Complex analysis, complex variables Books
World Scientific Publishing Co Pte Ltd Trends In Differential Geometry, Complex Analysis
Book SynopsisThis book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa-Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.Table of ContentsA Discrete Model for Kaehler Magnetic Fields on a Complex Hyperbolic Space; A Characterization of Clifford Minimal Hypersurfaces of a Sphere in Terms of Their Geodesics; Hyperbolic Gauss Maps and Parallel Surfaces in Hyperbolic Three-Space; Generalizations of Conjugate Connections; Heisenberg Relations in the General Case; A Short Note on the Double-Complex Laplace Operator; Monogenic, Hypermonogenic and Holomorphic; Cliffordian Functions - A Survey; On Multicomponent Evolution Equations on Symmetric Spaces with Constant Boundary Conditions; Relativistic Strain and Electromagnetic Photon-Like Objects; Cyclic Hyper-Scalar Systems; Poisson Structures of Equations Associated with Groups of Diffeomorphisms; On the Lax Pair for Two and Three Wave Interaction System; New Integrable Equations of MKdV Type; Persistence of Solutions for Some Integrable Shallow Water Equations; Mathematical Outlook of Fractals and Chaos Related to Simple Orthorhombic Ising-Onsager-Zhang Lattices.
£99.00
World Scientific Publishing Co Pte Ltd Schwarz's Lemma From A Differential Geometric
Book SynopsisThe subject matter in this volume is Schwarz's Lemma which has become a crucial theme in many branches of research in mathematics for more than a hundred years to date. This volume of lecture notes focuses on its differential geometric developments by several excellent authors including, but not limited to, L Ahlfors, S S Chern, Y C Lu, S T Yau and H L Royden.This volume can be approached by a reader who has basic knowledge on complex analysis and Riemannian geometry. It contains major historic differential geometric generalizations on Schwarz's Lemma and provides the necessary information while making the whole volume as concise as ever.Table of ContentsMean-Value Properties; Maximum Principles; A Quick Introduction to Hermitian Geometry; Classical Schwarz's Lemma; Poincare' Distance and Metric; General Schwarz's Lemma by Ahlfors, Chern-Lu, Yau, Royden and Others; Almost Maximum Principle; Chern-Lu Formula; Very Recent Developments on Differential Geometric Schwarz's Lemma.
£45.60
World Scientific Publishing Co Pte Ltd Advanced Courses Of Mathematical Analysis Iv -
Book SynopsisThis proceedings is a collection of articles by front-line researchers in Mathematical Analysis, giving the reader a wide perspective of the current research in several areas like Functional Analysis, Complex Analysis and Measure Theory.The works are a fundamental source for current and future developments in these research fields. The articles and surveys have been collected as well as reference results scattered in the corresponding literature and thus, are highly useful to researchers.Table of ContentsWeyl Type Theorems in the Theory of Bounded Linear Operators; Forward Shifts Between Spaces of Continuous Functions; Algebras of Holomorphic Functions; Finitely Additive Measures; Linear Preserver Problems; Diameter Preserving Mappings; The E Property and Many Other Geometric Properties in Banach Spaces.
£99.90
World Scientific Publishing Co Pte Ltd Modern Introduction To Particle Physics, A (3rd
Book SynopsisThe book provides a comprehensive account of particle physics linking various aspects of particle physics in a coherent manner. This self-contained book not only cover basic concepts and recent developments but also overlaps between Astrophysics, Cosmology and Particle Physics, known as astroparticle physics. Several appendices are included to make the book self-contained.Table of ContentsIntroduction; Scattering and Particle Interactions; Space-Time Symmetries; Internal Symmetries; Unitary Groups and SU(3); SU(6) and Quark Model; Colors, Gauge Principle and Quantum Chromodynamics; Heavy Flavor Physics; Heavy Quark Effective Theory; Neutrinos; Weak Interactions; Properties of Weak Hadronic Currents and Chiral Symmetry; Electroweak Unification; Deep Inelastic Scattering; Weak Decays of Heavy Flavor; Particle Mixing and CP-Violation; Grand Unification; Supersymmetry and Strings; Astroparticle Physics.
£64.60
World Scientific Publishing Co Pte Ltd Stochastic Processes In Genetics And Evolution:
Book SynopsisThe scope of this book is the field of evolutionary genetics. The book contains new methods for simulating evolution at the genomic level. It sets out applications using up to date Monte Carlo simulation methods applied in classical population genetics, and sets out new fields of quantifying mutation and selection at the Mendelian level. A serious limitation of Wright-Fisher process, the assumption that population size is constant, motivated the introduction of self regulating branching processes in this book. While providing a short review of the principles of probability and its application and using computer intensive methods whilst applying these principles, this book explains how it is possible to derive new formulas expressed in terms of matrix algebra providing new insights into the classical Wright-Fisher processes of evolutionary genetics. Also covered are the development of new methods for studying genetics and evolution, simulating nucleotide substitutions of a DNA molecule and on self regulating branching processes. Components of natural selection are studied in terms of reproductive success of each genotype whilst also studying the differential ability of genotypes to compete for resources and sexual selection. The concept of the gene is also reviewed in this book, and it provides a current definition of a gene based on very recent experiments with micro-array technologies. A development of stochastic models for simulating the evolution of model genomes concludes the studies in this book. Deserving of a place on the book shelves of workers in biomathematics, applied probability, stochastic processes and statistics, as well as in bioinformatics and phylogenetics, it will also be relevant to those interested in computer simulation, and evolutionary biologists interested in quantitative methods.Table of ContentsIntroduction of Mathematical Probability; Linkage and Recombination at Multiple Linker Loci; Nucleotide Substitution Models Formulated as Markov Processes in Continuous Time; Genealogies, Coalescence and Self Regulating Branching Processes; Two Sex Multi-type Self Regulating Branching Processes in Evolutionary Genetics; Selected Topics from Molecular Genetics; Detecting Genomic Signal of Selection; Suggestions of Further Research, Reading and Viewing; and other papers.
£198.00
World Scientific Publishing Co Pte Ltd Geometry And Analysis Of Automorphic Forms Of
Book SynopsisThis volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda's 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.Table of ContentsAutomorphic Form; Birch and Swinnerton-Dyer Conjecture; Borcherds Lift; Discrete Series; Fourier Coefficient; Fourier Transform; Hermite's Constant; Newton Polygon; Oda's Period Relation; Orbital Integral; p-Adic Group; p-Divisible Group; Real Symplectic Group; Siegel Modular Form; Siegel Modular Variety; Siegel Series; Spherical Function; Voronoi's Theorem; Whittaker Function.
