Integral calculus and equations Books
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Intégration: Chapitres 7 à 8
Book SynopsisCe volume du Livre d’Intégration, sixième Livre du traité, traite de l’intégration sur les groupes localement compacts et de ses applications. Les notions introduites, telles que les mesures de Haar et le produit de convolution, sont à la base de l’analyse harmonique. Il comprend les chapitres : -1. Mesure de Haar ; -2. Convolution et représentations.Table of ContentsMesure de Haar.- Convolution et Représentation.
£39.99
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Hamiltonian Methods in the Theory of Solitons
Book SynopsisThe main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.Trade Review Table of ContentsThe Nonlinear Schrödinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples and Their General Properties.- Fundamental Continuous Models.- Fundamental Models on the Lattice.- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models.- Conclusion.- Conclusion.
£42.74
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG The Analysis of Fractional Differential
Book SynopsisFractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations. Trade ReviewFrom the reviews:“This book treats a fast growing field of fractional differential equations, i.e., differential equations with derivatives of non-integer order. … The book consists of two parts, eight chapters, an appendix, references and an index. … The book is well written and easy to read. It could be used for, a course in the application of fractional calculus for students of applied mathematics and engineering.” (Teodor M. Atanacković, Mathematical Reviews, Issue 2011 j)“This monograph is intended for use by graduate students, mathematicians and applied scientists who have an interest in fractional differential equations. The Caputo derivative is the main focus of the book, because of its relevance to applications. … The monograph may be regarded as a fairly self-contained reference work and a comprehensive overview of the current state of the art. It contains many results and insights brought together for the first time, including some new material that has not, to my knowledge, appeared elsewhere.” (Neville Ford, Zentralblatt MATH, Vol. 1215, 2011)Table of ContentsFundamentals of Fractional Calculus.- Riemann-Liouville Differential and Integral Operators.- Caputo’s Approach.- Mittag-Leffler Functions.- Theory of Fractional Differential Equations.- Existence and Uniqueness Results for Riemann-Liouville Fractional Differential Equations.- Single-Term Caputo Fractional Differential Equations: Basic Theory and Fundamental Results.- Single-Term Caputo Fractional Differential Equations: Advanced Results for Special Cases.- Multi-Term Caputo Fractional Differential Equations.
£47.49
Birkhauser Verlag AG Analysis III
Book SynopsisThis third volume concludes our introduction to analysis, wherein we ?nish laying the groundwork needed for further study of the subject. As with the ?rst two, this volume contains more material than can treated in a single course. It is therefore important in preparing lectures to choose a suitable subset of its content; the remainder can be treated in seminars or left to independent study. For a quick overview of this content, consult the table of contents and the chapter introductions. Thisbookisalsosuitableasbackgroundforothercoursesorforselfstudy. We hope that its numerous glimpses into more advanced analysis will arouse curiosity and so invite students to further explore the beauty and scope of this branch of mathematics. In writing this volume, we counted on the invaluable help of friends, c- leagues, sta?, and students. Special thanks go to Georg Prokert, Pavol Quittner, Olivier Steiger, and Christoph Walker, who worked through the entire text cr- ically and so helped us remove errors and make substantial improvements. Our thanks also goes out to Carlheinz Kneisel and Bea Wollenmann, who likewise read the majority of the manuscript and pointed out various inconsistencies. Without the inestimable e?ortofour “typesetting perfectionist”, this volume could not have reached its present form: her tirelessness and patience with T X E and other software brought not only the end product, but also numerous previous versions,to a high degree of perfection. For this contribution, she has our greatest thanks.Trade ReviewFrom the reviews:“This third volume contains an introduction to Bochner-Lebesgue integral theory and differential forms’ calculus on smooth manifolds. … The text is clear and understandable and yet it provides a very detailed presentation of the covered topics from an advanced and abstract point of view. The reader can easily develop deep intuitive ideas following the numerous examples, exercises and pictures that are included.” (Tihomir Gyulov, Zentralblatt MATH, Vol. 1187, 2010)Table of ContentsElements of measure theory.- Integration theory.- Manifolds and differential forms.- Integration on manifolds.
