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Practical Numerical Integration
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Book Synopsis Practical Numerical Integration by : Gwynne Evans
Download or read book Practical Numerical Integration written by Gwynne Evans and published by . This book was released on 1993-08-24 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature. A full set of test examples is given and implemented for each method discussed, demonstrating its practical limitations.
Book Synopsis Methods of Numerical Integration by : Philip J. Davis
Download or read book Methods of Numerical Integration written by Philip J. Davis and published by Academic Press. This book was released on 2014-05-10 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods of Numerical Integration, Second Edition describes the theoretical and practical aspects of major methods of numerical integration. Numerical integration is the study of how the numerical value of an integral can be found. This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials. This book will be of great value to theoreticians and computer programmers.
Book Synopsis Riemann Solvers and Numerical Methods for Fluid Dynamics by : Eleuterio F. Toro
Download or read book Riemann Solvers and Numerical Methods for Fluid Dynamics written by Eleuterio F. Toro and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: High resolution upwind and centered methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics (CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Applications include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows.
Book Synopsis Practical Numerical Methods for Chemical Engineers by : Richard A. Davis
Download or read book Practical Numerical Methods for Chemical Engineers written by Richard A. Davis and published by CreateSpace. This book was released on 2014-10-02 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This NEW 3rd edition builds on the popular success of prior editions to expand the breadth of Practical Numerical Methods with more VBA macros that boost Excel's power for modeling and analysis. Engineers & scientists will find enhanced coverage of computational tools applicable to a wider variety of problems in their own disciplines. Excel is the de facto computational tool used by practicing engineers & scientists. Use this book to become proficient with VBA programming & customize your workbooks with time saving enhancements & powerful numerical techniques. Topics include an introduction to modeling, Excel & VBA programming, root-finding for systems of linear & nonlinear equations, eigenproblems, derivative approximation, optimization, experimental uncertainty analysis, least-squares regression & model validation, interpolation, integration, ordinary & partial differential equations. A companion web site has digital files for downloading 200 illustrations, examples, & the refined PNM3Suite workbook with 100 VBA user-defined functions, macros, & user forms for advanced numerical techniques. End-of-chapter practice problems for self-study are also available at the site (www.d.umn.edu/~rdavis/PNM/PNMExcelVBA3). Example files & macros are ready to be modified by users for their own needs. The introduction includes a primer on chemical reaction engineering for problems involving mass & energy balances with reactions. The next two chapters cover frequently overlooked features of Excel & VBA to apply numerical methods in Excel, as well as document results. The remaining chapters present powerful numerical techniques using Excel & VBA. Introduction to Numerical Methods & Mathematical Modeling Introduction to Excel: Documentation, Graphing, Worksheet Functions, Validation & Formatting, What-if Analysis VBA: Editor, Functions & Sub Procedures, Data Types, Structured Programming, Arithmetic & Worksheet Functions, Flow Control, Arrays, Communication, Message & Input Boxes, User Forms, Reading/Writing Files, Debugging Linear Equations: Matrix Algebra, Gaussian Elimination & Crout Reduction with Pivoting, Thomas, Cholesky, Power, Jacobi, & Interpolation Method for Eigenvalues & Eigenvectors, Jacobi & Gauss-Seidel Iteration, Relaxation Taylor Series Analysis: Finite Difference Derivative Approximations, Richardson's Extrapolation Nonlinear Equations: Root Finding, Bisection, Regula Falsi, Newton & Secant Methods, Wegstein, Quasi-Newton, Aitkin & Steffensen, Homotopy, Goal Seek & Solver, Bairstow's Method for Polynomial Roots Optimization: Solver, Luus-Jaakola, Quadratic Interpolation, Golden Section, Powell, Constraints, Scaling Uncertainty Analysis: Law of Propagation, Monte Carlo Simulations with Latin Hypercube Sampling Least-squares Regression: Linear & Nonlinear, LINEST, Gauss-Newton, Levenberg-Marquardt, Model Validation & Assessment, Parameter & Model Uncertainty Analysis, Weighted Regression Interpolation: Linear, Newton Divided Difference & Lagrange Polynomials, Rational, Stineman, Cubic & Constrained Splines, Linear & Spline Bivariate Interpolation Integration: Graphical, Trapezoidal, Midpoint for Improper Integrals, Romberg, Adaptive Simpson & Gauss-Kronrod, Multiple Integrals by Simpson, Guass-Kronrod & Monte Carlo Initial-value Problems: Single Step Euler & Backward Euler, Implicit Trapezoidal for Stiffness, Variable Step Runge-Kutta Cash Karp, Dormand-Prince, Multi-step Adams-Bashforth-Moulton, Differential-Algebraic Systems Boundary-value Problems & Partial Differential Equations: Shooting, Finite Difference, Orthogonal Collocation, Quasilinearization, Method of Lines, Crank-Nicholson Review: Summary Tables of Excel & VBA Functions, User-defined Functions, Macros, User Forms
Download or read book Quadrature Theory written by Helmut Brass and published by American Mathematical Soc.. This book was released on 2011-10-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.
