Engineering

## Computer Based Numerical and Statistical Techniques

This fifth edition has grown multifold in its utilitarian value for the readers of not only B.Tech. and M.Tech. but also for those of B.C.A and M.C.A. This recent revision in the syllabi (NCS 303 and NMCA 212) of Computer Based Numerical and Statistical Techniques (C.B.N.S.T) by U.P. Technical University, Lucknow has triggered the needful additions also incorporating the suggestions of learned readers over a period of time. However, the basic outline of the book and its underlying object remain unaltered.
Additional Info
• Publisher: Laxmi Publications
• Language: English
• ISBN : 978-93-81159-27-9
Total Price: 0
• Chapter 1

### Contents

The document contains the preface.

• Chapter 2

### Preface

The document contains the preface.

• Chapter 3

### Syllabus

The document contains the syllabus.

• Chapter 4

### Salient Features

The document contains the salient features.

• Chapter 5

### Foreword

The document contains the foreword.

• Chapter 6

### Chapter 1 - Introduction Price 0.11  |  0.11 Rewards Points

The limitations of analytical methods in practical applications have led mathematicians to evolve numerical methods.
We know that exact methods often fail in drawing plausible inferences from a given set of tabulated data or in finding roots of transcendental equations or in solving non-linear differential equations.

• Chapter 7

### Chapter 2 - Computer Arithmetic and Errors Price 0.11  |  0.11 Rewards Points

Following are the broad sources of errors in numerical analysis:
(1) Input errors: The input information is rarely exact since it comes from the experiments and any experiment can give results of only limited accuracy. Moreover, the quantity used can be represented in a computer for only a limited number of digits.
(2) Algorithmic errors: If direct algorithms based on a finite sequence of operations are used, errors due to limited steps don’t amplify the existing errors but if infinite algos are used, ideally exact results are expected only after an infinite number of steps. As this cannot be done in practice, the algorithm has to be stopped after a finite number of steps and as a consequence thereof the results are not exact.

• Chapter 8

### Chapter 3 - Roots of Equation Price 0.11  |  0.11 Rewards Points

Consider the equation of the form f(x) = 0
If f(x) is a quadratic, cubic or biquadratic expression then algebraic formulae are available for expressing the roots. But when f(x) is a polynomial of higher degree or an expression involving transcendental functions e.g. 1 + cos x – 5x, x tan x – cosh x, e–x – sin x etc. algebraic methods are not available.
Here, we shall describe some numerical methods for the solution of f(x) = 0, where f(x) is algebraic or transcendental or both.

• Chapter 9

### Chapter 4 - Interpolation Price 0.11  |  0.11 Rewards Points

1. There are no sudden jumps or falls in the values during the period under consideration.
2. The rise and fall in the values should be uniform.
e.g., if we are given data regarding deaths in various years in a particular town and some of the observations are for the years in which epidemic or war overtook the town then interpolation methods are not applicable in such cases.

• Chapter 10

### Chapter 4 - Interpolation Price 0.11  |  0.11 Rewards Points

1. There are no sudden jumps or falls in the values during the period under consideration.
2. The rise and fall in the values should be uniform.
e.g., if we are given data regarding deaths in various years in a particular town and some of the observations are for the years in which epidemic or war overtook the town then interpolation methods are not applicable in such cases.

• Chapter 11

### Chapter 5 - Curve-Fitting and Approximation Price 0.11  |  0.11 Rewards Points

Let there be two variables x and y which give us a set of n pairs of numerical values (x1, y1), (x2, y2),......., (xn, yn). In order to have an approximate idea about the relationship of these two variables, we plot these n paired points on a graph thus, we get a diagram showing the simultaneous variation in values of both the variables called scatter or dot diagram. From scatter diagram, we get only an approximate non-mathematical relation between two variables. Curve fitting means an exact relationship between two variables by algebraic equations, infact this relationship is the equation of the curve. Therefore, curve fitting means to form an equation of the curve from the given data. Curve fitting is considered of immense importance both from the point of view of theoretical and practical statistics.

• Chapter 12

### Chapter 6 - Numerical Differentiation and Integration Price 0.11  |  0.11 Rewards Points

Consider a function of a single variable y = f(x). If f(x) is defined as an expression, its derivative or integral may often be determined using the techniques of calculus.
However, when f(x) is a complicated function or when it is given in a tabular form, we use numerical methods.

• Chapter 13

### Chapter 7 - Solution of Simultaneous Linear Algebraic Equations Price 0.11  |  0.11 Rewards Points

The systems of simultaneous linear equations arise, both directly in modelling physical situations and indirectly in the numerical solution of other mathematical models.
Problems such as determining the potential in certain electrical networks, stresses in a building frame, flow rates in a hydraulic system etc., are all reduced to solving a set of algebraic equations simultaneously.

• Chapter 14

### Chapter 8 - Numerical Solution of Ordinary Differential Equations Price 0.11  |  0.11 Rewards Points

A physical situation that concerns with the rate of change of one quantity with respect to another gives rise to a differential equation.

• Chapter 15

### Chapter 9 - Statistical Techniques Price 0.11  |  0.11 Rewards Points

Statistical methods are devices by which complex and numerical data are so systematically treated as to present a comprehensible and intelligible view of them. In other words, the statistical method is a technique used to obtain, analyse and present numerical data.

• Chapter 16

### Tables

The document contains the tables.