e-books in Numerical Analysis category
by Giray Ökten - Florida State University , 2019
The book presents the theory and methods, together with the implementation of the algorithms using the Julia programming language. The book covers computer arithmetic, root-finding, numerical quadrature and differentiation, and approximation theory.
by M. Holst, M. Licht - arXiv.org , 2018
We present a new technique to apply finite element methods to partial differential equations over curved domains. Bramble-Hilbert lemma is key in harnessing regularity in the physical problem to prove finite element convergence rates for the problem.
by Svein Linge, Hans Petter Langtangen - Springer , 2016
This book presents Python programming as a key method for solving mathematical problems. The style is accessible and concise, the emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.
by Hans Petter Langtangen, Svein Linge - Springer , 2017
This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners.
by Hans Petter Langtangen, Anders Logg - Springer , 2017
This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, it guides readers through the essential steps to quickly solving a PDE in FEniCS.
by Justin Solomon - CRC Press , 2015
Using examples from a broad base of computational tasks, including data processing and computational photography, the book introduces numerical modeling and algorithmic design from a practical standpoint and provides insight into theoretical tools.
by Todd Young, Martin J. Mohlenkamp - Ohio University , 2017
The goals of these notes are to introduce concepts of numerical methods and introduce Matlab in an Engineering framework. The notes were developed by the author in the process of teaching a course on applied numerical methods for Civil Engineering.
by Jeffrey R. Chasnov - The Hong Kong University , 2012
This is primarily for non-mathematics majors and is required by several engineering departments. Contents: IEEE Arithmetic; Root Finding; Systems of equations; Least-squares approximation; Interpolation; Integration; Ordinary differential equations.
by Jeffrey R. Chasnov - Harvey Mudd College , 2013
This course consists of both numerical methods and computational physics. MATLAB is used to solve various computational math problems. The course is primarily for Math majors and supposes no previous knowledge of numerical analysis or methods.
by Daniele Venturi - arXiv , 2016
The purpose of this manuscript is to provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
by Leon Q. Brin - Southern Connecticut State University , 2014
A one semester introduction to numerical analysis. Includes typical introductory material, root finding, numerical calculus, and interpolation techniques. The focus is on the mathematics rather than application to engineering or sciences.
by Solomon I. Khmelnik, Inna S. Doubson - MiC , 2011
Hardware algorithms for computing of all elementary complex variable functions are proposed. Contents: A method 'digit-by-digit'; Decomposition; Compositions; Two-step-by-step operations; Taking the logarithm; Potentiation; and more.
by Gong Chen, et al. - Wikibooks , 2013
We start with finite-precision arithmetic. We then discuss how to solve ordinary differential equations and partial differential equations using the technique of separation of variables. We then introduce numerical time-stepping schemes...
by K. Nandakumar - University of Alberta , 1998
Contents: On mathematical models; Single nonlinear algebraic equation; System of linear and nonlinear algebraic equations; Numerical differentiation and integration; Ordinary differential equations; Boundary value problems; etc.
by H.B. Keller - Tata Institute Of Fundamental Research , 1986
These lectures introduce the modern theory and practical numerical methods for continuation of solutions of nonlinear problems depending upon parameters. The treatment is elementary, advanced calculus and linear algebra are the omly prerequisites.
by R. Glowinski - Tata Institute of Fundamental Research , 1980
Many physics problems have variational formulations making them appropriate for numerical treatment. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations.
by Bertrand Mercier - Tata Institute of Fundamental Research , 1979
Contents: Sobolev Spaces; Abstract Variational Problems and Examples; Conforming Finite Element Methods; Computation of the Solution of the Approximate Problem; Problems with an Incompressibility Constraint; Mixed Finite Element Methods; etc.
by P. Lascaux - Tata Institute of Fundamental Research , 1976
The solution of time dependent equations of hydrodynamics is a subject of great importance. This book is mainly concentrated on the study of the stability of the various schemes. We have considered only the stability for linearized problems.
by Ph. Ciarlet - Tata Institute of Fundamental Research , 1975
Our basic aim has been to present some of the mathematical aspects of the finite element method, as well as some applications of the finite element method for solving problems in Elasticity. This is why some important topics are not covered here.
by Mark Embree - Rice University , 2012
This course takes a tour through many algorithms of numerical analysis. We aim to assess alternative methods based on efficiency, to discern well-posed problems from ill-posed ones, and to see these methods in action through computer implementation.
by C.T. Kelley - SIAM , 1995
This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods.
by Yousef Saad - SIAM , 2011
This book discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods for solving matrix eigenvalue problems that arise in various engineering applications.
by Douglas W. Harder, Richard Khoury - University of Waterloo , 2010
Contents: Error Analysis, Numeric Representation, Iteration, Linear Algebra, Interpolation, Least Squares, Taylor Series, Bracketing, The Five Techniques, Root Finding, Optimization, Differentiation, Integration, Initial-value Problems, etc.