£123.30
World Scientific Publishing Co Pte Ltd Engineering Of Chemical Complexity
Book SynopsisThis review volume, co-edited by Nobel laureate G Ertl, provides a broad overview on current studies in the understanding of design and control of complex chemical systems of various origins, on scales ranging from single molecules and nano-phenomena to macroscopic chemical reactors. Self-organizational behavior and the emergence of coherent collective dynamics in reaction-diffusion systems, reactive soft matter and chemical networks are covered. Special attention is paid to the applications in molecular cell biology and to the problems of biological evolution, synthetic biology and design of artificial living cells. Starting with a detailed introduction on the history of research on complex chemical systems, its current state of the art and perspectives, the book comprises 19 chapters that survey the current progress in particular research fields. The reviews, prepared by leading international experts, yield together a fascinating picture of a rapidly developing research discipline that brings chemical engineering to new frontiers.Table of ContentsIntroduction: Analysis, Design and Control of Complex Chemical Systems (Alexander S Mikhailov and Gerhard Ertl); Single Molecules, Nanoscale Phenomena and Active Particles: Imaging and Manipulation of Single Molecules by Scanning Tunneling Microscopy (Leonhard Grill); Self-Organization at the Nanoscale in Far-From-Equilibrium Surface Reactions and Copolymerizations (Pierre Gaspard); Single Molecule and Collective Dynamics of Motor Protein Coupled with Mechano-Sensitive Chemical Reaction (Mitsuhiro Iwaki, Lorenzo Marcucci, Yuichi Togashi and Toshio Yanagida); Nanomotors Propelled by Chemical Reactions (Raymond Kapral); Biology of Nanobots (Wentao Duan, Ryan Pavlick and Ayusman Sen); Reaction - Diffusion Systems and Nonequilibrium Soft Matter: Wave Phenomena in Reaction - Diffusion Systems (Oliver Steinbock and Harald Engel); Self-Oscillating Polymer Gels as Smart Materials (Ryo Yoshida); Stochastic Fluctuations and Spontaneous Symmetry Breaking in the Chemotaxis Signaling System of Dicyostelium Cells (Tatsuo Shibata); Mechanochemical Pattern Formation in the Polarization of the One-Cell C. Elegans Embryo (Justin S Bois and Stephan W Grill); Oscillations and Synchronization: Synchronization of Electrochemical Oscillators (Mahesh Wickramasinghe and Istvan Z Kiss); Turbulence and Synchrony in Spatially Extended Electrochemical Oscillators (Vladimir Garcia-Morales and Katharina Krischer); Quorum Sensing and Synchronization in Populations of Coupled Chemical Oscillators (Annette F Taylor, Mark R Tinsley and Kenneth Showalter); Collective Decision-Making and Oscillatory Behaviors in Cell Populations (Koichi Fujimoto and Satoshi Sawai); Synchronization via Hydrodynamic Interactions (Franziska Kendelbacher and Holger Stark); Evolution, Synthetic Biology, and Protocells: Emergence and Selection of Biomodules: Steps in the Assembly of a Protocell (Susanna C Manrubia and Carlos Briones); From Catalytic Reaction Networks to Protocells (Kunihiko Kaneko); Constructive Approach Towards Protocells (Tadashi Sugawara, Kensuke Kurihara and Kentaro Suzuki); Network Reverse Engineering Approach in Synthetic Biology (Haoqian Zhang, Ao Liu, Yuheng Lu, Ying Sheng, Qianzhu Wu, Zhenzhen Yin, Yiwei Chen, Zairan Liu, Heng Pan and Qi Ouyang).
£117.00
World Scientific Publishing Co Pte Ltd Theta Functions And Knots
Book SynopsisThis book presents the relationship between classical theta functions and knots. It is based on a novel idea of Răzvan Gelca and Alejandro Uribe, which converts Weil's representation of the Heisenberg group on theta functions to a knot theoretical framework, by giving a topological interpretation to a certain induced representation. It also explains how the discrete Fourier transform can be related to 3- and 4-dimensional topology.Theta Functions and Knots can be read in two perspectives. Readers with an interest in theta functions or knot theory can learn how the two are related. Those interested in Chern-Simons theory will find here an introduction using the simplest case, that of abelian Chern-Simons theory. Moreover, the construction of abelian Chern-Simons theory is based entirely on quantum mechanics and not on quantum field theory as it is usually done.Both the theory of theta functions and low dimensional topology are presented in detail, in order to underline how deep the connection between these two fundamental mathematical subjects is. Hence the book is self-contained with a unified presentation. It is suitable for an advanced graduate course, as well as for self-study.Table of ContentsSome Historical Facts; A Quantum Mechanical Prototype; Surfaces and Curves; The Theta Functions Associated to a Riemann Surface; From Theta Functions to Knots; Some Results About 3- and 4-Dimensional Manifolds; The Discrete Fourier Transform and Topological Quantum Field Theory; Theta Functions and Quantum Groups; An Epilogue - Abelian Chern - Simons Theory.
£135.00
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions.Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text.Table of ContentsComplex Numbers; Elementary Functions; Complex Differentiability and the Cauchy - Riemann Equations; Contour Integration; Cauchy Integral Theorem and Its Consequences; Taylor and Laurent Series; Harmonic Functions.
£62.70
World Scientific Publishing Co Pte Ltd Friendly Approach To Complex Analysis, A
Book SynopsisThe book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series expansions.Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study. There are many figures illustrating the text.Table of ContentsComplex Numbers; Elementary Functions; Complex Differentiability and the Cauchy - Riemann Equations; Contour Integration; Cauchy Integral Theorem and Its Consequences; Taylor and Laurent Series; Harmonic Functions.
£33.25
World Scientific Publishing Co Pte Ltd Complex Analysis: An Invitation (2nd Edition)
Book SynopsisThis volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.Table of ContentsThe Residue Theorem; Picard's Two Theorems; The Riemann Mapping Theorem; Runge's Approximation Theorems; The Prime Number Theorem; Harmonic and Subharmonic Functions; Poisson's Formula; Jordan's Curve Theorem; Caratheodory's Extension Theorem; Compact Hulls, Half-plane Hulls and their Capacities; Caratheodory's Convergence Theorems; Loewner Theory in the Disc and in the Half-plane.
£76.95
World Scientific Publishing Co Pte Ltd Complex Analysis: An Invitation (2nd Edition)
Book SynopsisThis volume is an enlarged edition of a classic textbook on complex analysis. In addition to the classical material of the first edition it provides a concise and accessible treatment of Loewner theory, both in the disc and in the half-plane. Some of the new material has been described in research papers only or appears here for the first time. Each chapter ends with exercises.Table of ContentsThe Residue Theorem; Picard's Two Theorems; The Riemann Mapping Theorem; Runge's Approximation Theorems; The Prime Number Theorem; Harmonic and Subharmonic Functions; Poisson's Formula; Jordan's Curve Theorem; Caratheodory's Extension Theorem; Compact Hulls, Half-plane Hulls and their Capacities; Caratheodory's Convergence Theorems; Loewner Theory in the Disc and in the Half-plane.
£38.00
World Scientific Publishing Co Pte Ltd Evolution Equations With A Complex Spatial
Book SynopsisThis book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black-Merton-Scholes, Schrödinger and Korteweg-de Vries equations.The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought.For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane.
