theorems on Iteration Functions: 2.1 The solution of a fixed-point problem 2.2 Linear and superlinear convergence 2.3 The iteration calculus The Mathematics of Difference Relations: 3.1 Convergence of difference inequalities 3.2 A theorem on the solutions of certain inhomogeneous difference equations 3.3 On the roots of certain indicial equations 3.4 The asymptotic behavior of the solutions of certain difference equations Interpolatory Iteration Functions: 4.1 Interpolation and the solution of equations 4.2 The order of interpolatory iteration functions 4.3 Examples One-Point Iteration Functions: 5.1 The basic sequence $E_s$ 5.2 Rational approximations to $E_s$ 5.3 A basic sequence of iteration functions generated by direct interpolation 5.4 The fundamental theorem of one-point iteration functions 5.5 The coefficients of the error series of $E_s$ One-Point Iteration Functions With Memory: 6.1 Interpolatory iteration functions 6.2 Derivative-estimated one-point iteration functions with memory 6.3 Discussion of one-point iteration functions with memory Multiple Roots: 7.1 Introduction 7.2 The order of $E_s$ 7.3 The basic sequence $\scr{E}_s$ 7.4 The coefficients of the error series of $\scr{E}_s$ 7.5 Iteration functions generated by direct interpolation 7.6 One-point iteration functions with memory 7.7 Some general results 7.8 An iteration function of incommensurate order Multipoint Iteration Functions: 8.1 The advantages of multipoint iteration functions 8.2 A new interpolation problem 8.3 Recursively formed iteration functions 8.4 Multipoint iteration functions generated by derivative estimation 8.5 Multipoint iteration functions generated by composition 8.6 Multipoint iteration functions with memory Multipoint Iteration Functions: Continuation: 9.1 Introduction 9.2 Multipoint iteration functions of type 1 9.3 Multipoint iteration functions of type 2 9.4 Discussion of criteria for the selection of an iteration function Iteration Functions Which Require No Evaluation of Derivatives: 10.1 Introduction 10.2 Interpolatory iteration functions 10.3 Some additional iteration functions Systems of Equations: 11.1 Introduction 11.2 The generation of vector-valued iteration functions by inverse interpolation 11.3 Error estimates for some vector-valued iteration functions 11.4 Vector-valued iteration functions which require no derivative evaluations A Compilation of Iteration Functions: 12.1 Introduction 12.2 One-point iteration functions 12.3 One-point iteration functions with memory 12.4 Multiple roots 12.5 Multipoint iteration functions 12.6 Multipoint iteration functions with memory 12.7 Systems of equations Appendices: A. Interpolation B. On the $j$th derivative of the inverse function C. Significant figures and computational efficiency D. Acceleration of convergence E. Numerical examples F. Areas for future research Bibliography Index.
£55.80
Precalculus
Book SynopsisGet a good grade in your precalculus course with PRECALCULUS, Seventh Edition. Written in a clear, student-friendly style, the book also provides a graphical perspective so you can develop a visual understanding of college algebra and trigonometry. With great examples, exercises, applications, and real-life data--and a range of online study resources--this book provides you with the tools you need to be successful in your course.Table of Contents1. FUNDAMENTALS. Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles. 2. EQUATIONS AND INEQUALITIES. Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS. The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Functions. Iteration. Inverse Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS: APPLICATIONS TO OPTIMIZATION. Linear Functions. Quadratic Functions. Using Iteration to Model Populations Growth (Optional Section). Setting Up Equations That Devine Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay. 6. AN INTRODUCTION TO TRIGONOMETRY VIA RIGHT TRIANGLES. Trigonometric Functions of Acute Angles. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities. 7. THE TRIGONOMETRIC FUNCTIONS. Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry. 8. GRAPHS OF TRIGONOMETRIC FUNCTIONS. Trigonometric Functions of Real Numbers. Graphs of the Sine and Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx-C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions. 9. ANALYTICAL TRIGONOMETRY. The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions. 10. ADDITIONAL TOPICS IN TRIGONOMETRY. Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane: A Geometric Approach. Vectors in the Plane: An Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates. DeMoivre's Theorem. 11. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities. 12. THE CONIC SECTIONS. The Basic Equations. The Parabola. Tangents to Parabolas (Optional Section). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes. 13. ROOTS OF POLYNOMIAL EQUATIONS. Division of Polynomials. The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes's Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions. 14. ADDITIONAL TOPICS IN ALGEBRA. Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. Introduction to Limits. Appendix A.1: Significant Digits. Appendix A.2: ���2 is Irrational. Appendix A.3: The Complex Number System. Answers. Index.