£56.99
World Scientific Publishing Co Pte Ltd Path Integral Methods And Their Applications
Book SynopsisThis book presents the major developments in this field with emphasis on application of path integration methods in diverse areas. After introducing the concept of path integrals, related topics like random walk, Brownian motion and Wiener integrals are discussed. Several techniques of path integration including global and local time transformations, numerical methods as well as approximation schemes are presented. The book provides a proper perspective of some of the most recent exact results and approximation schemes for practical applications.Trade Review"... this book becomes not only useful to specialists primarily interested in path integration, but also understandable to nonspecialists from other fields of science and technology." Mathematical ReviewsTable of ContentsConcepts of Lagrangian and Hamiltonian path integrals; Wiener integrals and Brownian motion; representation of the statistical mechanical density matrix as a path integral; propagators for local and non-local quadratic actions; path integrals in polar and curvilinear coordinates and group manifolds; local and global time transformation techniques; approximation and numerical methods of evaluating path integrals and their applications to polaron; bi polaron; spectrum of disordered systems; path integrals with topological constraints and their applications
£56.00
World Scientific Publishing Co Pte Ltd Generalized Radon Transforms And Imaging By
Book SynopsisA generalized Radon transform (GRT) maps a function to its weighted integrals along a family of curves or surfaces. Such operators appear in mathematical models of various imaging modalities. The GRTs integrating along smooth curves and surfaces (lines, planes, circles, spheres, amongst others) have been studied at great lengths for decades, but relatively little attention has been paid to transforms integrating along non-smooth trajectories. Recently, an interesting new class of GRTs emerged at the forefront of research in integral geometry. The two common features of these transforms are the presence of a 'vertex' in their paths of integration (broken rays, cones, and stars) and their relation to imaging techniques based on physics of scattered particles (Compton camera imaging, single scattering tomography, etc).This book covers the relevant imaging modalities, their mathematical models, and the related GRTs. The discussion of the latter comprises a thorough exploration of their known mathematical properties, including injectivity, inversion, range description and microlocal analysis. The mathematical background required for reading most of the book is at the level of an advanced undergraduate student, which should make its content attractive for a large audience of specialists interested in imaging. Mathematicians may appreciate certain parts of the theory that are particularly elegant with connections to functional analysis, PDEs and algebraic geometry.
£76.00
World Scientific Publishing Co Pte Ltd Differential Calculus: Problems And Solutions
Book SynopsisThis volume contains more than 900 problems in differential calculus, covering limits, continuity, derivatives, and their applications. The applications are comprised of a variety of approximations, growth and decay, optimization, curve sketching techniques, and analytical tools to investigate properties of parametrically given planar curves. The problems are sorted by topic, each opening with with a summary of the relevant mathematical notions and their properties. Through a careful selection of appropriate problems in each chapter, the book clearly communicates some of the big ideas and applications in calculus: the notion of a function, the notion of an infinitesimal, the notion of a differentiable function, and the notion of an approximation, among others. The book provides the answers to each problem, often with a detailed sketch of the solution process.With about 260 true-false and multiple-choice questions, the book provides its users with an accessible way to assess and practice their understanding of calculus related facts and nuances. More than 180 figures are included to help readers to visualize properties of functions, illustrate word problems, depict solutions, and provide an extensive bank of polar curves.The purpose of this problem collection is to serve as a supplementary learning resource for students who are studying university-level differential calculus. The book also acts as a teaching resource for calculus instructors.
£85.50
World Scientific Publishing Co Pte Ltd Advances On Fractional Dynamic Inequalities On
Book SynopsisThis book is devoted on recent developments of linear and nonlinear fractional Riemann-Liouville and Caputo integral inequalities on time scales. The book is intended for the use in the field of fractional dynamic calculus on time scales and fractional dynamic equations on time scales. It is also suitable for graduate courses in the above fields, and contains ten chapters. The aim of this book is to present a clear and well-organized treatment of the concept behind the development of mathematics as well as solution techniques. The text material of this book is presented in a readable and mathematically solid format.