£67.45
World Scientific Publishing Co Pte Ltd Engineering Of Chemical Complexity Ii
Book SynopsisThis second review volume is a follow-up to the book “Engineering of Chemical Complexity” that appeared in 2013. Co-edited by the Nobel laureate Gerhard Ertl, this book provides a broad perspective over the current research aimed at understanding, the design and control of complex chemical systems of various origins, on the scales ranging from single molecules and nano-phenomena to macroscopic chemical reactors. Self-organization behavior and emergence of coherent collective dynamics in reaction-diffusion systems, in active soft matter and biochemical networks are discussed. Special attention is paid to applications in cell biology, to molecular motors and microfluidics effects. The reviews, prepared by leading international experts from the EU, USA, Russia and Japan, together yield a fascinating picture of a rapidly developing research discipline that brings chemical engineering to new frontiers.Table of ContentsOscillatory Behavior in Cellular Regulatory Networks; Chemically-Driven Biological Brownian Machines; Modeling Substrate-Based Motility of Eukaryotic Cells; Stimuli-Induced Reconfiguration and Directed Motion of Responsive Gels; From Colloid Thermophoresis to Thermophoretic Machines; Collective Motions in Populations of Microdroplets; Dissipative Patterns in Systems of Coupled Reactive Nano- and Microdroplets; Dynamics of Filaments of Scroll Waves; Control of Chemical Wave Propagation; Synchronization Phenomena during Elecrodissolution of Silicon; and other papers;
£90.25
World Scientific Publishing Co Pte Ltd Biomat 2014 - International Symposium On
Book SynopsisThis is a book of a series on interdisciplinary topics on the Mathematical and Biological Sciences. The chapters correspond to selected papers on special research themes, which have been presented at BIOMAT 2014 International Symposium on Mathematical and Computational Biology which was held in the Stefan Banach International Mathematical Centre at Bedlewo near Poznan, Poland on November 03 - 07, 2014. The treatment is both pedagogical yet advanced in order to motivate research students as well as to fulfill the requirements of professional practitioners. As in the other volumes of this series, there are new important results on the interdisciplinary fields of mathematical and biological sciences and comprehensive reviews written by prominent scientific leaders of famous research groups.Table of ContentsPopulation Dynamics: Modelling Sustainable Development for Decision Making (D Angulo, G Olivar and F Angulo); Wild Herbivores in Forests: Four Case Studies (Giorgio Sabetta and Ezio Venturino); Effect of Viral Disease in a Diffusive Plankton System (Nanda Das and Samares Pal); Pattern Recognition of Biological Phenomena: Exploration of Different Wave Patterns in a Model of the Bovine Estrous Cycle by Fourier Analysis (C Stotzel, R Ehrig, H M T Boer, J Plontzke and S Roblitz); A Spectral Similarity Measure between Time Series Applied to Identify Protein-Protein Interactions (G E Salcedo, A M Montoya and A F Arenas); Mathematical Modelling of Infectious Diseases: An Agent-based Modelling Framework to Study the Burden of Pertussis and the Impact of Preventive Measures (J-E Poirrier, C Philemotte and D Curran); Zoonotic Visceral Leishmaniasis: A Novel Model involving Dynamic Interactions of Humans, Dogs and Sandflies (H J Shimozako, Jianhong Wu and E Massad); Mathematical Models for Vaccination, Waning Immunity and Immune System Boosting: A General Framework (M V Barbarossa and G Rost); What is the Optimal Level of Information Dissemination during an Epidemic? (Marek Laskowski, Preeti Dubey, Murray E Alexander, Shannon Collinson, Jane M Heffernan and Seyed M Moghadas); Rich Dynamics of Hepatitis C Viral Infection with Logistic Proliferation (Sandip Banerjee); Computational Biology: In Silico Manipulation of Single DNA Molecules (P Cortini, M Barbi and P Carrivain); Very High Synchrony in Evolution of Organelles and Host Genomes (A I Chernyshova, Yu A Putintzeva and M G Sadovsky); A Method for Clustering Hemagglutinin Influenza Protein Sequences (X Li, H Jankowski, X Wang and Jane M Heffernan); Comparison of the Robustness of Entropy Measures for Protein Domain Families (R P Mondaini, Cecilia Mondaini and Edgar A G G do Amaral); Dynamic and Geometric Modelling of Biomolecular Structures: Dynamics of Z-Ring Formation in Liposomes (R A Barrio, C Varea, T Alarcon, C B Picallo and A Hernandez-Machado); Optimal Control of Protein Langevin Dynamics (R P Mondaini and S C de Albuquerque Neto); Time Asymmetry of Cross-correlation Functions as a Signature of Non-equilibrium Steady States (A Lemarchand and C Bianca); Modelling Physiological Disorders: Entropy of Protein Networks in Malignant Cells of Breast Cancer and Therapeutic Treatment (Jack A Tuszynski, N Carels and T M Tilli); Molecular Dynamics and Computational Drug Discovery: Molecular Dynamics and related Computational Methods with Applications to Drug Discovery (Jack A Tuszynski, T Luchko, P Vinter, Cassandra Churchill, K Sahu, F Gentile, Sara I Omar, N Nayebi, G Hu, K Wang and J Ruan); Multi-scale Models in Biological Sciences: On a Multi-scale Analysis of a Micro-model of Heat Transfer in Biological Tissues (Abdelhamid Ainouz); Multi-scale Modelling in Cell Dynamics (M Banerjee, M Benmir and V Volpert); Mathematical Morphology of Biological Structures: Topology of Cell Membranes (E I Kats and M I Monastyrsky); Geometry of Morphogenesis (N Morozova and R Penner); Comparing Shape Trajectories of Biological Soft Tissues in the Size-and-shape Space (V Varano, S Gabriele, L Teresi, I Dryden, P E Puddu, C Torromeo and P Piras);
£133.20
Springer Complex Geometric Analysis
Book Synopsis
£170.99
Oxford University Press Visual Complex Analysis
Book SynopsisThis new 25th anniversary edition of Visual Complex Analysis introduces this powerful method combining complex numbers with ordinary calculus, and includes new introductory content and brand-new captions that fully explain the geometrical reasoning.Trade ReviewVisual Complex Analysis is a delight, and a book after my own heart. By his innovative and exclusive use of the geometrical perspective, Tristan Needham uncovers many surprising and largely unappreciated aspects of the beauty of complex analysis. * Sir Roger Penrose *...it is comparable with Feynman's Lectures on Physics. At every point it asks "why" and finds a beautiful visual answer. * Newsletter of the European Mathematical Society *Newton would have approved... a fascinating and refreshing look at a familiar subject... essential reading for anybody with any interest at all in this absorbing area of mathematics. * Times Higher Education Supplement *One of the saddest developments in school mathematics has been the downgrading of the visual for the formal. I'm not lamenting the loss of traditional Euclidean geometry, despite its virtues, because it too emphasised stilted formalities. But to replace our rich visual tradition by silly games with 2 x 2 matrices has