£308.75
Taylor & Francis Ltd Generalized Functions Operator Theory and
Book SynopsisNobel prize winner Ilya Prigogine writes in his preface: Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory. Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume. This compilation of works grew out of material presented at the Hyperfunctions, Operator Theory and Dynamical Systems symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficuTable of ContentsPart I: Generalized Functions and Operator TheoryAn Introduction to Hyperfunctions and ?-expansions, G. LumerPartial Inner Product Spaces of Analytic Functions, J.-P. AntoineRigged Spectral States: A Proclivity for Eigenvalues, K. GustafsonDensities of Singular Measures and Generalized Spectral Decompositions, I. Antoniou and Z. SuchaneckiConvolution Kernels and Generalized Functions, B. Bäumer, G. Lumer, and F. NeubranderSpectral Theory of Closed Linear Operators on Banach Spaces from a Locally Convex Point of View, V. WrobelUltradistributions and the Levinson Condition, I. Cioranescu and L. ZsidoRepresentation of the Derivatives and Products of the Delta Function in Hilbert Space, Yu. MelnikovSeries Representations of the Complex Delta Function, I. Antoniou, Z. Suchanecki, and S. TasakiAntieigenvalues: An Extended Spectral Theory, K. GustafsonPart II: Operator Theory and Dynamical SystemsLaws of Nature, Probability, and Time Symmetry Breaking, I. Prigogine and T. PetroskyExtended Spectral Decompositions of Evolution Operators, I. Antoniou and S. ShkarinSome Little Things About Rigged Hilbert Spaces and Quantum Mechanics and All That, A. Bohm, M. Gadella, and S. WickramasekaraAxiomatics of Thermodynamics and Quantum Chaos, V. MaslovStochastic Evolution on Product Manifolds. S. Albeverio, A. Daletskii, and Yu. KondratievInteraction Problems with Distributions and Hyperfunctions Data, G. LumerAbsolute Continuity of Convolutions of Singular Measures and New Branches of Spectrum of Liouvillians and Few-Body Hamiltonians, L Bos and B PavlovOn Scattering Theories Involving Moving Boundaries, G. F. RoachThe Eigenvalue Problem for Networks of Beams, B Dekoninck and S NicaiseGeneralized Perturbations and Operator Relations, P Kurasov and B PavlovOn Spectral Analysis of a Class of Integral-Difference Collision Operators, Yu. MelnikivDynamical Aspects of Processes with Long-Range Memor
£166.25
CRC Press Dynamical Systems
Book SynopsisSeveral distinctive aspects make Dynamical Systems unique, including:treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student focusing on multidimensional systems of real variablesThe book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects.Trade Review"…was impressed with the teachability of this text and with the exercises at the end of each chapter, which seemed be nicely graded in difficulty."-D. Givoli, APPLIED MECHANICS REVIEWSTable of ContentsIntroductionOne Dimensional Dynamics by IterationChaos and Its MeasurementLinear SystemsAnalysis near Fixed Points and Periodic OrbitsHamiltonian SystemsBifurcation of Periodic PointsExamples of Hyperbolic Sets and AttractorsMeasurement of Chaos in Higher DimensionsGlobal Theory of Hyperbolic SystemsGeneric PropertiesSmoothness of Stable Manifolds and Applications
£175.75
MP-AMM American Mathematical Discovering Discrete Dynamical Systems
Book Synopsis
£46.80
Society for Industrial and Applied Mathematics Optimization and Nonsmooth Analysis By Frank H
Book SynopsisMathematical Reviews said of this book that it was 'destined to become a classical reference.' This book has appeared in Russian translation and has been praised both for its lively exposition and its fundamental contributions. The author first develops a general theory of nonsmooth analysis and geometry which, together with a set of associated techniques, has had a profound effect on several branches of analysis and optimization. Clarke then applies these methods to obtain a powerful, unified approach to the analysis of problems in optimal control and mathematical programming. Examples are drawn from economics, engineering, mathematical physics, and various branches of analysis in this reprint volume.
£49.99
SIAM - Society for Industrial and Applied Mathematics Introduction to Matrix Analysis Classics in
Book SynopsisWritten in lurid, concise terms, this book has long been considered to be a classic in its field, this was the first book in English to include three basic fields of the analysis of matrices - symmetric matrices and quadratic forms, matrices and differential equations, and positive matrices and their use in probability theory and mathematical economics.
£58.05
Society for Industrial and Applied Mathematics Convex Analysis and Variational Problems Classics
Book SynopsisNo one working in duality should be without a copy of Convex Analysis and Variational Problems. This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.
£55.00
Cambridge University Press Counterexamples in Measure and Integration
Book SynopsisOften it is more instructive to know ''what can go wrong'' and to understand ''why a result fails'' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling''s other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).Trade Review'This book is an admirable counterpart, both to the first author's well-known text Measures, Integrals and Martingales (Cambridge, 2005/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase the authors' preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.' N. H. Bingham, Imperial College'… an excellent reference text and companion reader for anyone interested in deepening their understanding of measure theory.' John Ross, MAA Reviews'… the unique nature of the book makes it an essential acquisition for any university with a doctoral program in pure mathematics … Essential.' M. Bona, Choice Connect'The book is well written, the demonstrations are clear and the bibliographic references are competent. We appreciate this work as extremely useful for those interested in measure theory and integration, starting with beginners and extending even to advanced researchers in the field.' Liviu Constantin Florescu, Mathematical Reviews/MathSciNet'Counterexamples in Measure and Integration is an ideal companion to help better understand canonically problematic examples in analysis … This collection of counterexamples is an excellent resource to researchers who rely on measure and integration theory. It would be helpful for students studying for their analysis qualifying exam as it draws on common misconceptions and enables readers to build intuition about why a given counterexample works and how conditions can be changed to make a particular statement hold.' Katelynn Kochalski, Notices of the AMS'This is a remarkable book covering Measure and Integration, perhaps one of the most important parts of Mathematics. It is written in a master style by following the best traditions in writing this kind of books. The authors are passionate about the topic. Look at the great care with which each of the counterexamples is presented. It is done in a way to help maximally the reader. The names of the counterexamples are chosen very carefully. Any name can be considered as a 'door' behind which is a treasure!' Jordan M. Stoyanov, zbMATH'… compendia of counterexamples remain a useful and thought-provoking resource, and this new text is a high-quality example in an analytic direction.' Dominic Yeo, The Mathematical GazetteTable of ContentsPreface; User's guide; List of topics and phenomena; 1. A panorama of Lebesgue integration; 2. A refresher of topology and ordinal numbers; 3. Riemann is not enough; 4. Families of sets; 5. Set functions and measures; 6. Range and support of a measure; 7. Measurable and non-measurable sets; 8. Measurable maps and functions; 9. Inner and outer measure; 10. Integrable functions; 11. Modes of convergence; 12. Convergence theorems; 13. Continuity and a.e. continuity; 14. Integration and differentiation; 15. Measurability on product spaces; 16. Product measures; 17. Radon–Nikodým and related results; 18. Function spaces; 19. Convergence of measures; References; Index.