£108.00
Springer Verlag, Singapore Time-Fractional Differential Equations: A Theoretical Introduction
Book SynopsisThis book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs.To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.Trade Review“The book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces.” (Syed Abbas, zbMATH 1485.34002, 2022)Table of Contents
£52.24
Springer Verlag, Singapore Delay Differential Equations and Applications to Biology
Book SynopsisThis book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.Trade Review“The author provides extensive references for each chapter … . It offers a breadth of ideas and approaches that could be fertile ground for further research.” (Bill Satzer, MAA Reviews, December 12, 2021)Table of ContentsPart I Qualitative and Quantitative Features of Delay Differential Equations: 1. Delay Differential Equations.- 2. Numerical Solutions of Delay Differential Equations.- 3. Stability Concepts of Numerical Solutions of Delay Differential Equations.- 4. Parameter Estimation with Delay Differential Equations.- Part II Applications of Delay Differential Equations: 5. Delay Differential Equations with Infectious Diseases.- 6. Delay Differential Equations with Cell Growth Dynamics.- 7. Delay Differential Equations with Tumour-Immure Interactions and External Treatments.- 8. Delay Differential Equations with Ecological Systems.- 9. Fractional-Order Delay Differential Equations with Applications.- 10. Sensitivity Analysis.
£98.99
World Scientific Publishing Co Pte Ltd Singular Bilinear Integrals
Book Synopsis'This is a deep and beautiful monograph in functional analysis, at the interface with mathematical physics.'Mathematical ReviewsThe integration of vector valued functions with respect to vector valued measures, especially spectral measures, is developed in view of applications in operator theory, scattering theory and semiclassical approximation in quantum physics. New techniques are developed for bilinear integration in cases where the classical approach does not apply.
£76.95
World Scientific Publishing Co Pte Ltd Integration For Calculus, Analysis, And
Book SynopsisThe book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.Keeping the reader constantly focused on the three principal epistemological questions: 'What for?', 'Why?', and 'How?', the book is designated as a supplementary instructional tool and consists ofThe Answers to all the 192 Problems are provided in the Answer Key. The book will benefit undergraduates, advanced undergraduates, and members of the public with an interest in science and technology, helping them to master techniques of integration at the level expected in a calculus course.
£52.25
World Scientific Publishing Co Pte Ltd Integration For Calculus, Analysis, And
Book SynopsisThe book assists Calculus students to gain a better understanding and command of integration and its applications. It reaches to students in more advanced courses such as Multivariable Calculus, Differential Equations, and Analysis, where the ability to effectively integrate is essential for their success.Keeping the reader constantly focused on the three principal epistemological questions: 'What for?', 'Why?', and 'How?', the book is designated as a supplementary instructional tool and consists ofThe Answers to all the 192 Problems are provided in the Answer Key. The book will benefit undergraduates, advanced undergraduates, and members of the public with an interest in science and technology, helping them to master techniques of integration at the level expected in a calculus course.
£33.25
Springer Verlag, Singapore Theory and Applications of Special Functions for
Book SynopsisThis book provides the knowledge of the newly-established supertrigonometric and superhyperbolic functions with the special functions such as Mittag-Leffler, Wiman, Prabhakar, Miller-Ross, Rabotnov, Lorenzo-Hartley, Sonine, Wright and Kohlrausch-Williams-Watts functions, Gauss hypergeometric series and Clausen hypergeometric series. The special functions can be considered to represent a great many of the real-world phenomena in mathematical physics, engineering and other applied sciences. The audience benefits of new and original information and references in the areas of the special functions applied to model the complex problems with the power-law behaviors.The results are important and interesting for scientists and engineers to represent the complex phenomena arising in applied sciences therefore graduate students and researchers in mathematics, physics and engineering might find this book appealing.Table of ContentsChapter 1 Preliminaries.- Chapter 2 Wright Function and Integral Transforms via Dunkl Transform.- Chapter 3 Mittag-Leffler, Supertrigonometric and Superhyperbolic Functions.- Chapter 4 Wiman, Supertrigonometric and Superhyperbolic Functions.- Chapter 5 Prabhakar, Supertrigonometric and Superhyperbolic Functions.- Chapter 6 Other Special Functions Related to Mittag-Leffler Function.- Chapter 7 Kohlrausch-Williams-Watts Function and Related Topics Bibliography.
