Learn Computer Oriented Numerical Methods with R.S. Salaria's Book
Introduction
Computer oriented numerical methods are techniques for solving mathematical problems using computers. They involve designing algorithms, implementing them in programming languages, and analyzing their accuracy and efficiency. Numerical methods are essential for many fields of science and engineering, such as physics, chemistry, biology, economics, statistics, etc., where analytical solutions are not available or too complex.
computer oriented numerical methods by rs salaria pdf download
In this article, we will review a book that covers various topics in computer oriented numerical methods. The book is titled Computer Oriented Numerical Methods by R.S. Salaria, published by Khanna Publishing House. The book provides a comprehensive coverage of the subject, with emphasis on conceptual understanding, formula derivation, algorithm development, programming exercises, multiple choice questions, and review exercises. The book is suitable for undergraduate and postgraduate students of computer science, mathematics, engineering, and other disciplines that require numerical methods.
Overview of the book by R.S. Salaria
The book by R.S. Salaria has 10 chapters, each covering a major topic in computer oriented numerical methods. The chapters are as follows:
Chapter 1: Errors and Approximations
Chapter 2: Solution of Algebraic and Transcendental Equations
Chapter 3: Interpolation and Curve Fitting
Chapter 4: Numerical Differentiation and Integration
Chapter 5: Solution of Simultaneous Linear Equations
Chapter 6: Eigenvalues and Eigenvectors
Chapter 7: Solution of Ordinary Differential Equations
Chapter 8: Solution of Partial Differential Equations
Chapter 9: Numerical Solution of Integral Equations
Chapter 10: Optimization Techniques
The book also has five appendices that provide additional information on topics such as floating-point representation, C/C++/FORTRAN programming languages, matrix operations, numerical libraries, and software tools.
The book has several features that make it a valuable resource for learning and applying numerical methods. Some of these features are:
Elementary presentation of numerical methods using computers for solving a variety of problems.
Geometrical illustrations used to explain how numerical algorithms are evolved.
Emphasis on implementation of numerical algorithms on computers.
Detailed discussion of IEEE standard for representing floating-point numbers.
Algorithms derived and presented using a simple English based structured language.
Truncation and rounding errors in numerical calculations explained.
Each chapter starts with learning goals and all methods illustrated with numerical examples.
Large number of programming exercises to test your programming skills acquired.
Large number of multiple choice questions and review exercises to test your conceptual understanding.
Majority of the algorithms are implemented in C/C++/FORTRAN languages.
Chapter 1: Errors and Approximations
The first chapter of the book introduces the concept of errors and approximations in numerical computations. It explains the sources and types of errors, such as absolute error, relative error, percentage error, round-off error, truncation error, etc. It also discusses the propagation and control of errors, as well as the accuracy and precision of numerical results. The chapter provides some examples of errors in numerical methods, such as finding roots of equations, interpolation, differentiation, integration, etc. The chapter also gives some guidelines for choosing appropriate methods and parameters to minimize errors.
Chapter 2: Solution of Algebraic and Transcendental Equations
The second chapter of the book deals with the methods for finding roots of nonlinear equations, also known as algebraic and transcendental equations. It explains the concept of bracketing and convergence of root-finding methods, as well as the criteria for stopping the iteration process. The chapter presents several methods for finding roots, such as bisection method, false position method, fixed point iteration method, Newton-Raphson method, secant method, etc. The chapter also compares the advantages and disadvantages of different methods, as well as their convergence rates and error bounds. The chapter provides some examples of solving nonlinear equations arising from various applications, such as engineering, physics, chemistry, etc.
Chapter 3: Interpolation and Curve Fitting
The third chapter of the book covers the methods for finding polynomial approximations of functions, also known as interpolation and curve fitting. It explains the concept of interpolation and its applications, such as data analysis, function evaluation, integration, differentiation, etc. The chapter presents several methods for interpolation, such as Lagrange interpolation, Newton interpolation, divided difference interpolation, spline interpolation, etc. The chapter also discusses the concept of curve fitting and its applications, such as regression analysis, data modeling, etc. The chapter presents several methods for curve fitting, such as least squares method, orthogonal polynomials method, Chebyshev polynomials method, etc. The chapter also compares the accuracy and efficiency of different methods for interpolation and curve fitting.
Chapter 4: Numerical Differentiation and Integration
The fourth chapter of the book deals with the methods for finding derivatives and integrals of functions, also known as numerical differentiation and integration. It explains the concept of differentiation and integration and their applications, such as rate of change, slope, area, volume, etc. The chapter presents several methods for differentiation, such as forward difference method, backward difference method 71b2f0854b