Listing 1 - 10 of 11 | << page >> |
Sort by
|
Choose an application
The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.
Definite integrals. --- Integrals. --- Calculus, Integral --- Integrals, Definite --- Integrals
Choose an application
Riemann integral. --- Integral, Riemann --- Definite integrals --- Integral de Riemann --- Integrals definides
Choose an application
Finite element method. --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Differential equations --- Numerical integration. --- Numerical solutions. --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- 517.91 Differential equations
Choose an application
This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis. Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems. This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.
Mathematics. --- Fourier analysis. --- Functional analysis. --- Measure and Integration. --- Real Functions. --- Fourier Analysis. --- Functional Analysis. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Mathematical analysis --- Math --- Science --- Riemann integral. --- Integral, Riemann --- Definite integrals --- Measure theory. --- Functions of real variables. --- Real variables --- Functions of complex variables --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)
Choose an application
Ce Petit traité d’intégration développe une approche originale de l’intégrale. Cette approche, que l’on pourrait qualifier de globale, est due aux deux mathématiciens Jaroslaw Kurzweil et Ralph Henstock. L’enseignement de l’intégration se fait d’ordinaire en deux temps. On débute en proposant des approximations de l’aire située sous le graphe de la fonction sous la forme de sommes de Riemann, ce qui est bien adapté au calcul différentiel et intégral portant sur des fonctions régulières. On présente ensuite l’intégrale de Lebesgue en lien avec la théorie de la mesure. L’approche de Kurzweil et Henstock est proche de celle de Riemann, à cela près que le pas des subdivisions de l’intervalle pour le calcul de l’aire peut ne pas être constant. L’intérêt de cette méthode est de contenir la théorie de Lebesgue et d’être optimale pour le calcul différentiel. Ce livre concerne au premier chef les étudiants de mathématiques de tous les cycles (licence, master, préparation aux concours de l’enseignement…). Il intéressera également les enseignants de mathématiques ou de physique et, plus généralement, les ingénieurs et scientifiques qui font usage de la théorie de l’intégration.
Integration, Functional. --- Riemann integral. --- Henstock-Kurzweil integral. --- Riemann, Bernhard, --- Lebesgue, Henri Léon, --- Gauge integral --- Generalized Riemann integral --- Henstock integrals --- HK integral --- Kurzweil-Henstock integral --- Kurzweil integral --- Riemann integral, Generalized --- Integral, Riemann --- Functional integration --- Lebeg, Anri, --- Riemann, B. --- Riman, Georg Fridrikh Bernkhard, --- Riman, Bernkhard, --- Riemann, Georg Friedrich Bernhard, --- Integrals, Generalized --- Definite integrals --- Functional analysis --- Lebesgue, Henri, --- Functions of several complex variables. --- Fonctions de plusieurs variables complexes. --- Intégration de fonctions.
Choose an application
This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The book focuses on providing insights into the interplay between coordinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by many examples, figures and code segments. Numerical experiments with applications from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even for integrands with hundreds of dimensions.
Calculus, Integral. --- Numerical grid generation (Numerical analysis). --- Numerical analysis --- Finance --- Risk --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Applied Mathematics --- Mathematics - General --- Mathematical models --- Numerical integration. --- Insurance --- Mathematical models. --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Mathematics. --- Economics, Mathematical. --- Computer mathematics. --- Computational Mathematics and Numerical Analysis. --- Quantitative Finance. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Economics --- Mathematical economics --- Econometrics --- Math --- Science --- Methodology --- Definite integrals --- Interpolation --- Computer science --- Finance. --- Funding --- Funds --- Currency question --- Economics, Mathematical .
Choose an application
Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi.
Numerical integration. --- Orthogonal polynomials. --- Gautschi, Walter. --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Mathematics. --- Computer science --- Approximation theory. --- Differential equations. --- Numerical analysis. --- History. --- Numerical Analysis. --- Mathematics of Computing. --- Approximations and Expansions. --- History of Mathematical Sciences. --- Ordinary Differential Equations. --- Definite integrals --- Interpolation --- Numerical analysis --- Computer science. --- Differential Equations. --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Informatics --- Mathematical analysis --- Computer science—Mathematics. --- Annals --- Auxiliary sciences of history --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Computer mathematics --- Electronic data processing --- Mathematics --- Chebyshev approximation. --- Gaussian quadrature formulas. --- Mathematicians.
Choose an application
The book addresses the problem of calculation of d-dimensional integrals (conditional expectations) in filter problems. It develops new methods of deterministic numerical integration, which can be used to speed up and stabilize filter algorithms. With the help of these methods, better estimates and predictions of latent variables are made possible in the fields of economics, engineering and physics. The resulting procedures are tested within four detailed simulation studies.
Statistics. --- Computer mathematics. --- Vibration. --- Dynamical systems. --- Dynamics. --- Econometrics. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Computational Mathematics and Numerical Analysis. --- Vibration, Dynamical Systems, Control. --- Statistical Physics and Dynamical Systems. --- Cubature formulas. --- Numerical integration. --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- Formulas, Cubature --- Numerical integration --- Computer science --- Statistical physics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Mathematics. --- Physics --- Mathematical statistics --- Cycles --- Mechanics --- Sound --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Economics, Mathematical --- Statistics --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistics . --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Statics
Choose an application
Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi-Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.
Monte Carlo method. --- Nets (Mathematics) --- Sequences (Mathematics) --- Numerical integration. --- Digital filters (Mathematics) --- Data smoothing filters --- Filters, Digital (Mathematics) --- Linear digital filters (Mathematics) --- Linear filters (Mathematics) --- Numerical filters --- Smoothing filters (Mathematics) --- Digital electronics --- Filters (Mathematics) --- Fourier transformations --- Functional analysis --- Numerical analysis --- Numerical calculations --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Moore-Smith convergence --- Net equations --- Net methods (Mathematics) --- Convergence --- Set theory --- Topology --- Artificial sampling --- Model sampling --- Monte Carlo simulation --- Monte Carlo simulation method --- Stochastic sampling --- Games of chance (Mathematics) --- Mathematical models --- Stochastic processes
Choose an application
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches. The second edition is substantially revised and enlarged, with many improvements in the presentation and additions concerning in particular non-canonical Hamiltonian systems, highly oscillatory mechanical systems, and the dynamics of multistep methods.
Numerical integration. --- Hamiltonian systems. --- Differential equations --- Numerical solutions. --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Numerical analysis. --- Biomathematics. --- Physics. --- Numerical Analysis. --- Analysis. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Numerical and Computational Physics. --- Mathematical and Computational Biology. --- 517.91 Differential equations --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Differentiable dynamical systems --- Integration, Numerical --- Mechanical quadrature --- Quadrature, Mechanical --- Definite integrals --- Interpolation --- Numerical analysis --- Global analysis (Mathematics). --- Mathematical physics. --- Numerical and Computational Physics, Simulation. --- Physical mathematics --- Physics --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis --- Mathematics --- Biology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- 517.1 Mathematical analysis --- Hamiltonian systems --- Differential equations - Numerical solutions --- 517.91 --- Numerical integration --- 519.62 --- 681.3*G17 --- 681.3*G17 Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- Ordinary differential equations: boundary value problems; convergence and stability; error analysis; initial value problems; multistep methods; single step methods; stiff equations (Numerical analysis) --- 519.62 Numerical methods for solution of ordinary differential equations --- Numerical methods for solution of ordinary differential equations --- Numerical solutions
Listing 1 - 10 of 11 | << page >> |
Sort by
|