always seemed to me to be the height of folly. It is therefore a special pleasure to see Tristan Needham's Visual Complex Analysis with its elegantly illustrated visual approach. Yes, he has 2 x 2 matrices--but his are interesting. * Ian Stewart, New Scientist *an engaging, broad, thorough, and often deep, development of undergraduate complex analysis and related areas from a geometric point of view. The style is lucid, informal, reader-friendly, and rich with helpful images (e.g. the complex derivative as an "amplitwist"). A truly unusual and notably creative look at a classical subject. * Paul Zorn, American Mathematical Monthly *If your budget limits you to only buying one mathematics book in a year then make sure that this is the one that you buy. * Mathematical Gazette *I was delighted when I came across Visual Complex Analysis. As soon as I thumbed through it, I realized that this was the book I was looking for ten years ago. * Ed Catmull, former president of Pixar and Disney Animation Studios *The new ideas and exercises bring together a body of information potentially invaluable to researchers in fields from topology to number theory... this is only the beginning of a long list of famous facts for which Needham offers attractive visual proofs: Cauchy's theorem is a satisfying example: you can see the contribution to the integral from each infinitesimal square vanish before your eyes. * Frank Farris, American Mathematical Monthly *This informal style is excellently judged and works extremely well. Many of the arguments presented will be new even to experts, and the book will be of great interest to professionals working in either complex analysis or in any field where complex analysis is used. * David Armitage, Mathematical Reviews *The arguments constructed are highly innovative; even veterans of the field will find new ideas here. This is a special book. Tristan Needham has not only completely rethought a classical field of mathematics, but has presented it in a clear and compelling way. Visual Complex Analysis is worthy of the accolades it has received * MAA Reviews *This new edition of Visual Complex Analysis applies Newton's geometrical methods from the Principia and his concept of ultimate equality to Complex Analysis. * MathSciNet *Table of Contents1: Geometry and Complex Arithmetic 2: Complex Functions as Transformations 3: Möbius Transformations and Inversion 4: Differentiation: The Amplitwist Concept 5: Further Geometry of Differentiation 6: Non-Euclidean Geometry 7: Winding Numbers and Topology 8: Complex Integration: Cauchy's Theorem 9: Cauchy's Formula and Its Applications 10: Vector Fields: Physics and Topology 11: Vector Fields and Complex Integration 12: Flows and Harmonic Functions
£999.99
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
LEGARE STREET PR Lectures on Quaternions Containing a Systematic Statement of a new Mathematical Method of Which the Principles Were Communicated in 1843 to the Royal Irish Academy and Which has Since Formed the Subject of Successive Courses of Lectures Del
a huge range and FREE tracked UK delivery on ALL orders.
£30.35
Princeton University Press Real Submanifolds in Complex Space and Their
Book SynopsisPresents many of the main developments in the study of real submanifolds in complex space, providing background material for researchers and advanced graduate students. This work addresses topics such as the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds.Table of ContentsPrefaceCh. IHypersurfaces and Generic Submanifolds in C[superscript N]3Ch. IIAbstract and Embedded CR Structures35Ch. IIIVector Fields: Commutators, Orbits, and Homogeneity62Ch. IVCoordinates for Generic Submanifolds94Ch. VRings of Power Series and Polynomial Equations119Ch. VIGeometry of Analytic Discs156Ch. VIIBoundary Values of Holomorphic Functions in Wedges184Ch. VIIIHolomorphic Extension of CR Functions205Ch. IXHolomorphic Extension of Mappings of Hypersurfaces241Ch. XSegre Sets281Ch. XINondegeneracy Conditions for Manifolds315Ch. XIIHolomorphic Mappings of Submanifolds349Ch. XIIIMappings of Real-algebraic Subvarieties379References390Index401
£117.30
Springer International Publishing AG Complex Analytic Cycles II
Book Synopsis
£143.99
Birkhauser Boston Geometry and Spectra of Compact Riemann Surfaces
Book SynopsisHyperbolic Structures.- Trigonometry.- Y-Pieces and Twist Parameters.- The Collar Theorem.- Bers' Constant and the Hairy Torus.- The Teichmüller Space.- The Spectrum of the Laplacian.- Small Eigenvalues.- Closed Geodesics and Huber's Theorem.- Wolpert's Theorem.- Sunada's Theorem.- Examples of Isospectral Riemann Surfaces.- The Size of Isospectral Families.- Perturbations of the Laplacian in Teichmüller Space.Trade ReviewFrom the reviews:"Anyone familiar with the author's hands-on approach to Riemann surfaces will be gratified by both the breadth and the depth of the topics considered here. The exposition is also extremely clear and thorough. Anyone not familiar with the author's approach is in for a real treat." —Mathematical Reviews“Originally published as Volume 106 in the series Progress in Mathematics, this version is a reprint of the classic monograph, 1992 edition, consisting of two parts. … An appendix is devoted to curves and isotopies. The book is a very useful reference for researches and also for graduate students interested in the geometry of compact Riemann surfaces of constant curvature -- 1 and their length and eigenvalue spectra.” (Liliana Răileanu, Zentralblatt MATH, Vol. 1239, 2012)“Geometry and Spectra of Compact Riemann Surfaces is a pleasure to read. There is a lot of motivation given, examples proliferate, propositions and theorems come equipped with clear proofs, and excellent drawings … . a fine piece of scholarship and a pedagogical treat.” (Michael Berg, The Mathematical Association of America, May, 2011)Table of ContentsHyperbolic Structures.- Trigonometry.- Y-Pieces and Twist Parameters.- The Collar Theorem.- Bers’ Constant and the Hairy Torus.- The Teichmüller Space.- The Spectrum of the Laplacian.- Small Eigenvalues.- Closed Geodesics and Huber’s Theorem.- Wolpert’s Theorem.- Sunada’s Theorem.- Examples of Isospectral Riemann Surfaces.- The Size of Isospectral Families.- Perturbations of the Laplacian in Teichmüller Space.
£98.99
Springer Spectral Analysis on Standard Locally Homogeneous
Book Synopsis
£999.99
Springer International Publishing AG Fixed Point of the Parabolic Renormalization Operator
Book SynopsisThis monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point. Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization. The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics.Trade Review“The book under review is devoted to the study of parabolic renormalization. … The book is very well written and self-contained … and most results are stated together with their proofs.” (Jasmin Raissy, zbMATH 1342.37051, 2016)Table of Contents1 Introduction.- 2 Local dynamics of a parabolic germ.- 3 Global theory.- 4 Numerical results.- 5 For dessert: several amusing examples.- Index.