£113.99
World Scientific Publishing Co Pte Ltd Henstock-kurzweil Integration On Euclidean Spaces
Book SynopsisThe Henstock-Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock-Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.Table of ContentsThe One-Dimensional Henstock-Kurzweil Integral; The Multiple Henstock-Kurzweil Integral; Lebesgue Integrable Functions; Further Properties of Henstock-Kurzweil Integrable Functions; The Henstock Variational Measure; Multipliers for the Henstock-Kurzweil Integral; Some Selected Topics in Trigonometric Series; Some Applications of the Henstock-Kurzweil Integral to Double Trigonometric Series.
£94.50
World Scientific Publishing Co Pte Ltd Theories Of Integration: The Integrals Of
Book SynopsisThe book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.Table of ContentsIntroduction: Areas; Exercises; Riemann Integral: Riemann's Definition; Basic Properties; Cauchy Criterion; Darboux's Definition; Fundamental Theorem of Calculus; Characterizations of Integrability; Improper Integrals; Exercises; Convergence Theorems and the Lebesgue Integral: Lebesgue's Descriptive Definition of the Integral; Measure; Lebesgue Measure in ℝn; Measurable Functions; Lebesgue Integral; Riemann and Lebesgue Integrals; Mikusinski's Characterization of the Lebesgue Integral; Fubini's Theorem; The Space of Lebesgue Integrable Functions; Exercises; Fundamental Theorem of Calculus and the Henstock - Kurzweil Integral: Denjoy and Perron Integrals; A General Fundamental Theorem of Calculus; Basic Properties; Unbounded Intervals; Henstock's Lemma; Absolute Integrability; Convergence Theorems; Henstock - Kurzweil and Lebesgue Integrals; Differentiating Indefinite Integrals; Characterizations of Indefinite Integrals; The Space of Henstock - Kurzweil Integrable Functions; Henstock - Kurzweil Integrals on ℝn; Exercises; Absolute Integrability and the McShane Integral: Defintions; Basic Properties; Absolute Integrability; Convergence Theorems; The McShane Integral as a Set Function; The Space of McShane Integrable Functions; McShane, Henstock - Kurzweil and Lebesgue Integrals; McShane Integrals on ℝn; Fubini and Tonelli Theorems; McShane, Henstock - Kurzweil and Lebesgue Integrals in ℝn; Exercises.
