Applied numerical methods with personal computers.

*(English)*Zbl 0653.65001
McGraw-Hill Chemical Engineering Series. New York etc.: McGraw-Hill Book Company. XIV, 626 p.; DM 51.90 (1987).

The book deals with numerical methods and their applications particularly to physical and chemical engineering problems. The diskette which comes with the book contains in Basic language all programs presented in the text. The contents chapter by chapter is as follows: Ch. 1: Introduction to personal computers and Basic programming. Ch. 2: Numerical solution of nonlinear algebraic equations. Ch. 3: Numerical solution of simultaneous linear algebraic equations. Ch. 4: Finite difference methods. Ch. 5: Numerical solution of ordinary differential equations. Ch. 6: Numerical solution of partial differential equations. Ch. 7: Linear and nonlinear regression analysis.

The first chapter provides the background on the fundamental characteristics of personal computers and the BASICA interpreter used in the programs. The programs run on an IBM PC or AT and most programs use graphic features as a part of their output to visualize the results. Clear instructions for the use of the programs are given on pp. 60-63. No programming is required to run the demonstration programs, since they can be started from the main menu. Because the source code is available each of the programs can also be run individually.

The emphasis of the book lies on pragmatic aspects rather than theoretic aspects of numerical methods. Thus essential features of methods are presented so that the reader will be able to understand the way in which the programs work. The problems at the end of each of the chapters require in many cases application of the programs. Several of these problems illuminate mathematical modelling in engineering applications. To faciliate the use of the programs the listings are given together with a clearly documented test run. Some sample programs which I tried worked without difficulties as in the test runs.

This textbook, which is intended mainly for students in engineering faculties, covers a surprising amount of material. The algorithms presented here are central for practical applications of numerical mathematics.

The first chapter provides the background on the fundamental characteristics of personal computers and the BASICA interpreter used in the programs. The programs run on an IBM PC or AT and most programs use graphic features as a part of their output to visualize the results. Clear instructions for the use of the programs are given on pp. 60-63. No programming is required to run the demonstration programs, since they can be started from the main menu. Because the source code is available each of the programs can also be run individually.

The emphasis of the book lies on pragmatic aspects rather than theoretic aspects of numerical methods. Thus essential features of methods are presented so that the reader will be able to understand the way in which the programs work. The problems at the end of each of the chapters require in many cases application of the programs. Several of these problems illuminate mathematical modelling in engineering applications. To faciliate the use of the programs the listings are given together with a clearly documented test run. Some sample programs which I tried worked without difficulties as in the test runs.

This textbook, which is intended mainly for students in engineering faculties, covers a surprising amount of material. The algorithms presented here are central for practical applications of numerical mathematics.

Reviewer: M.Vuorinen

##### MSC:

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |

65H05 | Numerical computation of solutions to single equations |

65Fxx | Numerical linear algebra |

65Lxx | Numerical methods for ordinary differential equations |

65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |

65Nxx | Numerical methods for partial differential equations, boundary value problems |

65C99 | Probabilistic methods, stochastic differential equations |

00A69 | General applied mathematics |

00A79 | Physics (Use more specific entries from Sections 70-XX through 86-XX when possible) |

15-04 | Software, source code, etc. for problems pertaining to linear algebra |

34-04 | Software, source code, etc. for problems pertaining to ordinary differential equations |

35-04 | Software, source code, etc. for problems pertaining to partial differential equations |

62-04 | Software, source code, etc. for problems pertaining to statistics |