In this new English edition, program codes have been revised in Fortran 77 to reflect the latest computer environment, which is characterized by personal computers and powerful work stations. The book contains many programs (written in double precision base, except for a few cases) for the computation of fundamental mathematical problems in science and technology. A floppy disk is also included, containing all source programs and subprograms, as well as sample programs as described in the text. The contents are classified into four categories: (1) instructions for using this program (including sample cases for different computers); (2) calculation of function values (for special functions, such as the Gamma function and its related functions, Bessel functions of the first and second kinds and their related functions, various orthogonal polynomials, exponential and trigonometric integrals, the error function and its related functions, the Fresnel integrals, the complete elliptic integrals and random number productions); (3) the methods for obtaining functions by solving equations (including cases of algebraic equations, Transcendental equations, ordinary differential equations, simultaneous linear equations, inverse matrices and eigenvalues problems of matrices); (4) manipulations of direct calculation for given data or functions (including calculations which can be calculated directly from the given data, such as, numerical integrals, least-square methods, optimization methods, interpolations, and Fourier transforms. All comments, error messages and explanations have been translated into English for this edition and have been checked using IBM PC MS-FORTRAN (Microsoft), which is common in Europe and USA.

• Introductory remarks, T. Oguni and T. Watanabe
• Bessel functions, M. Natori et al
• array-type Bessel functions, I. Tonozuka
• Kelvin functions, N. Toshima
• gamma functions, M. Mori
• exponential and trigonometric integrals, N. Toshima
• error function and normal distribution function, M. Mori
• Fresnel integrals, Y. Onodera and T. Watanabe
• complete elliptic integrals, Y. Onodera and T. Watanabe
• orthogonal polynomials, N. Toshima
• algebraic equations, Y. Onodera and T. Watanabe
• transcendental equations, T. Oguni
• ordinary differential equations, M. Sugihara and T. Watanabe
• numerical integration, M. Mori et al
• least-squares methods and optimization, Y. Oyanagi
• spline interpolation, T. Oguni
• Fourier transform, Y. Onodera and T. Watanabe
• simultaneous linear equations and inverse matrices, T. Oguni and H. Hasegawa
• eigenvalues and eigenvectors, T. Oguni and Y. Onodera
• random number generation, Y. Oyanagi
• supplement I - Fortran 77 statements
• supplement II - intrinsic functions in Fortran 77.