£40.49
Springer International Publishing AG The Spectrum of Hyperbolic Surfaces
Book SynopsisThis text is an introduction to the spectral theory of the Laplacian on compact or finite area hyperbolic surfaces. For some of these surfaces, called “arithmetic hyperbolic surfaces”, the eigenfunctions are of arithmetic nature, and one may use analytic tools as well as powerful methods in number theory to study them. After an introduction to the hyperbolic geometry of surfaces, with a special emphasis on those of arithmetic type, and then an introduction to spectral analytic methods on the Laplace operator on these surfaces, the author develops the analogy between geometry (closed geodesics) and arithmetic (prime numbers) in proving the Selberg trace formula. Along with important number theoretic applications, the author exhibits applications of these tools to the spectral statistics of the Laplacian and the quantum unique ergodicity property. The latter refers to the arithmetic quantum unique ergodicity theorem, recently proved by Elon Lindenstrauss. The fruit of several graduate level courses at Orsay and Jussieu, The Spectrum of Hyperbolic Surfaces allows the reader to review an array of classical results and then to be led towards very active areas in modern mathematics.Trade Review“The French book under review gives an introduction to hyperbolic surfaces with an emphasis on the Selberg conjecture. … it is intended for advanced graduate students but is also well suited for all those who want to acquaint themselves with harmonic analysis on hyperbolic surfaces and automorphic forms.” (Frank Monheim, zbMATH, August, 2017)“This book gives a very nice introduction to the spectral theory of the Laplace-Beltrami operator on hyperbolic surfaces of constant negative curvature. … mainly intended for students with a knowledge of basic differential geometry and functional analysis but also for people doing research in other domains of mathematics or mathematical physics and interested in the present day problems in this very active field of research. … book gives one of the best introductions to this fascinating field of interdisciplinary research.” (Dieter H. Mayer, Mathematical Reviews, August, 2017)Table of ContentsPreface.- Introduction.- Arithmetic Hyperbolic Surfaces.- Spectral Decomposition.- Maass Forms.- The Trace Formula.- Multiplicity of lambda1 and the Selberg Conjecture.- L-Functions and the Selberg Conjecture.- Jacquet-Langlands Correspondence.- Arithmetic Quantum Unique Ergodicity.- Appendices.- References.- Index of notation.- Index.- Index of names.
£999.99
Birkhäuser Complex Variables with Applications
Book SynopsisAlgebraic and Geometric Preliminaries.- Topological and Analytic Preliminaries.- Bilinear Transformations and Mappings.- Elementary Functions.- Analytic Functions.- Power Series.- Complex Integration and Cauchy's Theorem.- Applications of Cauchy's Theorem.- Laurent Series and the Residue Theorem.- Harmonic Functions.- Conformal Mapping and the Riemann Mapping Theorem.- Entire and Meromorphic Functions.- Analytic Continuation.Trade Review"A good point of the book is the selections of questions and exercises at the end of each section. They are very carefully selected and will help students with reading comprehension and with application of the material of the current section. Most of the time the exercises progress nicely from simple applications of concepts to problems that will expand the student’s horizons." –MAA Reviews "By using this book the reader can get a good background on complex analysis and become ready for further study of deeper chapters of Complex Analysis and its Applications."–Zentralblatt MathTable of ContentsAlgebraic and Geometric Preliminaries.- Topological and Analytic Preliminaries.- Bilinear Transformations and Mappings.- Elementary Functions.- Analytic Functions.- Power Series.- Complex Integration and Cauchy’s Theorem.- Applications of Cauchy’s Theorem.- Laurent Series and the Residue Theorem.- Harmonic Functions.- Conformal Mapping and the Riemann Mapping Theorem.- Entire and Meromorphic Functions.- Analytic Continuation.
£999.99
Cambridge University Press Numbers and Functions
Book SynopsisIn this updated edition of Numbers and Functions, the reader is invited to tackle each of the key concepts of mathematical analysis in turn, progressing from experience through a structured sequence of over 800 problems to concepts, definitions and proofs of classical real analysis.Trade Review'This third edition of Numbers and Functions continues the author's long-term commitment to support every reader in making sense of mathematics by responding to a succession of well-chosen questions that encourage personal reflection and discussion with others. Groups of questions are followed by a summary to build the bigger picture. Every chapter includes details of the historical development and ends with a full list of solutions. The author is aware of the difficulties that students encounter with the complexity of the limit concept and begins with a pragmatic approach to null sequences. This broadens into a full study of limits of sequences, completeness, and a full range of tests for convergence of infinite series … This latest edition maintains the original chapters of the original, while benefiting from detailed improvements that have arisen from the experience of many readers. Thoroughly recommended.' David Tall, University of Warwick'… written in a very comprehensible but exact way … an excellent guide through the basic course of mathematical analysis at university.' European Mathematical Society NewsletterTable of ContentsPreface to first edition; Preface to second edition; Preface to third edition; Glossary; Part I. Numbers: 1 Mathematical induction; 2. Inequalities; 3. Sequences: a first bite at infinity; 4. Completeness: what the rational numbers lack; 5. Series: infinite sums; Part II. Functions: 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness: functions on intervals; 8. Derivatives: tangents; 9. Differentiation and completeness: mean value theorems, Taylor's Theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendix 1. Properties of the real numbers; Appendix 2. Geometry and intuition; Appendix 3. Questions for student investigation and discussion; Bibliography; Index.
£46.99
Springer Abels Theorem in Problems and Solutions Based on the Lectures of Professor V I Arnold The Kluwer International Series in Engineering Computer Science
Book SynopsisFrom the contents:Preface for the English edition; V.I. Arnold.- Preface.- Introduction.- 1: Groups.- 2: The complex numbers.- 3: Hints, Solutions and Answers.- Appendix. Solvability of equations by explicit formulae; A. Khovanskii.- Bibliography.- Appendix; V.I. Arnold.- Index. Trade ReviewFrom the reviews: "This very special and brilliant text has been written for bright non-specialists in mathematics, but it leads the reader up to topical research problems in the field, and that in a masterly manner. The book is absolutely self-contained, in its own particular fashion, and it is therefore perfectly suited for self-study, ranging from advanced high school to graduate level. No doubt, the thorough and serious working with this outstanding text could turn very beginners into creative almost-experts in the field." (Werner Kleinert, Zentralblatt MATH, Vol. 1065 (16), 2005)Table of ContentsPreface for the English edition; V.I. Arnold. Preface. Introduction. 1: Groups. 1.1. Examples. 1.2. Groups of transformations. 1.3. Groups. 1.4. Cyclic groups. 1.5. Isomorphisms. 1.6. Subgroups. 1.7. Direct product. 1.8. Cosets. Lagrange's theory. 1.9. Internal automorphisms. 1.10. Normal subgroups. 1.11. Quotient groups. 1.12. Commutant. 1.13. Homomorphisms. 1.14. Soluble groups. 1.15. Permutations. 2: The complex numbers. 2.1. Fields and polynomials. 2.2. The field of complex numbers. 2.3. Uniqueness of the field of complex numbers. 2.4. Geometrical descriptions of the field of complex numbers. 2.5. The trigonometric form of the complex numbers. 2.6. Continuity. 2.7. Continuous curves. 2.8. Images of curves: the basic theorem of the algebra of complex numbers. 2.9. The Riemann surface of the function w = SQRTz. 2.10. The Riemann surfaces of more complicated functions. 2.11. Functions representable by radicals. 2.12. Monodromy groups of multi-valued functions. 2.13. Monodromy groups of functions representable by radicals. 2.14. The Abel theorem. 3: Hints, Solutions and Answers. 3.1.Problems of Chapter 1. 3.2. Problems of Chapter 2. Drawings of Riemann surfaces; F. Aicardi. Appendix. Solvability of equations by explicit formulae; A. Khovanskii. A.1. Explicit solvability of equations. A.2. Liouville's theory. A.3. Picard-Vessiot's theory. A.4. Topological obstructions for the representation of functions by quadratures. A.5. S-functions. A.6. Monodromy group. A.7. Obstructions for the representability of functions by quadratures. A.8. Solvability of algebraic equations. A.9. The monodromy pair. A.10. Mapping of the semi-plane to a polygon bounded by arcs of circles. A.11. Topological obstructions for the solvability of differential equations. A.12. Algebraic functions of several variables. A.13. Functions of several complex variables representable by quadratures and generalized quadratures. A.14. SC-germs. A.15. Topological obstruction for the solvability of the holonomic systems of linear differential equations. A.16. Topological obstruction for the solvability of the holonomic systems of linear differential equations. Bibliography. Appendix; V.I. Arnold. Index.