£66.60
World Scientific Publishing Co Pte Ltd Integral Equations, Boundary Value Problems And
Book SynopsisIn this volume, we report new results about various theories and methods of integral equation, boundary value problems for partial differential equations and functional equations, and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theories and methods for inverse problems of mathematical physics, Clifford analysis and related problems.Table of ContentsSome Properties of a Kind of Singular Integral Operator for K-Monogenic Function in Clifford Analysis (L P Wang, Z L Xu and Y Y Qiao); Some Results Related with Mobius Transformation in Clifford Analysis (Z X Zhang); The Scattering of SH Wave on the Array of Periodic Cracks in a Piezoelectric Substrate Bonded a Half-Plane of Functionally Graded Materials (J Q Liu, X Li, S Z Dong, X Y Yao and C F Wang); Anti-Plane Problem of Two Collinear Cracks in a Functionally Graded Coating - Substrate Structure (S H Ding and X Li); A Kind of Riemann Boundary Value Problem for Triharmonic Functions in Clifford Analysis (L F Gu); A New Dynamical Systems Method for Nonlinear Operator Equations (X J Luo, F C Li and S H Yang); A Class of Integral Inequality and Application (W S Wang); An Efficient Spectral Boundary Integral Equation Method for the Simulation of Earthquake Rupture Problems (W S Wang and B W Zhang); High-Frequency Asymptotics for the Modified Helmholtz Equation in a Half-Plane (H M Huang); An Inverse Boundary Value Problem Involving Filtration for Elliptic Systems of Equations (Z L Xu and L Yan); Fixed Point Theorems of Contractive Mappings in Extended Cone Metric Spaces (H P Huang and X Li); Positive Solutions of Singular Third-Order Three-Point Boundary Value Problems (B Q Yan and X Liu); Modified Neumann Integral and Asymptotic Behavior in the Half-Space (Y H Zhang, G T Deng and Z Z Wei); Piecewise Tikhonov Regularization Scheme to Reconstruct Discontinuous Density in Computerized Tomography (J Cheng, Y Jiang, K Lin and J W Yan); About the Quaternionic Jacobian Conjecture (H Liu); Interaction Between Antiplane Circular Inclusion and Circular Hole of Piezoelectric Materials (L H Chang and X Li); Convergence of Numerical Algorithm for Coupled Heat and Mass Transfer in Textile Materials (M B Ge, J X Cheng and D H Xu); Haversian Cortical Bone with a Radial Microcrack (X Wang); Spectra of Unitary Integral Operators on L2(ℝ) with Kernels k(xy) (D W Ma and G Chen); The Numerical Simulation of Long-Period Ground Motion on Basin Effects (Y Q Li and X Li); Complete Plane Strain Problem of a One-Dimensional Hexagonal Quasicrystals with a Doubly-Periodic Set of Cracks (X Li and P P Shi); The Problem About an Elliptic Hole with III Asymmetry Cracks in One-Dimensional Hexagonal Piezoelectric Quasicrystals (H S Huo and X Li); The Second Fundamental Problem of Periodic Plane Elasticity of a One-Dimensional Hexagonal Quasicrystals (J Y Cui, P P Shi and X Li); The Optimal Convex Combination Bounds for the Centroidal Mean (H Liu and X J Meng); The Method of Fundamental Solution for a Class of Elliptical Partial Differential Equations with Coordinate Transformation and Image Technique (L N Wu and Q Jiang); Various Wavelet Methods for Solving Fractional Fredholm - Volterra Integral Equations (P P Shi, X Li and X Li).
£103.50
World Scientific Publishing Co Pte Ltd Asymptotic Methods For Integrals
Book SynopsisThis book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
£180.00
World Scientific Publishing Co Pte Ltd Kurzweil-stieltjes Integral: Theory And
Book SynopsisThe book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.Table of ContentsIntroduction: Variation and Semi-Variation; Regulated Functions; Riemann-Stieltjes Integrals; Kurzweil-Stieltjes Integral in R; Abstract Kurzweil-Stieltjes Integral: Definition and Basic Properties; Existence; Integration-by-Parts; Saks-Henstock Lemma; Convergence Theorems; Kurzweil-Stieltjes Integral as a Function of the Upper Limit; Kurzweil-Stieltjes Integral and Functional Analysis: General Forms of Continuous Linear Functionals on Some Function Spaces; Multiplication of Distributions; Generalized Ordinary Differential Equations: Linear Equations; Nonlinear Equations; Continuous Dependence of Solutions on a Parameter; Differential Equations with Impulses; Dynamic Equations on Time-Scales; Functional Differential Equations;
£121.50
World Scientific Publishing Co Pte Ltd First Course In Integral Equations, A
