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Numerical Methods in Engineering & Science (with Programs in C,C++ &MATLAB)

This license does not permit uploading of the Work onto the Internet or on a network of any kind without the writ- ten consent of the Publisher. Duplication or dissemination of any text, code, simulations, images, etc.

The author, developers, and the publisher of any accompanying content, and anyone involved in the composition, production, and manufacturing of this work will not be liable for damages of any kind arising out of the use of or the inability to use the algorithms, source code, computer programs, or textual material contained in this publication.

This includes, but is not limited to, loss of revenue or profit, or other incidental, physical, or consequential damages arising out of the use of this Work. The sole remedy in the event of a claim of any kind is expressly limited to re- placement of the book, and only at the discretion of the Publisher. All rights reserved. This publication, portions of it, or any accompanying software may not be reproduced in any way, stored in a retrieval system of any type, or transmitted by any means, media, electronic display or mechanical display, including, but not limited to, photocopy, recording, Internet postings, or scanning, without prior permission in writing from the publisher.

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All of our titles are available in digital format at authorcloudware. Chapter 1 Approximations and Errors in Computation 1 1. Chapter 2 Solution of Algebraic and Transcendental Equations 19 2.

Chapter 3 Solution of Simultaneous Algebraic Equations 93 3. Chapter 4 Matrix Inversion and Eigenvalue Problem 4. Chapter 5 Empirical Laws and Curve-Fitting 5. Chapter 6 Finite Differences 6. Chapter 7 Interpolation 7. Chapter 8 Numerical Differentiation and Integration 8. Chapter 9 Difference Equations 9.

Chapter 12 Linear Programming Chapter 13 A Brief Review of Computers We know that exact methods often fail in drawing plausible inferences from a given set of tabulat- ed data or in finding roots of transcendental equations or in solving non-linear differential equations.

There are many more such situations where analytical methods are unable to produce desirable results. Even if analytical solutions are available, these are not amenable to direct numerical interpretation.

The aim of numerical analysis is therefore, to provide constructive methods for obtaining answers to such problems in a numerical form. With the advent of high speed computers and increasing demand for numerical solution to various problems, numerical techniques have become indispensible tools in the hands of engineers and scientists.

The input information is rarely exact since it comes from some mea- surement or the other and the method also introduces further error. As such, the error in the final result may be due to an error in the initial data or in the method or both. Our effort will be to minimize these errors, so as to get the best possible results. We therefore begin by explaining various kinds of approximations and errors which may occur in a problem and de- rive some results on error propagation in numerical calculations.

Approximate numbers. There are two types of numbers: exact and ap- proximate. These may be approximated by numbers 1. Such numbers which represent the given numbers to a cer- tain degree of accuracy are called approximate numbers.

Significant figures. The digits used to express a number are called signif- icant digits figures. Thus each of the numbers , 3. Similarly the numbers and Rounding off. There are numbers with large number of digits, e. In practice, it is desirable to limit such numbers to a manageable number of digits such as 3. This process of dropping unwanted digits is called rounding off.

Rule to round off a number to n significant figures: i Discard all digits to the right of the nth digit. For instance, the following numbers rounded off to three significant figures are: 7. The numbers thus rounded off to n significant figures or NOTE n decimal places are said to be correct to n significant figures or n decimal places. Inherent errors. Errors which are already present in the statement of a problem before its solution, are called inherent errors.

Such errors arise either due to the given data being approximate or due to the limitations of mathematical tables, calculators, or the digital computer. Inherent er- rors can be minimized by taking better data or by using high precision computing aids. Rounding errors arise from the process of rounding off the numbers during the computation.

Such errors are unavoidable in most of the cal- culations due to the limitations of the computing aids. Rounding errors can, however, be reduced: i by changing the calculation procedure so as to avoid subtraction of nearly equal numbers or division by a small number; or ii by retaining at least one more significant figure at each step than that given in the data and rounding off at the last step.

Truncation errors are caused by using approximate results or on replacing an infinite process by a finite one. If we are using a decimal computer having a fixed word length of four digits, rounding off Absolute, Relative, and Percentage errors.

The relative and percentage errors are independent of NOTE the units used while absolute error is expressed in terms of these units. For example, if the number is 3. Let us verify this result by finding the relative error in the number This proves rule 2. This proves rule 4. Round off the following numbers correct to four significant figures: 3. Round off the number to four significant digits and then calculate the absolute error and percentage error.