£41.93
Cambridge University Press Functional Analysis
Book SynopsisThis textbook is designed for a year-long introductory course in Functional Analysis and the theory of Operator Algebras. It guides graduate students and researchers through a wide range of topics including Hilbert spaces, Weak Topologies and C*-algebras. With numerous problems and examples, it is suitable for classroom teaching and self-learning.Table of ContentsPreface; Notation; 1. Preliminaries; 2. Normed Linear Spaces; 3. Hilbert Spaces; 4. Dual Spaces; 5. Operators on Banach Spaces; 6. Weak Topologies; 7. Spectral Theory; 8. C*-Algebras; 9. Measure and Integration; 10. Normal Operators on Hilbert Spaces; Appendices; A.1 The Stone–Weierstrass Theorem; A.2 The Radon–Nikodym Theorem; Bibliography; Index.
£37.99
Taylor & Francis Ltd A First Course in Ergodic Theory
Book SynopsisA First Course in Ergodic Theory provides readers with an introductory course in Ergodic Theory. This textbook has been developed from the authorsâ own notes on the subject, which they have been teaching since the 1990s. Over the years they have added topics, theorems, examples and explanations from various sources. The result is a book that is easy to teach from and easy to learn from â designed to require only minimal prerequisites.Features Suitable for readers with only a basic knowledge of measure theory, some topology and a very basic knowledge of functional analysis Perfect as the primary textbook for a course in Ergodic Theory Examples are described and are studied in detail when new properties are presented. Trade Review"A First Course in Ergodic Theory by Dajani and Kalle provides not only a crystal clear introduction to the core of ergodic theory, but also goes down paths previously accessible only through the research literature. The book covers ergodic theorems, invariant measures, entropy and the variational principle. But it also covers piecewise monotone interval maps, Perron-Frobenius operators, natural extensions, and the useful lemma of Knopp. Another theme is the theory of conservative nonsingular and infinite measure preserving transformations. All of this is illustrated via numerous examples from (not necessarily regular) continued fractions and other number expansions, the authors’ specialty. Throughout the book, the proofs patiently explain details often ignored. An excellent appendix provides a reference to needed results from topology, measure theory, probability and functional analysis."– E. Arthur (Robbie) Robinson, Jr., Professor of Mathematics at George Washington University and co-author of The Mathematics of Politics"This textbook is a delightful introduction to Ergodic Theory. It starts at a basic level, giving intuitive explanations and motivations, and concludes with more advanced topics such as variational principle and infinite ergodic theory. The style is very crisp, and many of the results are proved. Examples which are primarily taken from number theory run as a red thread through the manuscript. This makes this textbook quite different from other classic textbooks on the subject. It’s very easy to build an advanced UG or a postgraduate lecture course around this material."– Sebastian van Strien, Imperial College LondonTable of ContentsPreface. Author Bios. 1. Measure preservingness and basic examples. 1.1. What is Ergodic Theory. 1.2. Measure Preserving Transformations. 1.3. Basic Examples. 2. Recurrence and Ergodicity. 2.1. Recurrence. 2.2. Ergodicity. 2.3. Examples of Ergodic Transformations. 3. The Pointwise Ergodic Theorem and its consequences. 3.2. Normal Numbers. 3.3. Characterization of Irreducible Markov Chains. 3.4. Mixing. 4. More Ergodic Theorem. The mean Ergodic Theorem. 4.2. The Hurewicz Erogdic Theorem. 5. Measure Preserving Isomorphisms. 5.2. Factor Maps. 5.3. Natural Extensions. 6. The Perron–Frobenius Operator. 6.1. Absolutely Continuous Invariants Measures. 6.2. Exactness. Densities for Piecewise Monotnoe Interval Maps. 7. Invariant Measures for Continuous Transformations. 7.1. Existence. 7.2. Unique Ergodicity and Inform Distributions. 7.3. Some Topological Dynamics. 8. Continued Fractions. 8.1. Basic Properties of Regular Continue Fractions. 8.2. Ergodic Properties of Gauss Map. 8.3. Natural Extension and the Doeblin–Lenstra Conjecture. 8.4. Other Continue Fraction Transformation. 9. Entropy. 9.1. Randomness and Information. 9.2. Definitions and Properties. Calculation of Entropy and Examples. 9.4. The Shannon–McMillan–Breiman Theorem. 9.5. Lochs’ Theorem. 10. The Variational Principle. 10.1 Topological Entropy. 10.2. Main Theorem. 10.3. Measures of Maximal Entropy. 11. Infinite Ergodic Theory. 11.1 Examples of Infinite Measure Dynamical Systems. 11.2. Conservative and Dissipative Part. 11.3. Induced Systems. 11.4. Jump Transformations. 11.5. Ergodic Theorem for Infinite Measure Systems. 12. Appendix. 12.1. Topology. 12.2. Measure Theory. 12.3 Lebesgue Spaces. 12.4. Lebesgue Integration and Convergence Results. 12.5. Hilbert’s Spaces. 12.6. Borel Measures on Compact Metric Spaces. 12.7. Functions of Bounded Variation. Bibliography. Index.