Book SynopsisThis second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods.This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.Click here for solutions manual.Table of ContentsClassifications of Integral Equations; Fredholm Integral Equations; Volterra Integral Equations; Fredholm Integro-Differential Equations; Volterra Integro-Differential Equations; Singular Integral Equations; Nonlinear Fredholm Integral Equations; Nonlinear Volterra Integral Equations; Applications of Integral Equations;
£69.35
World Scientific Publishing Co Pte Ltd First Course In Integral Equations, A: Solutions
Book SynopsisThe second edition of A First Course in Integral Equations integrates the newly developed methods with classical techniques to give modern and robust approaches for solving integral equations. The manual accompanying this edition contains solutions to all exercises with complete step-by-step details. To interested readers trying to master the concepts and powerful techniques, this manual is highly useful, focusing on the readers' needs and expectations. It contains the same notations used in the textbook, and the solutions are self-explanatory. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.Table of ContentsClassifications of Integral Equations; Fredholm Integral Equations; Volterra Integral Equations; Fredholm Integro-Differential Equations; Volterra Integro-Differential Equations; Singular Integral Equations; Nonlinear Fredholm Integral Equations; Nonlinear Volterra Integral Equations; Applications of Integral Equations;
£30.40
Springer Lebesgues Theory of Integration
Book SynopsisThe Integration before Riemann.- The Definition of Integral Given by Riemann.- Geometric Definition of the Integral.- The Functions of the Bounded Variation.- The Search for Primitive Functions.- The Integration Defined with the Help of Primitive Functions.- The Definite Integral of Summable Functions.- The Indefinite Integral of Summable Functions.- The Seach of Primitive Functions. The Existence of Derivatives.- The Totalisation.- The Integral of Steiltjes.
£53.99
Springer Verlag, Singapore Measure and Integration
Book SynopsisDesigned for senior undergraduate and graduate students in mathematics, this textbook offers a comprehensive exploration of measure theory and integration. It acts as a pivotal link bridging the Riemann integral and the Lebesgue integral, with a primary focus on tracing the evolution of measure and integration from their historical roots. A distinctive feature of the book is meticulous guidance, providing a step-by-step journey through the subject matter, thus rendering complex concepts more accessible to beginners. A fundamental grasp of differential and integral calculus, as well as Riemann integration, is recommended to ensure a smoother comprehension of the material. This textbook comprises 10 well-structured chapters, each thoughtfully organized to lead students from fundamental principles to advanced complexities. Beginning with the establishment of Lebesgue's measure on the real line and an introduction to measurable functions, the book then delves into exploring the cardinalities of various set classes. As readers progress, the subtleties of the Lebesgue integral emerge, showcasing its generalization of the Riemann integral and its unique characteristics in higher dimensions. One of the book's distinctive aspects is its indepth comparison of the Lebesgue integral, improper Riemann integral, and Newton integral, shedding light on their distinct qualities and relative independence. Subsequent chapters delve into the realm of general measures, Lebesgue-Stieltje's measure, Hausdorff 's measure, and the concept of measure and integration in product spaces. Furthermore, the book delves into function spaces, such as 𝘓𝘱 spaces, and navigates the intricacies of signed and complex measures, providing students with a comprehensive foundation in this vital area of mathematics.
£49.49
Springer Special Integrals
Book SynopsisBinomial Series.- Trigonometrical Series.- Special Integrals.- Pseudo-Exponential Functions.- Series Sums using Special Integrals.- Solutions to Binomial Series.- Solutions to Trigonometrical Series.
£52.24
Springer Measure Theory for Analysis and Probability
Book Synopsis1. Measure Theory: Why and What.- 2. Measures: Construction and Properties.- 3. Measurable Functions and Integration.- 4. Random Variables and Random Vectors.- 5. Product Spaces.- 6. Radon-Nikodym Theorem and Lp Spaces.- 7. Convergence and Laws of Large Numbers.- 8. Weak convergence and Central Limit Theorem.- 9. Conditioning: The Right Approach.- 10. Infinite Products.- 11. Brownian Motion: A Brief Journey.
£49.49
World Scientific Publishing Co Pte Ltd Approximation And Regularisation Methods For
Book Synopsis
£66.50
