Kategoria BISAC: Mathematics >> Number Systems

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the...

Line Integral Methods for Conservative Problems explains the numerical solution of differential equations within the framework of geometric integration, a branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution) relevant geometric properties of the continuous vector field. The book focuses on a large set of differential systems named conservative problems, particularly Hamiltonian systems.

Assuming only basic knowledge of numerical quadrature and Runge Kutta methods, this self-contained book begins with an...

The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional Laplacian explores applications of the fractional Laplacian in science, engineering, and other areas where long-range interactions and conceptual or physical particle jumps resulting in an irregular diffusive or conductive flux are encountered.

• Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential...

Covering a wide range of numerical applications that have immediate relevancy for engineers, the book describes forty-nine...

One of the masters in the differential equations community, the late F.V. Atkinson contributed seminal research to multiparameter spectral theory and Sturm-Liouville theory. His ideas and techniques have long inspired researchers and continue to stimulate discussion. With the help of co-author Angelo B. Mingarelli, Multiparameter Eigenvalue Problems: Sturm-Liouville Theory reflects much of Dr. Atkinson's final work.

After covering standard multiparameter problems, the book investigates the conditions for eigenvalues to be real and form a discrete set. It...

Besides giving readers the techniques for solving polynomial equations and congruences, An Introduction to Mathematical Thinking provides preparation for understanding more advanced topics in Linear and Modern Algebra, as well as Calculus. This book introduces proofs and mathematical thinking while teaching basic algebraic skills involving number systems, including the integers and complex numbers. Ample questions at the end of each chapter provide opportunities for learning and practice; the Exercises are routine applications of the material in the chapter, while...

Exploring new variations of classical methods as well as recent approaches appearing in the field, Computational Fluid Dynamics demonstrates the extensive use of numerical techniques and mathematical models in fluid mechanics. It presents various numerical methods, including finite volume, finite difference, finite element, spectral, smoothed particle hydrodynamics (SPH), mixed-element-volume, and free surface flow.

Taking a unified point of view, the book first introduces the basis of finite volume, weighted residual, and spectral approaches. The contributors present the SPH method, a...

Many of today s complex scientific applications now require a vast amount of computational power. General purpose graphics processing units (GPGPUs) enable researchers in a variety of fields to benefit from the computational power of all the cores available inside graphics cards.

Understand the Benefits of Using GPUs for Many Scientific Applications

Designing Scientific Applications on GPUs shows you how to use GPUs for applications in diverse scientific fields, from physics and mathematics to computer science. The book explains the methods necessary for designing or porting your...

For a variety of reasons, the MATLAB(r)-Java interface was never fully documented. This is really quite unfortunate: Java is one of the most widely used programming languages, having many times the number of programmers and programming resources as MATLAB. Also unfortunate is the popular claim that while MATLAB is a fine programming platform for prototyping, it is not suitable for real-world, modern-looking applications. Undocumented Secrets of MATLAB(r)-Java Programming aims to correct this misconception.

This book shows how using Java can significantly improve MATLAB program...

This book provides a rigorous treatment of spectral analysis using Fourier-based techniques in the geosciences, specifically geodesy and geophysics that deal with global and regional spatial data. It emphasizes spatial -frequency analysis for data on the plane and sphere. It includes applications to stochastic processes on the plane and sphere, which are important for many estimation problems that are based on some kind of stochastic constraints in inverse theory. It also briefly outlines wavelet analysis, although unusual, it is included to illustrate the contrast to traditional spectral...