£113.99
Springer Complex Analysis
Book SynopsisPreface to Second Edition.- Preface to First Edition.- Standard Notation and Commonly Used Symbols.- 1 The Fundamental Theorem in Complex Function Theory.- 2 Foundations.- 3 Power Series.- 4 The Cauchy Theory - A Fundamental Theorem.- 5 The Cauchy Theory - Key Consequences.- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- 7 Sequences and Series of Holomorphic Functions.- 8 Conformal Equivalence and Hyperbolic Geometry.- 9 Harmonic Functions.- 10 Zeros of Holomorphic Functions.- Bibliographical Notes.- Bibliography.- Index.Trade ReviewFrom the reviews of the second edition:“The book under review is a second edition of a book by the same authors and with the same title, also published by Springer in 2007. It contains some amount of new information. … The book is carefully written and each chapter has an interesting list of exercises. I found it very useful as am Undergraduate and Graduate Text in Mathematics.” (José M. Ansemil, The European Mathematical Society, euro-math-soc.eu, January, 2014)From the reviews:“The book is written in a clear and easily readable manner, completed with a well cared selection of exercises. The book, which is certainly useful for all specialists and lecturers in complex analysis, I also recommend to beginners in this area.” (Fernando Perez-Gonzalez, Zentralblatt MATH, Vol. 1262, 2013)"This is a fairly conventional text for a first course in complex analysis. It is an interesting mix of the concrete and the abstract, and of the formulaic and the geometric. It has good exercises … . It is nominally a graduate text (it is in Springer’s series of Graduate Texts in Mathematics) … . The book covers all the usual topics for a first course and includes a lot of advanced topics … ." (Allen Stenger, MathDL, February, 2008)"This book is based on the original courses of Complex Analysis that was delivered by the well-known American specialist and lecturer in Analysis, Professor Lipman Bers. … the book is written in a clear and easily readable manner. … this book is useful for all specialists and lecturers in Complex Analysis … and also all specialists who deal with applications of Complex Analysis. I also recommend this book to beginners who want to study Complex Analysis … ." (Peter Zabreiko, Zentralblatt MATH, Vol. 1139 (17), 2008)Table of ContentsPreface to Second Edition.- Preface to First Edition.- Standard Notation and Commonly Used Symbols.- 1 The Fundamental Theorem in Complex Function Theory.- 2 Foundations.- 3 Power Series.- 4 The Cauchy Theory - A Fundamental Theorem.- 5 The Cauchy Theory - Key Consequences.- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- 7 Sequences and Series of Holomorphic Functions.- 8 Conformal Equivalence and Hyperbolic Geometry.- 9 Harmonic Functions.- 10 Zeros of Holomorphic Functions.- Bibliographical Notes.- Bibliography.- Index.
£71.24
Springer Analysis on Fock Spaces
Book SynopsisPreface.- Chapter 1. Preliminaries.- Chapter 2. Fock Spaces.- Chapter 3. The Berezin Transform and BMO.- Chapter 4. Interpolating and Sampling Sequences.- Chapter 5. Zero Sets for Fock Spaces.- Chapter 6. Toeplitz Operators.- Chapter 7. Small Hankel Operators.- Chapter 8. Hankel Operators.- References.- Index.Trade ReviewFrom the reviews:“Excellent books exist in the literature on the theory of Hardy spaces … but no textbook concerning the theory of Fock spaces has appeared before. The purpose of the author is to fill this gap and provide to any researcher in the field or graduate students the appropriate place to find the results or the bibliographical references needed for their use. … author succeeds with his goal. … a great addition to the literature and in the future will become a classic in the field.” (Jordi Pau, Mathematical Reviews, January, 2013)“This book is intended to provide a convenient reference to Fock spaces. … Each chapter ends with a series of exercises. The material is presented in a pedagogical way. The reference list contains 259 relevant items. This book is well written and it is a good reference for graduate students who are interested in Fock spaces.” (Atsushi Yamamori, Zentralblatt MATH, Vol. 1262, 2013)Table of ContentsPreface.- Chapter 1. Preliminaries.- Chapter 2. Fock Spaces.- Chapter 3. The Berezin Transform and BMO.- Chapter 4. Interpolating and Sampling Sequences.- Chapter 5. Zero Sets for Fock Spaces.- Chapter 6. Toeplitz Operators.- Chapter 7. Small Hankel Operators.- Chapter 8. Hankel Operators.- References.- Index.
£59.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Real Methods in Complex and CR Geometry: Lectures given at the C.I.M.E. Summer School held in Martina Franca, Italy, June 30 - July 6, 2002
Book SynopsisThe geometry of real submanifolds in complex manifolds and the analysis of their mappings belong to the most advanced streams of contemporary Mathematics. In this area converge the techniques of various and sophisticated mathematical fields such as P.D.E.s, boundary value problems, induced equations, analytic discs in symplectic spaces, complex dynamics. For the variety of themes and the surprisingly good interplaying of different research tools, these problems attracted the attention of some among the best mathematicians of these latest two decades. They also entered as a refined content of an advanced education. In this sense the five lectures of this volume provide an excellent cultural background while giving very deep insights of current research activity.Table of ContentsPreface.- M. Abate: Angular Derivatives in Several Complex Variables.- J.E. Fornaess: Real Methods in Complex Dynamics.- X. Huang: Local Equivalence Problems for Real Submanifolds in Complex Spaces.- J.-P. Rosay: Introduction to a General Theory of Boundary Values.- A. Tumanov: Extremal Discs and the Geometry of CR Manifolds.
