Numerical Methods For Scientists And Engineers (EPUB) By R. W. Hamming

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Numerical Methods for Scientists and Engineers: A Classic Text by R. W. Hamming

Numerical methods are essential tools for solving various problems in science and engineering. They involve applying mathematical techniques to approximate the solutions of equations that cannot be solved analytically or exactly. Numerical methods can also help to analyze data, optimize functions, and perform statistical inferences.

One of the most influential books on numerical methods is Numerical Methods for Scientists and Engineers by R. W. Hamming, a renowned mathematician and computer scientist who contributed to many fields such as information theory, coding theory, signal processing, and numerical analysis. The book was first published in 1973 by McGraw-Hill and later reprinted by Dover Publications in 1986.

The book covers a wide range of topics, such as roundoff error, linear algebraic equations, interpolation, differentiation, integration, nonlinear algebraic equations, optimization, statistical inferences, functional approximations, eigenvalue problems, ordinary differential equations, integral equations, and partial differential equations. The book emphasizes the practical aspects of numerical computation and discusses various techniques in sufficient detail to enable their implementation in solving a wide range of problems.

The book also provides many examples and exercises to illustrate the applications of numerical methods in different fields. The book is written in a clear and concise style that makes it accessible to students and practitioners alike. The book is suitable for undergraduate and graduate courses on numerical methods, as well as for self-study and reference.

The book is available in EPUB format from various online sources, such as Internet Archive, SpringerLink, and Google Books. The EPUB format is compatible with most e-readers and devices that support digital books.

Numerical Methods for Scientists and Engineers by R. W. Hamming is a classic text that has influenced generations of scientists and engineers who use numerical methods in their work. It is a valuable resource for anyone who wants to learn more about the theory and practice of numerical computation.

In this section, we will briefly review some of the main topics covered in the book and highlight some of the key concepts and methods.

Roundoff Error

Roundoff error is the difference between the exact value of a number and its representation in a finite-precision arithmetic system. Roundoff error can affect the accuracy and stability of numerical computations and can propagate through successive operations. Therefore, it is important to understand the sources and effects of roundoff error and how to minimize it.

Some of the topics discussed in this chapter are:

The representation of numbers in binary and decimal systems and the conversion between them.

The floating-point arithmetic system and its characteristics, such as precision, range, overflow, underflow, and rounding modes.

The analysis of roundoff error using Taylor series expansions and error propagation formulas.

The techniques for reducing roundoff error, such as scaling, balancing, pivoting, and error correction methods.

Linear Algebraic Equations

Linear algebraic equations are equations of the form Ax = b, where A is a matrix, x is a vector of unknowns, and b is a vector of constants. Solving linear algebraic equations is one of the most common problems in numerical methods and has many applications in science and engineering.

Some of the topics discussed in this chapter are:

The properties of matrices and vectors, such as rank, determinant, inverse, transpose, norm, condition number, orthogonality, and eigenvalues.

The direct methods for solving linear algebraic equations, such as Gaussian elimination, LU decomposition, Cholesky decomposition, QR decomposition, and singular value decomposition.

The iterative methods for solving linear algebraic equations, such as Jacobi method, Gauss-Seidel method, successive overrelaxation method, conjugate gradient method, and Krylov subspace methods.

The methods for solving special types of linear algebraic equations, such as tridiagonal systems, banded systems, sparse systems, symmetric positive definite systems, least squares problems, and eigenvalue problems. aa16f39245