Computer Oriented Numerical Methods by R.S. Salaria: A Review
Computer Oriented Numerical Methods is a book by R.S. Salaria that provides a comprehensive coverage of the subject of numerical methods for solving various problems using computers. The book is intended for students who have only basic level knowledge of mathematics and programming. The book covers topics such as errors and approximations, solutions of algebraic and transcendental equations, interpolation and curve fitting, numerical differentiation and integration, solutions of ordinary differential equations, matrix operations and eigenvalue problems, and solutions of partial differential equations. The book also includes formulae for different numerical methods, examples and exercises with solutions, and programs in C language for implementing the numerical methods.
The book is divided into 14 chapters, each covering a specific topic of numerical methods. The first chapter introduces the concept of numerical methods and their applications, as well as the sources and types of errors that occur in numerical computations. The second chapter deals with the solutions of algebraic and transcendental equations using methods such as bisection method, false position method, Newton-Raphson method, and secant method. The third chapter discusses the interpolation and curve fitting techniques such as Lagrange's interpolation, Newton's divided difference interpolation, spline interpolation, least squares method, and regression analysis. The fourth chapter explains the numerical differentiation and integration methods such as forward difference method, backward difference method, central difference method, Simpson's rule, Trapezoidal rule, and Romberg's method. The fifth chapter covers the solutions of ordinary differential equations using methods such as Euler's method, modified Euler's method, Runge-Kutta method, predictor-corrector method, and boundary value problems. The sixth chapter introduces the matrix operations and eigenvalue problems such as addition, subtraction, multiplication, inversion, determinant, rank, Gauss elimination method, Gauss-Jordan method, Jacobi method, Gauss-Seidel method, power method, and QR method. The seventh chapter deals with the solutions of partial differential equations using methods such as finite difference method, Crank-Nicolson method, explicit method, implicit method, Thomas algorithm, and relaxation method.
The remaining chapters cover some advanced topics of numerical methods such as optimization techniques (chapter 8), Monte Carlo methods (chapter 9), numerical linear algebra (chapter 10), Fourier analysis (chapter 11), fast Fourier transform (chapter 12), wavelet analysis (chapter 13), and fractals (chapter 14). These chapters provide an overview of the concepts and applications of these topics without going into much detail or complexity. The book also includes appendices that contain some useful mathematical formulae and tables.
Computer Oriented Numerical Methods by R.S. Salaria is a useful book for students who want to learn the basics of numerical methods and their applications using computers. The book is written in a simple and clear language that makes it easy to understand and follow. The book also provides ample examples and exercises to reinforce the concepts and test the understanding of the readers. The book also provides programs in C language for implementing the numerical methods that can help the readers to practice their programming skills and see the results of their computations. The book is suitable for undergraduate students of engineering, science, mathematics, computer science, and other related disciplines. 061ffe29dd