Hardcover, color print on 70lb white paper. Other e- and printed color and b&w editions are or will be also available. About the book: An excellent textbook established at several universities. Primarily written for students at technical universities, it is also a very useful handbook for engineers, PhD students and scientists. Now available at all continents. This textbook introduces the reader into various types of approximations of functions, which are defined either explicitly or by their values in the distinct set of points, as well as into the economization of existing approximation formulas. Why the approximation of functions is so important? Simply, various functions (such as trigonometric functions and logarithms) cannot be calculated without approximation. Approximation formulas for some of these functions are already implemented in calculators and standard computer libraries, providing accuracy to all the bits in which a value is stored. High accuracy is usually not required and requires more numerical operations then necessary. Economised approximation formulas can provide the required accuracy with less numerical operations, and can make numerical algorithms faster, especially when such formulas are nested in loops. The other important use of approximation is in calculating functions that are defined by values at a chosen set of points. The book is divided into five chapters. The first chapter briefly explaines Maclaurin, Taylor or Pade expansion, principles of approximations with orthogonal series and principles of the least squares approximations. In the second chapter, various types of least squares polynomial approximations, particularly those using Legendre, Jacobi, Laguerre, Hermite, Zernike and Gram orthogonal polynomials are explained. The third chapter explains approximations with Fourier series, which are the base for developing approximations with Chebyshev polynomials (fourth chapter). Uniform approximation and further usage of Chebyshev polynomials in the almost uniform approximation, as well as in the economisation of the existing approximation formulas, are described in the fifth chapter. Practical application of the described approximation procedures is supported by 40 examples and 37 algorithms. In addition to its practical usage, the given text with 37 figures and 12 tables represents a valuable background for understanding, using, developing and applying various numerical methods, such as interpolation, numerical integration and solving partial differential equations, which are topics covered in the following volumes of the series Numerical Methods. Author: Boris Obsieger, D.Sc., professor at the University of Rijeka, Croatia. Head of Section for Machine Elements at the Faculty of Engineering in Rijeka. Holds lectures on Machine Elements Design, Robot Elements Design, Numerical Methods in Design and Boundary Element Method. Several invited lectures. President of CADAM Conferences. Main editor of international journal Advanced Engineering. Author of several books and a lot of scientific papers. Reviewed by: Prof. Maja Fosner, D.Sc. University of Maribor, Slovenia Prof. Damir Jelaska, D.Sc. University of Split, Croatia Prof. Valery Lysenko, D.Sc. Academic of the Russian Metrological Academy Russian Research Institute for Metrological Service Prof. Iztok Potrc, D.Sc. University of Maribor. Slovenia Prof. Evgeny Pushkar, D.Sc. Member correspondent of the Russian Academy of Natural Sciences Moscow State Industrial University, Russia Proof reading by: Jasenka Toplicanec, prof. Rijeka, Croatia"