by Jan Awrejcewicz - InTech , 2011
The book introduces theoretical approach to numerical analysis as well as applications of various numerical methods to solving numerous theoretical and engineering problems. The book is useful for both theoretical and applied research.
by Dennis Deturck, Herbert S. Wilf - University of Pennsylvania , 2002
Contents: Differential and Difference Equations (Linear equations with constant coefficients, Difference equations, Stability theory); The Numerical Solution of Differential Equations (Euler's method); Numerical linear algebra.
by George Benthien , 2006
Tutorial describing many of the standard numerical methods used in Linear Algebra. Topics include Gaussian Elimination, LU and QR Factorizations, The Singular Value Decomposition, Eigenvalues and Eigenvectors via the QR Method, etc.
by George Benthien , 2006
Tutorial discussing some of the numerical aspects of practical harmonic analysis. Topics include Historical Background, Fourier Series and Integral Approximations, Convergence Improvement, Differentiation of Fourier Series and Sigma Factors, etc.
by Kurt Mehlhorn, Chee Yap - New York University , 2004
Contents: Introduction to Geometric Nonrobustness; Modes of Numerical Computation; Geometric Computation; Arithmetic Approaches; Geometric Approaches; Exact Geometric Computation; Perturbation; Filters; Algebraic Background; Zero Bounds; etc.
by M.N. Spijker - Leiden University , 1998
Stability estimates and resolvent conditions in the numerical solution of initial value problems. Contents: Partial differential equations and numerical methods; Linear algebra; Stability in the numerical solution of differential equations; etc.
by B. Piette - University of Durham , 2004
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.
by L. M. Milne Thomson - Macmillan and co , 1933
The object of this book is to provide a simple account of the subject of Finite Differences and to present the theory in a form which can be readily applied -- not only the useful material of Boole, but also the more modern developments.
by Adrian Sandu - Virginia Tech , 2001
Contents: a quick tour of fortran 95; the building blocks of a fortran application; flow control; computer arithmetic; applications; intrinsic functions; input and output; arrays; more on procedures; parametrized intrinsic types; derived types; etc.
by N. V. Kopchenova, I. A. Maron , 1975
This is a manual on solving problems in computational mathematics. The book is intended primarily for engineering students, but may also prove useful for economics students, graduate engineers, and postgraduate students in the applied sciences.
by Yousef Saad - PWS , 1996
The book gives an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.
by R. Hosking, S. Joe, D. Joyce, and J. Turner , 1998
This book provides an excellent introduction to the elementary concepts and methods of numerical analysis for students meeting the subject for the first time. The subject matter is organized into fundamental topics and presented as a series of steps.
by James M. McDonough - University of Kentucky , 2001
These notes cover the following topics: Numerical linear algebra; Solution of nonlinear equations; Approximation theory; Numerical solution of ordinary differential equations; Numerical solution of partial differential equations.
by William H. Press, at al. - Cambridge University Press , 1996
Numerical Recipes in Fortran 90 contains a detailed introduction to the Fortran 90 language and to the basic concepts of parallel programming, plus source code for all routines from the second edition of Numerical Recipes.
by M. Abramowitz, I. A. Stegun - GPO , 1964
Students and professionals in the fields of mathematics, physics, engineering, and economics will find this reference work invaluable. A classic resource for special functions, standard trig, and exponential logarithmic definitions and extensions.
by Ian Craw - University of Aberdeen , 2002
The book describes the simplex algorithm and shows how it can be used to solve real problems. It shows how previous results in linear algebra give a framework for understanding the simplex algorithm and describes other optimization algorithms.
by Ian Craw - University of Aberdeen , 2003
The overall aim of the course is to present modern computer programming techniques in the context of mathematical computation and numerical analysis and to foster the independence needed to use these techniques as appropriate in subsequent work.
by Steven E. Pav - University of California at San Diego , 2005
From the table of contents: A 'Crash' Course in octave/Matlab; Solving Linear Systems; Finding Roots; Interpolation; Spline Interpolation; Approximating Derivatives; Integrals and Quadrature; Least Squares; Ordinary Differential Equations.
by George W. Collins, II - NASA ADS , 2003
'Fundamental Numerical Methods and Data Analysis' can serve as the basis for a wide range of courses that discuss numerical methods used in science. The author provides examples of the more difficult algorithms integrated into the text.
by Autar K Kaw, Egwu Eric Kalu - Lulu.com , 2008
The textbook is written for engineering undergraduates taking a course in numerical methods. It offers a treatise to numerical methods based on a holistic approach and short chapters. The authors included examples of real-life applications.
by Richard Barrett et al. - Society for Industrial Mathematics , 1987
The book focuses on the use of iterative methods for solving large sparse systems of linear equations. General and reusable templates are introduced to meet the needs of both the traditional user and the high-performance specialist.