Book Synopsis Practical Numerical Analysis by : Gwynne Evans
Download or read book Practical Numerical Analysis written by Gwynne Evans and published by . This book was released on 1995 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough and comprehensive introduction to the major topics of numerical analysis, for example, the solution of linear and non-linear equations, eigenvalue problems, approximation theory, quadrature, the numerical solution of ordinary differential equations and partial differential equations, and optimization. Each chapter gives a sound graded introduction to the topic, followed by up-to-date coverage of the more advanced areas. Contains a wealth of exercises, with selected hints and answers, ranging from those soluble by hand or a simple calculator to more extensive computer-oriented examples.
Book Synopsis Practical Numerical Methods with C# by : Jack Xu
Download or read book Practical Numerical Methods with C# written by Jack Xu and published by UniCAD. This book was released on 2019 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this book builds all the code example within a single project by incorporating new advancements in C# .NET technology and open-source math libraries. It also uses C# Interactive Window to test numerical computations without compiling or running the complete project code. The second edition includes three new chapters, including "Plotting", Fourier Analysis" and "Math Expression Parser". As in the first edition, this book presents an in-depth exposition of the various numerical methods used in real-world scientific and engineering computations. It emphasizes the practical aspects of C# numerical methods and mathematical functions programming, and discusses various techniques in details to enable you to implement these numerical methods in your .NET application. Ideal for scientists, engineers, and students who would like to become more adept at numerical methods, the second edition of this book covers the following content: - Overview of C# programming. - The mathematical background and fundamentals of numerical methods. - plotting the computation results using a 3D chart control. - Math libraries for complex numbers and functions, real and complex vector and matrix operations, and special functions. - Numerical methods for generating random numbers and random distribution functions. - Various numerical methods for solving linear and nonlinear equations. - Numerical differentiation and integration. - Interpolations and curve fitting. - Optimization of single-variable and multi-variable functions with a variety of techniques, including advanced simulated annealing and evolutionary algorithms. - Numerical techniques for solving ordinary differential equations. - Numerical methods for solving boundary value problems. - Eigenvalue problems. - Fourier analysis. - mathematical expression parser and evaluator. In addition, this book provides testing examples for every math function and numerical method to show you how to use these functions and methods in your own .NET applications in a manageable and step-by-step fashion. Please visit the author's website for more information about this book at https://drxudotnet.com https://drxudotnet.com and https://gincker.com.
Book Synopsis Numerical Methods in Computational Electrodynamics by : Ursula van Rienen
Download or read book Numerical Methods in Computational Electrodynamics written by Ursula van Rienen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: treated in more detail. They are just specimen of larger classes of schemes. Es sentially, we have to distinguish between semi-analytical methods, discretiza tion methods, and lumped circuit models. The semi-analytical methods and the discretization methods start directly from Maxwell's equations. Semi-analytical methods are concentrated on the analytical level: They use a computer only to evaluate expressions and to solve resulting linear algebraic problems. The best known semi-analytical methods are the mode matching method, which is described in subsection 2. 1, the method of integral equations, and the method of moments. In the method of integral equations, the given boundary value problem is transformed into an integral equation with the aid of a suitable Greens' function. In the method of moments, which includes the mode matching method as a special case, the solution function is represented by a linear combination of appropriately weighted basis func tions. The treatment of complex geometrical structures is very difficult for these methods or only possible after geometric simplifications: In the method of integral equations, the Greens function has to satisfy the boundary condi tions. In the mode matching method, it must be possible to decompose the domain into subdomains in which the problem can be solved analytically, thus allowing to find the basis functions. Nevertheless, there are some ap plications for which the semi-analytic methods are the best suited solution methods. For example, an application from accelerator physics used the mode matching technique (see subsection 5. 4).
Book Synopsis Numerical Python by : Robert Johansson
Download or read book Numerical Python written by Robert Johansson and published by Apress. This book was released on 2015-10-07 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Python by Robert Johansson shows you how to leverage the numerical and mathematical modules in Python and its Standard Library as well as popular open source numerical Python packages like NumPy, FiPy, matplotlib and more to numerically compute solutions and mathematically model applications in a number of areas like big data, cloud computing, financial engineering, business management and more. After reading and using this book, you'll get some takeaway case study examples of applications that can be found in areas like business management, big data/cloud computing, financial engineering (i.e., options trading investment alternatives), and even games. Up until very recently, Python was mostly regarded as just a web scripting language. Well, computational scientists and engineers have recently discovered the flexibility and power of Python to do more. Big data analytics and cloud computing programmers are seeing Python's immense use. Financial engineers are also now employing Python in their work. Python seems to be evolving as a language that can even rival C++, Fortran, and Pascal/Delphi for numerical and mathematical computations.
