Numerical Methods for Engineers, Second Edition

Numerical Methods for Engineers: A Programming Approach is devoted to solving engineering problems using numerical methods. It covers all areas of introductory numerical methods and emphasizes techniques of programming in FORTRAN 77, and developing subprograms using FORTRAN functions and subroutines. In this way, the book serves as an introduction to using powerful mathematical subroutine libraries. Over 40 main programs are provided in the text and all subroutines are listed in the Appendix. Each main program is presented with a sample data-set and output, and all FORTRAN programs and subroutines described in the text can be obtained on disk from the publisher. Numerical Methods for Engineers: A Programming Approach is an excellent choice for undergraduates in all engineering disciplines, providing a much needed bridge between classical mathematics and computer code-based techniques.

Table of Contents:
List of Programs. Preface. Acknowledgements. INTRODUCTION AND PROGRAMMING PRELIMINARIES. Introduction. Software and Hardware. Mathematical Subroutine Libraries. Functions and Subroutines. Errors. Conclusions. Further Reading. LINEAR ALGEBRAIC EQUATIONS. Introduction. Gaussian Elimination. Equation Solution Using LU Factorization. Equations with Symmetrical Coefficient Matrix. Banded Equations. Compact Storage for Variable Bandwidths. Pivoting. Equations with Prescribed "Variables". Iterative Methods. Gradient Methods. Comparison of Direct and Iterative Methods. Exercises. Further Reading. NONLINEAR EQUATIONS. Introduction. Iterative Substitution. Multiple Roots and Other Difficulties. Interpolation Methods. Extrapolation Methods. Acceleration of Convergence. Systems of Nonlinear Equations. Exercises. Further Reading. EIGENVALUE EQUATIONS. Introduction. Orthogonality and Normalization of Eigenvectors. Solution Methods for Eigenvalue Equations. Vector Iteration. Calculation of Intermediate Eigenvalues-Deflation. The Generalized Eigenvalue Problem Ax=lBx. Transformation Methods. Characteristic Polynomial Methods. Exercises. Further Reading. INTERPOLATION AND CURVE FITTING. Introduction. Interpolating Polynomials. Numerical Differentiation. Curve Fitting. Exercises. Further Reading. NUMERICAL INTEGRATION. Introduction. Newton-Cotes Rules. Gauss-Legendre Rules. Special Integration Rules. Multiple Integrals. Exercises. Further Reading. NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS. Introduction. Definitions and Types of Differential Equations. Initial Value Problems. Boundary Value Problems. INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS. Introduction. Some Definitions. First Order Equations. Second Order Equations. Finite Differences in Two Dimensions. Elliptic Systems. Parabolic Systems. Hyperbolic Systems. Exrecises. Further Reading. APPENDIX 1: Alphabetic Description of Subroutine Library. APPENDIX 2: Alphabetic Listing of Subroutine Library in FORTRAN. INDEX.