Find the percentage error if The height of an observation tower was estimated to be 47 m, whereas its actual height was 45 m. Calculate the percentage relative error in the measurement. Suppose that you have a task of measuring the lengths of a bridge and a rivet, and come up with and 9 cm, respectively. If the true values are 10, and 10 cm, respectively, compute the percentage relative error in each case.

Find the relative errors in their sum and difference. Two numbers are 3. Find their product. Find the absolute error and the relative error in the product of If the head is 75 cm and an error of 0. If the number p is correct to 3 significant digits, what will be the maxi- mum relative error? It is necessary to understand the way the error propagates with progressive computation.

How ac- curately should the diameter be measured? Solution: Since the absolute error is greatest in 3. On the other hand, if the accuracy required in a series approximation is preassigned, then we can find n, the number of terms which would yield the desired accuracy. Find the order of approximation for the sum and product of the follow- ing expansions:.

Determine the order of approximation for their sum and product. Exercises 1. The relative error in the number Round off values of If both the digits of the number 8. If f x contains some other functions such as trigonometric, log- arithmic, exponential etc.

The process of finding the roots of an equation is known as the solution of that equation. This is a problem of basic importance in applied math- ematics. If f x is a quadratic, cubic, or a biquadratic expression, algebraic solu- tions of equations are available. But the need often arises to solve higher degree or transcendental equations for which no direct methods exist. Such equations can best be solved by approximate methods.

In this chapter, we shall discuss some numerical methods for the solution of algebraic and tran- scendental equations. Every equation of the nth degree has only n roots real or imaginary.

If a polynomial of degree n vanishes for more than n NOTE values of x, it must be identically zero. Intermediate value property. Since f x is continuous between a and b, so while x changes from a to b, f x must pass through all the values from f a to f b [Figure 2.

In an equation with real coefficients, imaginary roots occur in conjugate pairs, i.

Numerical Methods in Engineering and Science (C, C++, and MATLAB)

A collocation method with quartic splines has been developed to solve third order boundary value problems. The proposed method tested on third order nonlinear boundary value problem. The solution. Grewal at Indigo. Free shipping and pickup in store on eligible orders. We additionally offer variant types and also type of the books to browse. The enjoyable book, fiction, history, novel, scientific research, as with ease as various further sorts of books are readily manageable.

The book comprises of chapters on algebra, geometry and vectors, calculus, series, differential equations, complex analysis, transforms, and numerical techniques. In addition, the book consists of several solved and unsolved questions for thorough revision and final practice. This book is essential for engineering students preparing for various competitive exams like Graduate Aptitude Test in Engineering. The book provides a clear exposition of essential tools of applied mathematics from a modern point of view and meets complete requirements of engineering and computer science students. Every effort has been made to keep the presentation at once simple and lucid. It is written with the firm conviction that a good book is one that can be read with minimum guidance from the instructor.

Numerical Methods in Engineerin - B. S. Grewal.pdf

This license does not permit uploading of the Work onto the Internet or on a network of any kind without the writ- ten consent of the Publisher. Duplication or dissemination of any text, code, simulations, images, etc. The author, developers, and the publisher of any accompanying content, and anyone involved in the composition, production, and manufacturing of this work will not be liable for damages of any kind arising out of the use of or the inability to use the algorithms, source code, computer programs, or textual material contained in this publication. This includes, but is not limited to, loss of revenue or profit, or other incidental, physical, or consequential damages arising out of the use of this Work. The sole remedy in the event of a claim of any kind is expressly limited to re- placement of the book, and only at the discretion of the Publisher.

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The book comprises of chapters on algebra, geometry and vectors, calculus, series, differential equations, complex analysis, transforms, and numerical techniques. In addition, the book consists of several solved and unsolved questions for thorough revision and final practice. This book is essential for engineering students preparing for various competitive exams like Graduate Aptitude Test in Engineering. The book provides a clear exposition of essential tools of applied mathematics from a modern point of view and meets complete requirements of engineering and computer science students. Every effort has been made to keep the presentation at once simple and lucid.

numerical method in engineering and science by bs grewal ebook

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Numerical Methods In Engineering Science By Dr B S Grewal

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