£43.69
Taylor & Francis Ltd Quaternion and Clifford Fourier Transforms
Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth.The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and
£43.69
Taylor & Francis Ltd Real Analysis and Foundations
Book SynopsisThrough four editions this popular textbook attracted a loyal readership and widespread use. Students find the book to be concise, accessible, and complete. Instructors find the book to be clear, authoritative, and dependable. The primary goal of this new edition remains the same as in previous editions. It is to make real analysis relevant and accessible to a broad audience of students with diverse backgrounds while also maintaining the integrity of the course. This text aims to be the generational touchstone for the subject and the go-to text for developing young scientists. This new edition continues the effort to make the book accessible to a broader audience. Many students who take a real analysis course do not have the ideal background. The new edition offers chapters on background material like set theory, logic, and methods of proof. The more advanced material in the book is made more apparent.This new edition offers a new chapter on metric spaces and their applications. Metric spaces are important in many parts of the mathematical sciences, including data mining, web searching, and classification of images. The author also revised the material on sequences and series adding examples and exercises that compare convergence tests and give additional tests.The text includes rare topics such as wavelets and applications to differential equations. The level of difficulty moves slowly, becoming more sophisticated in later chapters. Students have commented on the progression as a favorite aspect of the textbook.The author is perhaps the most prolific expositor of upper division mathematics. With over seventy books in print, thousands of students have been taught and learned from his books.
£54.14
CRC Press Map of the World
Book SynopsisCarl Friedrich Gauss, the foremost of mathematicians, was a land surveyor. Measuring and calculating geodetic networks on the curved Earth was the inspiration for some of his greatest mathematical discoveries. This is just one example of how mathematics and geodesy, the science and art of measuring and mapping our world, have evolved together throughout history.This text is for students and professionals in geodesy, land surveying, and geospatial science who need to understand the mathematics of describing the Earth and capturing her in maps and geospatial data: the discipline known as mathematical geodesy. Map of the World: An Introduction to Mathematical Geodesy aims to provide an accessible introduction to this area, presenting and developing the mathematics relating to maps, mapping, and the production of geospatial data. Described are the theory and its fundamental concepts, its application for processing, analyzing, transforming, and projecting geospatial data, and how these are used in producing charts and atlases. Also touched upon are the multitude of cross-overs into other sciences sharing in the adventure of discovering what our world really looks like.FEATURESâ Written in a fluid and accessible style, replete with exercises; adaptable for courses on different levels.â Suitable for students and professionals in the mapping sciences, but also for lovers of maps and map making.Trade Review"Map of the World: An Introduction to Mathematical Geodesy is organized, written and presented in an impressively accessible style that is replete with exercises -- making it highly adaptable textbook for curriculum courses on different levels. Especially and unreservedly recommended for students and professionals in the mapping sciences, Map of the World will prove to be an ideal and instructive source for non-specialist readers with an interest in maps and map making. While a critically important addition to college and university library collections, it should be noted for personal reading lists that Maps of the World is also available in a digital book format."—Midwest Book Review"This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application. [. . .] This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. [. . .] this is a concise review of the theory and development of coordinate reference systems."—Tom Schulte, MAA Reviews ". . .(T)his text, by a geodesist (Vermeer) and a mathematician (Rasila), focuses primarily on the mathematics enabling map projections, coordinate systems, and transformation of three-dimensional coordinate representations, ranging from Euclidean to Reimannian geometries. Although the geometry is beyond what most geography students would need to address, the detailed mathematics offers a bridge for integration of collaborative teaching appropriate for upper-level mathematics and physics students, with applications to both cartography and geophysics. Each chapter concludes with exercises that provide an opportunity for learning the explicit mathematics behind the calculation presented. Interesting historical anecdotes about mathematicians and the evolution of geodesy are also included throughout. Students and readers of mathematics and geophysics as well as scientists working in the interdisciplinary area of geodesy will appreciate this book."– Choice Review, C. A. Badurek, SUNY Cortland"Map of the World: An Introduction to Mathematical Geodesy is organized, written and presented in an impressively accessible style that is replete with exercises -- making it highly adaptable textbook for curriculum courses on different levels. Especially and unreservedly recommended for students and professionals in the mapping sciences, Map of the World will prove to be an ideal and instructive source for non-specialist readers with an interest in maps and map making. While a critically important addition to college and university library collections, it should be noted for personal reading lists that Maps of the World is also available in a digital book format."