Book Synopsis Numerical Methods in Science and Engineering – A Practical Approach by : Rajasekaran S.
Download or read book Numerical Methods in Science and Engineering – A Practical Approach written by Rajasekaran S. and published by S. Chand Publishing. This book was released on 2003 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past two decades,owing to the advent of digital computers,numerical methods of analysis have become very popular for the solution of complex problems in physical and management sciences and in engineering.As the price of hardware keeps decreasing repidly,experts predict that in the near future one may have to pay onliy for sodtware.This underscores the importance of numerical computation to the scientist and engineers and,today,most undergraduates and postgraduates are being given training in the use of computers and access to the computers for the solution of problems.
Book Synopsis Numerical Methods for Scientists and Engineers by : Richard Wesley Hamming
Download or read book Numerical Methods for Scientists and Engineers written by Richard Wesley Hamming and published by . This book was released on 1962 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Precise Numerical Methods Using C++ by : Oliver Aberth
Download or read book Precise Numerical Methods Using C++ written by Oliver Aberth and published by Academic Press. This book was released on 1998 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A First Course in Numerical Methods by : Uri M. Ascher
Download or read book A First Course in Numerical Methods written by Uri M. Ascher and published by SIAM. This book was released on 2011-07-14 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers students a practical knowledge of modern techniques in scientific computing.
Book Synopsis Numerical Methods by : George Lindfield
Download or read book Numerical Methods written by George Lindfield and published by Academic Press. This book was released on 2018-10-10 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth edition of Numerical Methods Using MATLAB® provides a clear and rigorous introduction to a wide range of numerical methods that have practical applications. The authors’ approach is to integrate MATLAB® with numerical analysis in a way which adds clarity to the numerical analysis and develops familiarity with MATLAB®. MATLAB® graphics and numerical output are used extensively to clarify complex problems and give a deeper understanding of their nature. The text provides an extensive reference providing numerous useful and important numerical algorithms that are implemented in MATLAB® to help researchers analyze a particular outcome. By using MATLAB® it is possible for the readers to tackle some large and difficult problems and deepen and consolidate their understanding of problem solving using numerical methods. Many worked examples are given together with exercises and solutions to illustrate how numerical methods can be used to study problems that have applications in the biosciences, chaos, optimization and many other fields. The text will be a valuable aid to people working in a wide range of fields, such as engineering, science and economics. Features many numerical algorithms, their fundamental principles, and applications Includes new sections introducing Simulink, Kalman Filter, Discrete Transforms and Wavelet Analysis Contains some new problems and examples Is user-friendly and is written in a conversational and approachable style Contains over 60 algorithms implemented as MATLAB® functions, and over 100 MATLAB® scripts applying numerical algorithms to specific examples
Book Synopsis Numerical Methods in Engineering Practice by : Amir Wadi Al-Khafaji
Download or read book Numerical Methods in Engineering Practice written by Amir Wadi Al-Khafaji and published by . This book was released on 1986 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Integration by : T.O. Espelid
Download or read book Numerical Integration written by T.O. Espelid and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Develop ments, Software and Applications', held at the University of Bergen, Bergen, Norway, June 17-21,1991. The Workshop was attended by thirty-eight scientists. A total of eight NATO countries were represented. Eleven invited lectures and twenty-three contributed lectures were presented, of which twenty-five appear in full in this volume, together with three extended abstracts and one note. The main focus of the workshop was to survey recent progress in the theory of methods for the calculation of integrals and show how the theoretical results have been used in software development and in practical applications. The papers in this volume fall into four broad categories: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software. It is five years since the last workshop of this nature was held, at Dalhousie University in Halifax, Canada, in 1986. Recent theoretical developments have mostly occurred in the area of integration rule construction. For polynomial integrating rules, invariant theory and ideal theory have been used to provide lower bounds on the numbers of points for different types of multidimensional rules, and to help in structuring the nonlinear systems which must be solved to determine the points and weights for the rules. Many new optimal or near optimal rules have been found for a variety of integration regions using these techniques.
Book Synopsis Applied Numerical Methods Using MATLAB by : Won Y. Yang
Download or read book Applied Numerical Methods Using MATLAB written by Won Y. Yang and published by John Wiley & Sons. This book was released on 2005-05-20 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main benefit is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online.
