Numerical Methods for Engineers

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.