—Midwest Book Review"This is a textbook covering mathematics applied to geodesy: the measuring and mapping of our ellipsoid spheroid earth that includes an overview of earth measurement and mapping back to remote times. The mathematics of describing the Earth through maps and geospatial data is covered from underpinnings to application. [. . .] This textbook, including some exercises (without solutions), is aimed at students and practitioners in geodesy, land surveying, and geospatial science. It is easy to see this as a reference work. [. . .] this is a concise review of the theory and development of coordinate reference systems."—Tom Schulte, MAA Reviews Table of Contents1. A Brief History of Mapping. 2. Popular Conformal Map Projections. 3. The Complex Plane and Conformal Mappings. 4. Complex Analysis. 5. Conformal Mappings. 6. Transversal Mercator Projections. 7. Sperical Trigonometry. 8. The Geometry of the Ellipsoid of Revolution. 9. Three-dimensional Co-ordinates and Transformations. 10. Co-ordinate Reference Systems. 11. Co-ordinates of Heaven and Earth. 12. The Orbital Motion of Satellites. 13. The Surface Theory of Gauss. 14. Riemann Surfaces and Charts. 15. Map Projections in the Light of Surface Theory. 16. Appendices
£39.99
Taylor & Francis Ltd Partial Differential Equations
Book SynopsisPartial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners' course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The teaching-by-examples approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book's level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses. Highlights: Table of Contents Introduction Basic definitions Examples First-order equations Linear first-order equations General solution Initial condition Quasilinear first-order equations Characteristic curves Examples Second-order equations Classification of second-order equations Canonical forms Hyperbolic equations Elliptic equations Parabolic equations The Sturm-Liouville Problem General consideration Examples of Sturm-Liouville Problems One-Dimensional Hyperbolic Equations Wave Equation Boundary and Initial Conditions Longitudinal Vibrations of a Rod and Electrical Oscillations Rod oscillations: Equations and boundary conditions Electrical Oscillations in a Circuit Traveling Waves: D'Alembert Method Cauchy problem for nonhomogeneous wave equation D'Alembert's formula The Green's function Well-posedness of the Cauchy problem Finite intervals: The Fourier Method for Homogeneous Equations The Fourier Method for Nonhomogeneous Equations The Laplace Transform Method: simple cases Equations with Nonhomogeneous Boundary Conditions The Consistency Conditions and Generalized Solutions Energy in the Harmonics Dispersion of waves Cauchy problem in an infinite region Propagation of a wave train One-Dimensional Parabolic Equations Heat Conduction and Diffusion: Boundary Value Problems Heat conduction Diffusion equation One-dimensional parabolic equations and initial and boundary conditions The Fourier Method for Homogeneous Equations Nonhomogeneous Equations The Green's function and Duhamel's principle The Fourier Method for Nonhomogeneous Equations with Nonhomogeneous Boundary Conditions Large time behavior of solutions Maximum principle The heat equation in an infinite region Elliptic equations Elliptic differential equations and related physical problems Harmonic functions Boundary conditions Example of an ill-posed problem Well-posed boundary value problems Maximum principle and its consequences Laplace equation in polar coordinates Laplace equation and interior BVP for circular domain Laplace equation and exterior BVP for circular domain Poisson equation: general notes and a simple case Poisson Integral Application of Bessel functions for the solution of Poisson equations in a circle Three-dimensional Laplace equation for a cylinder Three-dimensional Laplace equation for a ball Axisymmetric case Non-axisymmetric case BVP for Laplace Equation in a Rectangular Domain The Poisson Equation with Homogeneous Boundary Conditions Green's function for Poisson equations Homogeneous boundary conditions Nonhomogeneous boundary conditions Some other important equations Helmholtz equation Schrӧdinger equation Two Dimensional Hyperbolic Equations Derivation of the Equations of Motion Boundary and Initial Conditions Oscillations of a Rectangular Membrane The Fourier Method for Homogeneous Equations with Homogeneous Boundary Conditions The Fourier Method for Nonhomogeneous Equations with Homogeneous Boundary Conditions The Fourier Method for Nonhomogeneous Equations with Nonhomogeneous Boundary Conditions Small Transverse Oscillations of a Circular Membrane The Fourier Method for Homogeneous Equations with Homogeneous Boundary Conditions Axisymmetric Oscillations of a Membrane The Fourier Method for Nonhomogeneous Equations with Homogeneous Boundary Conditions Forced Axisymmetric Oscillations The Fourier Method for Equations with Nonhomogeneous Boundary Conditions Two-Dimensional Parabolic Equations Heat Conduction within a Finite Rectangular Domain The Fourier Method for the Homogeneous Heat Equation (Free Heat Exchange) The Fourier Method for Nonhomogeneous Heat Equation with Homogeneous Boundary conditions Heat Conduction within a Circular Domain The Fourier Method for the Homogeneous Heat Equation The Fourier Method for the Nonhomogeneous Heat Equation Heat conduction in an Infinite Medium Heat Conduction in a Semi-Infinite Medium Nonlinear equations Burgers equation Kink solution Symmetries of the Burgers equation General solution of the Cauchy problem. Interaction of kinks Korteweg-de Vries equation Symmetry properties of the KdV equation Cnoidal waves Solitons Bilinear formulation of the KdV equation Hirota's method Multisoliton solutions Nonlinear Schrӧdinger equation Symmetry properties of NSE Solitary waves Appendix A. Fourier Series, Fourier and Laplace Transforms Appendix B. Bessel and Legendre Functions Appendix C. Sturm-Liouville problem and auxiliary functions for one and two dimensions Appendix D. D1. The Sturm-Liouville problem for a circle D2. The Sturm-Liouville problem for the rectangle Appendix E. E1. The Laplace and Poisson equations for a rectangular domain with nonhomogeneous boundary conditions. E2. The heat conduction equations with nonhomogeneous boundary conditions.
