## An Introduction to Numerical Methods in C++This text on numerical computing, presented through the medium of the C++ language, is designed for students of science and engineering who are serriously studying nummerical methods for the first time. It should also be of interest to computing scientists who wish to see how C++ can be used in earnest for nummerical computation. The mathematical prerequisites are those which an undergraduate student of science or engineering might be expected to possess after the earlier years of study: elementary calculus, linear algebra, and differential equations. In computing, a good knowledge, such as Basic, Fortran, or Pascal, is asumed, while a working knowledge of C would be an advantage. However, no prior knowledge of C++ is assumed. The language is developed in step with its numerical applications. Features of the language not used here are ignored. What remains, however, is a powerful framework for numerical computations and more than enough for an introductory text. |

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### Contents

Preliminaries | 1 |

Expressions statements | 2 |

functions | 20 |

l0 The function main | 52 |

Errors theorems and speed | 55 |

Roots of nonlinear equations | 69 |

Classes | 94 |

Derived classes and streams | 120 |

Interpolation and data fitting | 280 |

Graphics | 305 |

Differentiation and integration | 334 |

Orthogonal polynomials 357 | 346 |

Differential equations | 383 |

More about differential equations | 413 |

Recursive data typeslists | 438 |

Elements of Fourier analysis | 471 |

Integer arithmetic | 145 |

Tests of randomness | 171 |

Vectors and matrices | 188 |

Direct solution of linear equations | 204 |

Errors in matrix manipulation | 227 |

Matrix eigenvalue problems | 250 |

Addendum Programming in Windows | 481 |

533 | |

random h | 539 |

Appendix H screen h | 546 |

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### Common terms and phrases

approximation arithmetic array base class bisection method bool bytes char class complex class string coefficients COLORREF complex numbers computation consider const double constructor convergence coprime cout data members data pointer declared default defined defmed delete derived class destructor differential equations duple eigenvalue eigenvectors error Euler method example floating point floating point numbers function calls gauss given header file initial value initial value problem inline inline function input and output integer interpolation interval iter linear LPSTR matrix maxiter member function method midpoint midpoint method mult multiplications Newton's method node norm object obtain orthogonal ostream& PaintDC parameters pixel pointer prime quicksort rational recursive result root routine RPoint screen sequence solution statement static sub-interval symmetric matrix template theorem tion trapezoidal tridiagonal TurboC++ typedef value problem variable vector virtual function void window wrinen write zero