Solving Transcendental Equations

Solving Transcendental Equations PDF

Author: John P. Boyd

Publisher: SIAM

Published: 2014-09-23

Total Pages: 446

ISBN-13: 161197352X

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Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute--not always needed, but indispensible when it is. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations.

Solving Transcendental Equations

Solving Transcendental Equations PDF

Author: John P. Boyd

Publisher: SIAM

Published: 2014-10-23

Total Pages: 446

ISBN-13: 1611973511

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Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute?not always needed, but indispensable when it is. The author?s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding, and it includes three chapters on analytical methods?explicit solutions, regular pertubation expansions, and singular perturbation series (including hyperasymptotics)?unlike other books that give only numerical algorithms for solving algebraic and transcendental equations. This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations.

Fundamental Numerical Methods for Electrical Engineering

Fundamental Numerical Methods for Electrical Engineering PDF

Author: Stanislaw Rosloniec

Publisher: Springer Science & Business Media

Published: 2008-07-17

Total Pages: 294

ISBN-13: 3540795197

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Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.

Applied Artificial Neural Network Methods For Engineers And Scientists: Solving Algebraic Equations

Applied Artificial Neural Network Methods For Engineers And Scientists: Solving Algebraic Equations PDF

Author: Snehashish Chakraverty

Publisher: World Scientific

Published: 2021-01-26

Total Pages: 192

ISBN-13: 9811230226

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The aim of this book is to handle different application problems of science and engineering using expert Artificial Neural Network (ANN). As such, the book starts with basics of ANN along with different mathematical preliminaries with respect to algebraic equations. Then it addresses ANN based methods for solving different algebraic equations viz. polynomial equations, diophantine equations, transcendental equations, system of linear and nonlinear equations, eigenvalue problems etc. which are the basic equations to handle the application problems mentioned in the content of the book. Although there exist various methods to handle these problems, but sometimes those may be problem dependent and may fail to give a converge solution with particular discretization. Accordingly, ANN based methods have been addressed here to solve these problems. Detail ANN architecture with step by step procedure and algorithm have been included. Different example problems are solved with respect to various application and mathematical problems. Convergence plots and/or convergence tables of the solutions are depicted to show the efficacy of these methods. It is worth mentioning that various application problems viz. Bakery problem, Power electronics applications, Pole placement, Electrical Network Analysis, Structural engineering problem etc. have been solved using the ANN based methods.

Engineering Analysis

Engineering Analysis PDF

Author: Yen-Ching Pao

Publisher: CRC Press

Published: 2019-04-24

Total Pages: 374

ISBN-13: 9781420049619

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This book provides a concise introduction to numerical concepts in engineering analysis, using FORTRAN, QuickBASIC, MATLAB, and Mathematica to illustrate the examples. Discussions include: matrix algebra and analysis solution of matrix equations methods of curve fit methods for finding the roots of polynom

Fundamentals of Numerical Mathematics for Physicists and Engineers

Fundamentals of Numerical Mathematics for Physicists and Engineers PDF

Author: Alvaro Meseguer

Publisher: John Wiley & Sons

Published: 2020-06-16

Total Pages: 400

ISBN-13: 1119425670

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Introduces the fundamentals of numerical mathematics and illustrates its applications to a wide variety of disciplines in physics and engineering Applying numerical mathematics to solve scientific problems, this book helps readers understand the mathematical and algorithmic elements that lie beneath numerical and computational methodologies in order to determine the suitability of certain techniques for solving a given problem. It also contains examples related to problems arising in classical mechanics, thermodynamics, electricity, and quantum physics. Fundamentals of Numerical Mathematics for Physicists and Engineers is presented in two parts. Part I addresses the root finding of univariate transcendental equations, polynomial interpolation, numerical differentiation, and numerical integration. Part II examines slightly more advanced topics such as introductory numerical linear algebra, parameter dependent systems of nonlinear equations, numerical Fourier analysis, and ordinary differential equations (initial value problems and univariate boundary value problems). Chapters cover: Newton’s method, Lebesgue constants, conditioning, barycentric interpolatory formula, Clenshaw-Curtis quadrature, GMRES matrix-free Krylov linear solvers, homotopy (numerical continuation), differentiation matrices for boundary value problems, Runge-Kutta and linear multistep formulas for initial value problems. Each section concludes with Matlab hands-on computer practicals and problem and exercise sets. This book: Provides a modern perspective of numerical mathematics by introducing top-notch techniques currently used by numerical analysts Contains two parts, each of which has been designed as a one-semester course Includes computational practicals in Matlab (with solutions) at the end of each section for the instructor to monitor the student's progress through potential exams or short projects Contains problem and exercise sets (also with solutions) at the end of each section Fundamentals of Numerical Mathematics for Physicists and Engineers is an excellent book for advanced undergraduate or graduate students in physics, mathematics, or engineering. It will also benefit students in other scientific fields in which numerical methods may be required such as chemistry or biology.

Heat Conduction

Heat Conduction PDF

Author: M. Necati Özışık

Publisher: John Wiley & Sons

Published: 1993-03-22

Total Pages: 716

ISBN-13: 9780471532569

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This Second Edition for the standard graduate level course in conduction heat transfer has been updated and oriented more to engineering applications partnered with real-world examples. New features include: numerous grid generation--for finding solutions by the finite element method--and recently developed inverse heat conduction. Every chapter and reference has been updated and new exercise problems replace the old.

Computer Programming and Numerical Analysis Revised Edition with C: A Integrated Approach

Computer Programming and Numerical Analysis Revised Edition with C: A Integrated Approach PDF

Author: N. Datta

Publisher: Universities Press

Published: 2003-10

Total Pages: 520

ISBN-13: 9788173714511

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The availability of high-speed digital computers has led to the widespread study of computer programming and numerical analysis in Indian universities and technological institutes. This book presents the theory and applications of numerical methods for the solution of various types of computational problems in science and engineering.