£43.99
Taylor & Francis Ltd Principles of Analysis
Book SynopsisPrinciples of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level. The book also helps them prepare for qualifying exams in real analysis. It is designed so that the reader or instructor may select topics suitable to their needs. The author presents the text in a clear and straightforward manner for the readers' benefit. At the same time, the text is a thorough and rigorous examination of the essentials of measure, integration and functional analysis.The book includes a wide variety of detailed topics and serves as a valuable reference and as an efficient and streamlined examination of advanced real analysis. The text is divided into four distinct sections: Part I develops the general theory of Lebesgue integration; Part II is organized as a course in functional analysis; Part IITrade Review"The author's aim for the book under review is to provide a rigorous and detailed treatment of the essentials of measure and integration, as well as other topics in functional analysis at the graduate level. Although he assumes readers to have an undergraduate background, such as real analysis (including some experience in dealing with limits, continuity, di erentiation, Riemann integration, and uniform convergence, including elementary set theory), a standard course of complex analysis (function theory, Cauchy's integral equation), and a knowledge of basic linear algebra, this book could also be very useful for a reader with a weaker mathematical background. This is possible since the excellently constructed introduction in Chapter 0 is a very good base for systematizing and developing the mathematical background for a broad group of readers. The book is divided into four parts.In Part I, which consists of Chapters 1{7, the author develops a detailed course concerning the general theory of Lebesgue integration as well as Fourier analysis on Rd (Chapter 6) and measures on locally compact spaces (Chapter 7). A short course on the general theory of Lebesgue integration could be based on Chapters 1{5 only but the full variant looks more attractive. It must be noted that the author's exposition is on a very high level as well as very clear and easily understandable.Part II is presented as a course in functional analysis. The author considers Chapters 8{12 to be the core of such a course. Chapter 13 could be an optional choice, but can be also included in the course. Chapter 14 plays an important role concerning Part I and Part II. This chapter includes not only deeper theorems in functional analysis but also several well-chosen applications. Note that some of them are related to the measure and integration developed in Part I and the others with the applications in the remainder of the book.Part III (Chapters 15{17) is a key part in the book since it includes many topics and applications that depend on, and indeed are meant to illustrate, the power of topics developed in the first two parts. It must be noted that these chapters are almost independent. Their goal is to provide a relatively quick overview of the subjects treated therein. The detailed exposition that this approach allows means that the reader can follow the development with relative ease. In addition to allowing the reader to consult the themes considered, some specialized sources are listed in the bibliography.Part IV consists of two appendices with proofs of the change of variables theorem and a theorem on separate and joint continuity. A reader may choose to safely omit the proofs without disturbing the flow of the text, as the author notes. An advantage for the readers is that the book contains a lot of exercises (nearly 700). It is very convenient that hints and/or a framework of intermediate steps are given for the more di□cult exercises. Many of these are extensions of material in the text or are of special independent interest. Additionally, the exercises related in a critical way to material elsewhere in the text are marked with either an upward arrow, referring to earlier results, or a downward arrow, referring to later material. Instructors may obtain complete solutions to theexercises from the publisher.In conclusion, I strongly recommend the book because it will be helpful for every level of reader. I only regret that it was not written when I was a student."- Andrey I. Zahariev - Mathematical Reviews Clippings February 2019Table of ContentsMeasurable Sets. Measurable Functions. Integration. Further Topics in Measure Theory. Banach Spaces. Hilbert Spaces. Locally Convex Spaces. Banach Algebras. Harmonic Analysis on Locally Compact Groups. Probability Theory. Operator Theory. Appendices.
£41.79
Taylor & Francis Ltd Differential Calculus in Several Variables
Book SynopsisThe aim of this book is to lead the reader out from the ordinary routine of computing and calculating by engaging in a more dynamic process of learning. This Learning-by-Doing Approach can be traced back to Aristotle, who wrote in his Nicomachean Ethics that âœFor the things we have to learn before we can do them, we learn by doing themâ.The theory is illustrated through many relevant examples, followed by a large number of exercises whose requirements are rendered by action verbs: find, show, verify, check and construct. Readers are compelled to analyze and organize analytical skills.Rather than placing the exercises in bulk at the end of each chapter, sets of practice questions after each theoretical concept are included. The reader has the possibility to check their understanding, work on the new topics and gain confidence during the learning activity. As the theory unfolds, the exercises become more complex â sometimes they span over several topics. Hints have been added in order to guide the reader in the process.This book stems from the Differential Calculus course which the author taught for many years. The goal of this book is to immerse the reader in the subtleties of Differential Calculus through an active perspective. Particular attention was paid to continuity and differentiability topics, presented in a new course of action.Table of ContentsCh 1. Vectors and Sets Ch 2. Functions of several variables Ch 3. Limits and continuity Ch 4. Differentiable functions Ch 5. Chain rule and the Mean Value Theorem Ch 6. Directional derivative Ch 7. Higher order derivatives Ch 8. Taylor’s theorem and approximations Ch 9. Inverse and Implicit Function Theorem Ch 10. Maxima and Minima Ch 11. Constrained optimisation and applications Ch 12. Solutions
£49.39
CRC Press Measure and Integral
Book SynopsisThis accessible introduction to the topic covers the theory of measure and integral, as introduced by Lebesgue and developed in the first half of the 20th century. It leads naturally to Banach spaces of functions and linear operators acting on them.This material in Measure and Integral: Theory and Practice is typically covered in a graduate course and is almost always treated in an abstract way, with little or no motivation. The author employs a plethora of examples and exercises and strives to motivate every concept with its historical background. This textbook is accessible to a wider range of students, including at the undergraduate level.A major problem facing anyone teaching measure theory is how to combine the elementary approach (measure on the real line or in the plane) and the abstract measure theory. The author develops a theory of measure in the plane, then shows how to generalize these ideas to an abstract setting.The result is a textbook accessible to a wider range of students.The material requires a good understanding of topics often referred to as advanced calculus, such as Riemann integration on Euclidean spaces and series of functions. Also, a reader is expected to be proficient in the basics of set theory and point-set topology, preferably including metric spaces.