£40.99
De Gruyter Topics in Complex Analysis
Book SynopsisThis graduate-level mathematics textbook provides an in-depth and readable exposition of selected topics in complex analysis. The material spans both the standard theory at a level suitable for a first-graduate class on the subject and several advanced topics delving deeper into the subject and applying the theory in different directions. The focus is on beautiful applications of complex analysis to geometry and number theory. The text is accompanied by beautiful figures illustrating many of the concepts and proofs. Among the topics covered are asymptotic analysis; conformal mapping and the Riemann mapping theory; the Euler gamma function, the Riemann zeta function, and a proof of the prime number theorem; elliptic functions, and modular forms. The final chapter gives the first detailed account in textbook format of the recent solution to the sphere packing problem in dimension 8, published by Maryna Viazovska in 2016 — a groundbreaking proof for which Viazovska was awarded the Fields Medal in 2022. The book is suitable for self-study by graduate students or advanced undergraduates with an interest in complex analysis and its applications, or for use as a textbook for graduate mathematics classes, with enough material for 2-3 semester-long classes. Researchers in complex analysis, analytic number theory, modular forms, and the theory of sphere packing, will also find much to enjoy in the text, including new material not found in standard textbooks.
£65.08
De Gruyter Differential Equations: A First Course on ODE and a Brief Introduction to PDE
Book SynopsisThe first part of this book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught at the undergraduate level, such as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample flexibility to make it appropriate either as a course stressing application, or a course stressing rigor and analytical thinking. It also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of the chapters. In this edition complete solutions to all even number problems are given in the back of the book.The 2nd edition also includes some new problems and examples. An effort has been made to make the material more suitable and self-contained for undergraduate students with minimal knowledge of Calculus. For example, a detailed review of matrices and determinants has been added to the chapter on systems of equations. The second edition also contains corrections of some misprints and errors in the first edition.
£77.90
De Gruyter Optimal Control: From Variations to Nanosatellites
Book SynopsisThis book may serve as a basis for students and teachers. The text should provide the reader with a quick overview of the basics for Optimal Control and the link with some important conceptes of applied mathematical, where an agent controls underlying dynamics to find the strategy optimizing some quantity. There are broad applications for optimal control across the natural and social sciences, and the finale to this text is an invitation to read current research on one such application. The balance of the text will prepare the reader to gain a solid understanding of the current research they read.
£86.45
Springer International Publishing AG Mixed Twistor D-modules
Book SynopsisWe introduce mixed twistor D-modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense, mixed twistor D-modules can be regarded as a twistor version of M. Saito's mixed Hodge modules. Alternatively, they can be viewed as a mixed version of the pure twistor D-modules studied by C. Sabbah and the author. The theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem and it would form a foundation for the Hodge theory of holonomic D-modules which are not necessarily regular singular.Table of ContentsIntroduction.- Preliminary.- Canonical prolongations.- Gluing and specialization of r-triples.- Gluing of good-KMS r-triples.- Preliminary for relative monodromy filtrations.- Mixed twistor D-modules.- Infinitesimal mixed twistor modules.- Admissible mixed twistor structure and variants.- Good mixed twistor D-modules.- Some basic property.- Dual and real structure of mixed twistor D-modules.- Derived category of algebraic mixed twistor D-modules.- Good systems of ramified irregular values.
£44.99
LEGARE STREET PR Institutiones Calculi Differentialis...
£31.30
LEGARE STREET PR A Textbook of Differential Calculus
£13.95
LEGARE STREET PR Institutionum Calculi Integralis Volumes 12...
£31.30
Lulu Press Introduktion till analytiska funktioner
£14.38
Orthogonal Publishing L3c A First Course in Complex Analysis
£12.60
Springer International Publishing AG Complex Integration: A Compendium of Smart and Little-Known Techniques for Evaluating Integrals and Sums
Book SynopsisIntegrals and sums are not generally considered for evaluation using complex integration. This book proposes techniques that mainly use complex integration and are quite different from those in the existing texts. Such techniques, ostensibly taught in Complex Analysis courses to undergraduate students who have had two semesters of calculus, are usually limited to a very small set of problems. Few practitioners consider complex integration as a tool for computing difficult integrals. While there are a number of books on the market that provide tutorials on this subject, the existing texts in this field focus on real methods. Accordingly, this book offers an eye-opening experience for computation enthusiasts used to relying on clever substitutions and transformations to evaluate integrals and sums. The book is the result of nine years of providing solutions to difficult calculus problems on forums such as Math Stack Exchange or the author's website, residuetheorem.com. It serves to detail to the enthusiastic mathematics undergraduate, or the physics or engineering graduate student, the art and science of evaluating difficult integrals, sums, and products.Table of Contents1. Review of foundational concepts1.1. Sequences and Series 1.1.1. Sequences of Real Numbers and their Series – sequences, limits, series, convergence, harmonic numbers, summation by parts, change in the order of summation 1.1.2. Power Series and Generating Functions – definitions, radius of convergence, generating function representations of sequences, convolution 1.2. Integrals 1.2.1. Riemann Sums – definition, direct evaluation of certain sums 1.2.2. Fundamental Theorem - definition of definite integral, statement of theorem, verifications 1.2.3. Multiple Integrals – double integrals, conditions for reversal or order of integration 1.3. Evaluation Techniques 1.3.1. Integration by Parts - review 1.3.2. Conversion to Multiple Integrals – “Feynman’s Technique,” replacing a portion of an integrand with an integral representation and reversing the order of integration 1.3.3. Green’s Theorem – review, path integrals and parametrization, Stokes’ Theorem, applications 1.3.4. Partial Fractions review 1.4. Problems 2. Complex Integration 2.1. Analytic Functions 2.1.1. Cauchy-Riemann Conditions – complex functions and their derivatives, defining analytic functions as a direction-independent derivative, harmonic functions 2.1.2. Evaluating Complex Integrals – numerical examples of parametrizations 2.1.3. Path Independence – demonstrate for analytic functions and demonstrate invalidity for nonanalytic integrands 2.2. Cauchy’s Theorems 2.2.1. Winding Numbers – definition in terms of a complex integral 2.2.2. Cauchy’s Integral Theorem – derivation and illustration for a wide variety of integrands and contours 2.2.3. Cauchy’s Theorem – statement, examples, Liouville’s Theorem, Morera’s Theorem 2.3. Useful Results 2.3.1. Taylor Series – review, error analysis in complex plane, convergence 2.3.2. Laurent Series – regions of validity (e.g., annuli), analytic continuation 2.3.3. Argument Principle – derivation for zeroes and poles 2.3.4. Rouche’s Theorem – derivation, illustration for determining poles within integration contours 