Numerical Methods for Engineers

 INTRODUCTION AND PROGRAMMING PRELIMINARIES
Introduction
Running Programs
Hardware
External Fortran Sub-Program Libraries
A Simple Fortran Program
Some Simple Fortran Constructs
Intrinsic Functions
User-Supplied Functions and Subroutines
Errors and Accuracy
Graphical Output
Conclusions

LINEAR ALGEBRAIC EQUATIONS
Introduction
Gaussian Elimination
Equation Solution Using Factorization
Equations with a Symmetrical Coefficient Matrix
Banded Equations
Compact Storage for Variable Bandwidths
Pivoting
Equations with Prescribed Solutions
Iterative Methods
Gradient Methods
Unsymmetrical Systems
Preconditioning
Comparison of Direct and Iterative Methods
Exercises

NONLINEAR EQUATIONS
Introduction
Iterative Substitution
Multiple Roots and Other Difficulties
Interpolation Methods
Extrapolation Methods
Acceleration of Convergence
Systems of Nonlinear Equations
Exercises

EIGENVALUE EQUATIONS
Introduction
Vector Iteration
Intermediate Eigenvalues by Deflation
The Generalized Eigenvalue Problem [K] {x} = ?[M] {x}
Transformation Methods
Characteristic Polynomial Methods
Exercises

INTERPOLATION AND CURVE FITTING
Introduction
Interpolating Polynomials
Interpolation Using Cubic Spline Functions
Numerical Differentiation
Curve Fitting
Exercises

NUMERICAL INTEGRATION
Introduction
Newton-Cotes Rules
Gauss-Legendre Rules
Adaptive Integration Rules
Special Integration Rules
Multiple Integrals
Exercises

NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
Introduction
Definitions and Types of ODE
Initial Value Problems
Boundary Value Problems
Exercises

INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS
Introduction
Definitions and Types of PDE
First Order Equations
Second Order Equations
Finite Difference Method
Finite Element Method
Exercises

APPENDIX A: Descriptions of Library Subprograms
APPENDIX B: Fortran 95 Listings of Library Subprograms
APPENDIX C: References and Additional Reading