£999.99
CRC Press Gaussian Integrals and their Applications
Book SynopsisGaussian Integrals form an integral part of many subfields of applied mathematics and physics, especially in topics such as probability theory, statistics, statistical mechanics, quantum mechanics and so on. They are essential in computing quantities such as the statistical properties of normal random variables, solving partial differential equations involving diffusion processes, and gaining insight into the properties of particles. In Gaussian Integrals and their Applications, the author has condensed the material deemed essential for undergraduate and graduate students of physics and mathematics, such that for those who are very keen would know what to look for next if their appetite for knowledge remains unsatisfied by the time they finish reading this book. Features A concise and easily digestible treatment of the essentials of Gaussian Integrals Suitable for advanced undergraduates and graduate students in mathematics
£48.99
CRC Press A Course in Abstract Harmonic Analysis
Book SynopsisA Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right. This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its app
£54.14
Springer New York Numerical Approximation of Hyperbolic Systems of
Book SynopsisThis monograph is devoted to the theory and approximation by finite volume methods of nonlinear hyperbolic systems of conservation laws in one or two space variables.Table of ContentsNonlinear hyperbolic systems in one space dimension.- Gas dynamics and reacting flows.- Finite volume schemes for one-dimensional systems.- The case of multidimensional systems.- An introduction to boundary conditions.- Source terms.
£143.99
Cambridge University Press Normal Approximations with Malliavin Calculus From Steins Method to Universality 192 Cambridge Tracts in Mathematics Series Number 192
Book SynopsisStein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, BreuerâMajor theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wiTrade Review'This monograph is a nice and excellent introduction to Malliavin calculus and its application to deducing quantitative central limit theorems in combination with Stein's method for normal approximation. It provides a self-contained and appealing presentation of the recent work developed by the authors, and it is well tailored for graduate students and researchers.' David Nualart, Mathematical Reviews'The book contains many examples and exercises which help the reader understand and assimilate the material. Also bibliographical comments at the end of each chapter provide useful references for further reading.' Bulletin of the American Mathematical SocietyTable of ContentsPreface; Introduction; 1. Malliavin operators in the one-dimensional case; 2. Malliavin operators and isonormal Gaussian processes; 3. Stein's method for one-dimensional normal approximations; 4. Multidimensional Stein's method; 5. Stein meets Malliavin: univariate normal approximations; 6. Multivariate normal approximations; 7. Exploring the Breuer–Major Theorem; 8. Computation of cumulants; 9. Exact asymptotics and optimal rates; 10. Density estimates; 11. Homogeneous sums and universality; Appendix 1. Gaussian elements, cumulants and Edgeworth expansions; Appendix 2. Hilbert space notation; Appendix 3. Distances between probability measures; Appendix 4. Fractional Brownian motion; Appendix 5. Some results from functional analysis; References; Index.
£68.39
Cambridge University Press A Basic Course in Measure and Probability Theory
Book SynopsisOriginating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a two-term course or for self-study. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'take-off point' for them as they specialize in areas that exploit mathematical machinery.Table of ContentsPreface; Acknowledgements; 1. Point sets and certain classes of sets; 2. Measures: general properties and extension; 3. Measurable functions and transformations; 4. The integral; 5. Absolute continuity and related topics; 6. Convergence of measurable functions, Lp-spaces; 7. Product spaces; 8. Integrating complex functions, Fourier theory and related topics; 9. Foundations of probability; 10. Independence; 11. Convergence and related topics; 12. Characteristic functions and central limit theorems; 13. Conditioning; 14. Martingales; 15. Basic structure of stochastic processes; References; Index.
£108.75
Cambridge University Press A Course in Mathematical Analysis Volume 2 A
Book SynopsisThe three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.Table of ContentsIntroduction; Part I. Metric and Topological Spaces: 1. Metric spaces and normed spaces; 2. Convergence, continuity and topology; 3. Topological spaces; 4. Completeness; 5. Compactness; 6. Connectedness; Part II. Functions of a Vector Variable: 7. Differentiating functions of a vector variable; 8. Integrating functions of several variables; 9. Differential manifolds in Euclidean space; Appendix A. Linear algebra; Appendix B. Quaternions; Appendix C. Tychonoff's theorem; Index.
