Numerical Calculus
Numerical Calculus

Author: William Edmund Milne

Publisher: Princeton University Press

Published: 2015-12-08

Total Pages: 404

ISBN-13: 1400875900

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The calculus of finite differences is here treated thoroughly and clearly by one of the leading American experts in the field of numerical analysis and computation. The theory is carefully developed and applied to illustrative examples, and each chapter is followed by a set of helpful exercises. The book is especially designed for the use of actuarial students, statisticians, applied mathematicians, and any scientists forced to seek numerical solutions. It presupposes only a knowledge of algebra, analytic geometry, trigonometry, and elementary calculus. The object is definitely practical, for while numerical calculus is based on the concepts of pure mathematics, it is recognized that the worker must produce a numerical result. Originally published in 1949. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Tensor Spaces and Numerical Tensor Calculus
Tensor Spaces and Numerical Tensor Calculus

Author: Wolfgang Hackbusch

Publisher: Springer Nature

Published: 2019-12-16

Total Pages: 622

ISBN-13: 3030355543

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Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Numerical Methods for Two-Point Boundary-Value Problems
Numerical Methods for Two-Point Boundary-Value Problems

Author: Herbert B. Keller

Publisher: Courier Dover Publications

Published: 2018-11-14

Total Pages: 417

ISBN-13: 0486828344

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Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.

Numerical Methods for Fractional Calculus
Numerical Methods for Fractional Calculus

Author: Changpin Li

Publisher: CRC Press

Published: 2015-05-19

Total Pages: 300

ISBN-13: 148225381X

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Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs.The book introduces the basic definitions and propertie

Python Programming and Numerical Methods
Python Programming and Numerical Methods

Author: Qingkai Kong

Publisher: Academic Press

Published: 2020-11-27

Total Pages: 482

ISBN-13: 0128195509

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Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings. - Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice - Summaries at the end of each chapter allow for quick access to important information - Includes code in Jupyter notebook format that can be directly run online

Applied Numerical Methods
Applied Numerical Methods

Author: Brice Carnahan

Publisher:

Published: 1969-01-15

Total Pages: 636

ISBN-13:

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Interpolation and approximation; Numerical integration; Solution of equations; Matrices and related topics; Systems of equations; The approximation of the solution of ordinary differential equations; Approximation of the solution of partial differential equations; Statistical methods.

Precise Numerical Methods Using C++
Precise Numerical Methods Using C++

Author: Oliver Aberth

Publisher: Academic Press

Published: 1998

Total Pages: 260

ISBN-13: 9780120417506

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This book explains how precise numerical analysis is constructed with C++. Included is a CD-ROM which contains executable Windows 95 programs for the PC and which demonstrates how these programs can be used to solvetypical problems of elementary numerical analysis with precision. The book also provides exercises which illustrate points from the text and references for the methods presented.

Numerical Methods for Ordinary Differential Equations
Numerical Methods for Ordinary Differential Equations

Author: J. C. Butcher

Publisher: John Wiley & Sons

Published: 2004-08-20

Total Pages: 442

ISBN-13: 0470868260

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This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography.

Introduction to Numerical Analysis
Introduction to Numerical Analysis

Author: J. Stoer

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 674

ISBN-13: 1475722729

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On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.