2.4. Multivalued Functions – branch points, branch cuts, Riemann surfaces 2.5. Problems 3. Evaluation of Real Integrals and Sums 3.1. Preliminary Matters 3.1.1. Poles and Residue Theory – residue definition, residue computation 3.1.2. Essential Singularities – computation of residues of essential singularities 3.1.3. Branch Points – illustration of a unified approach to expressing an integral of a function in terms of its singularities 3.2. Definite Integrals 3.2.1. Integrands Having Both Poles and Branch Points – e.g., integrands featuring logs and exponents less than -1 3.2.2. Integrands Defined Over - insertion of one higher power of log(z) in the integrand, residue backpropagation 3.2.3. Integrands Having Rational Functions of Polynomials and Trigonometric Functions – integration over the unit circle, modifying the unit circle in the presence of singularities, replacing monomial with a branch point in constructing a contour integral 3.2.4. Alternative Contours: Wedges, Rectangles, and Others – reducing the number of singularities in a contour to simplify calculation 3.2.5. Integrands Having Algebraic Functions and the Residue At Infinity – whole new paradigm in evaluating definite integrals with finite limits of an integrand having branch points at the finite limits, defining the residue at infinity, branch point at infinity 3.3. Sums 3.3.1. Complex Integral Representations – selection of integrand and contour to produce sums, demonstration of convergence of complex integral as contour expands to infinity 3.3.2. Examples – rational summands, summands with trigonometric functions 3.4. Problems 4. Cauchy Principal Value 4.1. Integrands Having Poles On the Contour 4.1.1. Definition of a Cauchy Principal Value – definition as a limit, illustration with simple examples 4.1.2. Managing Divergent Terms of a Contour Integral – detailed illustrations of evaluating definite integrals via complex integrals having contributions with divergent terms that cancel 4.2. Analytic Signals and Hilbert Transforms – equivalence of Cauchy-Riemann equations and Hilbert transforms of real and imaginary parts of an analytic function, illustrations of analytic signals having harmonic real and imaginary parts, examples of deriving imaginary parts of analytic function from real part 4.3. Problems 5. Integral Transforms 5.1. Preliminary Matters 5.1.1. The Dirac Delta Function – derivation via self-transform in Hilbert transform integrals, review of properties 5.1.2. A General Discussion of Integral Transforms - integral transforms require a computable inverse to be of any use, conditions under which inverses exist, general format of integral transforms 5.2. The Fourier Transform 5.2.1. Definition and Plancherel’s Theorem – mean square error, and inner product spaces, the Fourier Transform as a Principal Value 5.2.2. Jordan’s Lemma – evaluating Fourier integrals using complex integration, convergence conditions 5.2.3. Parseval’s Theorem – statement, examples of integral evaluations, Fourier series and application of theorem to sums 5.2.4. Convolution Theorem – statement and derivation, applications 5.2.5. Analyticity of the Fourier Transform In the Complex Plane - theorem relating rates of convergence of Fourier transforms and their inverses in the complex plane, strips of convergence, causality 5.2.6. Poisson Sum Formula – derivation, application to computation of error function to machine precision anywhere in the complex plane 5.3. The Laplace Transform 5.3.1. Definition – extending the discussion of analyticity of the Fourier transform with an exponentially decaying kernel rather than an oscillatory kernel, derivation of inverse as an integral in the complex plane 5.3.2. Convolution Theorem – derivation, examples, application to computing certain classes of definite integrals 5.3.3. Inversion Via Complex Integration 5.3.3.1. Solutions to Ordinary Differential Equations and Rational Transforms – initial conditions, homogeneous and inhomogeneous equations, inversion via the residue theorem 5.3.3.2. Solutions to Partial Differential Equations and Multivalued Transforms – heat equation produces multivalued transforms, evaluation of inverse Laplace transforms to derive solutions 5.4. The Mellin Transform 5.4.1. Definition discussion of strip of convergence, inverse Mellin transform 5.4.2. Convolution Theorem – derivation; NB this will be used in the next chapter 5.4.3. Scaling – expression of scaled integrals in terms of residues 5.5. Problems 6. Asymptotic Analysis 6.1. Definitions 6.1.1. Big-O, Little-O, and The Squiggle – i.e., definitions of asymptotic equivalence in specific limits 6.1.2. Asymptotic Series – definition, properties, numerical calculations, summation acceleration techniques 6.2. Integration by Parts – development of asymptotic series; limitations 6.2.1. Euler-Maclurin Formula – derivation of asymptotic series using integration by parts, application to evaluation of sums 6.3. Watson’s Lemma and h-Transforms – asymptotic behavior of monotonic integrands, application of Mellin transforms in derivation 6.3.1. Application to Complex Integration – evaluation of integrals with branch points at infinity using h-transforms 6.4. Laplace’s Method – asymptotic behavior of nonmonotomic, nonoscillatory integrals 6.5. The Method of Steepest Descents – deriving asymptotic behavior of complex integrals, derive behavior of real integrals by using Cauchy’s Theorem 6.6. Problems
£63.06
Society for Industrial & Applied Mathematics,U.S. Solving Problems in Multiply Connected Domains
Book SynopsisWhenever two or more objects or entities—be they bubbles, vortices, black holes, magnets, colloidal particles, microorganisms, swimming bacteria, Brownian random walkers, airfoils, turbine blades, electrified drops, magnetized particles, dislocations, cracks, or heterogeneities in an elastic solid—interact in some ambient medium, they make holes in that medium. Such holey regions with interacting entities are called multiply connected.This book describes a novel mathematical framework for solving problems in two-dimensional, multiply connected regions. The framework is built on a central theoretical concept: the prime function, whose significance for the applied sciences, especially for solving problems in multiply connected domains, has been missed until recent work by the author.This monograph is a one-of-a-kind treatise on the prime function associated with multiply connected domains and how to use it in applications. The book contains many results familiar in the simply connected, or single-entity, case that are generalized naturally to any number of entities, in many instances for the first time.Solving Problems in Multiply Connected Domains is aimed at applied and pure mathematicians, engineers, physicists, and other natural scientists; the framework it describes finds application in a diverse array of contexts. The book provides a rich source of project material for undergraduate and graduate courses in the applied sciences and could serve as a complement to standard texts on advanced calculus, potential theory, partial differential equations and complex analysis, and as a supplement to texts on applied mathematical methods in engineering and science.
£78.20
Taylor & Francis Ltd Real and Complex Analysis
a huge range and FREE tracked UK delivery on ALL orders.
£61.99
Taylor & Francis Ltd An Introduction to Complex Analysis and the Laplace Transform
a huge range and FREE tracked UK delivery on ALL orders.
£130.06
Springer Complex Analysis with Applications in Science and Engineering
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Cambridge University Press Transcendental Dynamics and Complex Analysis London Mathematical Society Lecture Note Series Series Number 348
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Springer The Cauchy Method of Residues Volume 2
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
Springer Complex Potential Theory
a huge range and FREE tracked UK delivery on ALL orders.
£999.99