£89.30
Cambridge University Press Probability The Classical Limit Theorems
Book SynopsisProbability theory has been extraordinarily successful at describing a variety of phenomena, from the behaviour of gases to the transmission of messages, and is, besides, a powerful tool with applications throughout mathematics. At its heart are a number of concepts familiar in one guise or another to many: Gauss' bell-shaped curve, the law of averages, and so on, concepts that crop up in so many settings they are in some sense universal. This universality is predicted by probability theory to a remarkable degree. This book explains that theory and investigates its ramifications. Assuming a good working knowledge of basic analysis, real and complex, the author maps out a route from basic probability, via random walks, Brownian motion, the law of large numbers and the central limit theorem, to aspects of ergodic theorems, equilibrium and nonequilibrium statistical mechanics, communication over a noisy channel, and random matrices. Numerous examples and exercises enrich the text.Trade Review'… packs a great deal of material into a moderate-sized book, starting with a synopsis of measure theory and ending with a taste of current research into random matrices and number theory. The book ranges more widely than the title might suggest … There are numerous exercises sprinkled throughout the book. Most of these are exhortations to fill in details left out of the main discussion or illustrative examples. The exercises are a natural part of the book, unlike the exercises in so many books that were apparently grafted on after-the-fact at a publisher's insistence. McKean has worked in probability and related areas since obtaining his PhD under William Feller in 1955. His book contains invaluable insights from a long career.' John D. Cook, MAA Reviews'The scope is wide, not restricted to 'elementary facts' only. There is an abundance of pretty details … This book is highly recommendable …' Jorma K. Merikoski, International Statistical ReviewTable of ContentsPreface; 1. Preliminaries; 2. Bernoulli trials; 3. The standard random walk; 4. The standard random walk in higher dimensions; 5. LLN, CLT, iterated log, and arcsine in general; 6. Brownian motion; 7. Markov chains; 8. The ergodic theorem; 9. Communication over a noisy channel; 10. Equilibrium statistical mechanics; 11. Statistical mechanics out of equilibrium; 12. Random matrices; Bibliography; Index.
£126.90
Cambridge University Press Calculus for the Ambitious
Book SynopsisThis short introduction is perfect for any 16- to 18-year-old, about to begin studies in mathematics, or anyone who would like to see a different account of the calculus from that given in the standard texts. Easy to read, this book will enthuse a new generation of mathematicians.Table of ContentsIntroduction; 1. Preliminary ideas; 2. The integral; 3. Functions, old and new; 4. Falling bodies; 5. Compound interest and horse kicks; 6. Taylor's theorem; 7. Approximations, good and bad; 8. Hills and dales; 9. Differential equations via computers; 10. Paradise lost; 11. Paradise regained; Bibliography; Index.
£95.40
Cambridge University Press Lectures on Lyapunov Exponents Cambridge Studies in Advanced Mathematics
Book SynopsisThe theory of Lyapunov exponents originated over a century ago in the study of the stability of solutions of differential equations. Written by one of the subject's leading authorities, this book is both an account of the classical theory, from a modern view, and an introduction to the significant developments relating the subject to dynamical systems, ergodic theory, mathematical physics and probability. It is based on the author's own graduate course and is reasonably self-contained with an extensive set of exercises provided at the end of each chapter. This book makes a welcome addition to the literature, serving as a graduate text and a valuable reference for researchers in the field.Table of ContentsPreface; 1. Introduction; 2. Linear cocycles; 3. Extremal Lyapunov exponents; 4. Multiplicative ergodic theorem; 5. Stationary measures; 6. Exponents and invariant measures; 7. Invariance principle; 8. Simplicity; 9. Generic cocycles; 10. Continuity; References; Index.
£52.24
Cambridge University Press Linear Algebra
Book SynopsisLinear Algebra offers a unified treatment of both matrix-oriented and theoretical approaches to the course, which will be useful for classes with a mix of mathematics, physics, engineering, and computer science students. Major topics include singular value decomposition, the spectral theorem, linear systems of equations, vector spaces, linear maps, matrices, eigenvalues and eigenvectors, linear independence, bases, coordinates, dimension, matrix factorizations, inner products, norms, and determinants.Trade Review'This is a book for anyone who wants to really understand linear algebra. Instead of mere cookbook recipes or dry proofs, it provides explanations, examples, pictures - and, yes, algorithms and proofs too, but only after the reader is able to understand them. And while it is aimed at beginners, even experts will have something to learn from this book.' John Baez, University of California, Riverside'This is an exciting and entertaining book. It keeps an informal tone, but without sacrificing accuracy or clarity. It takes care to address common difficulties (and the classroom testing shows), but without talking down to the reader. It uses the modern understanding of how to do linear algebra right, but remains accessible to first-time readers.' Tom Leinster, University of Edinburgh'Linear algebra is one of the most important topics in mathematics, as linearity is exploited throughout applied mathematics and engineering. Therefore, the tools from linear algebra are used in many fields. However, they are often not presented that way, which is a missed opportunity. The authors have written a linear algebra book that is useful for students from many fields (including mathematics). A great feature of this book is that it presents a formal linear algebra course that clearly makes (coordinate) matrices and vectors the fundamental tools for problem solving and computations.' Eric de Sturler, Virginia Polytechnic Institute and State University'It is a book well worth considering both for learning and teaching this important area of mathematics.' John Baylis, The Mathematical GazetteTable of Contents1. Linear systems and vector spaces; 2. Linear maps and matrices; 3. Linear independence, bases, and coordinates; 4. Inner products; 5. Singular value decomposition and the spectral theorem; 6. Determinants.
£54.14
