Numerical Methods for Engineers

Part 1 Modeling, Computers, and Error Analysis 1 Mathematical Modeling and Engineering Problem Solving 2 Programming and Software 3 Approximations and Round-Off Errors 4 Truncation Errors and the Taylor Series Part 2 Roots of Equations 5 Bracketing Methods 6 Open Methods 8 Engineering Applications: Roots of Equations Part 3 Linear Algebraic Equations 9 Gauss Elimination 10 LU Decomposition and Matrix Inversion 11 Special Matrices and Gauss-Seidel 12 Engineering Applications: Linear Algebraic Equations Part 4 Optimization 13 One-Dimensional Unconstrained Optimization 14 Multidimensional Unconstrained Optimization 15 Constrained Optimization 16 Engineering Applications: Optimization Part 5 Curve Fitting 17 Least-Squares Regression 18 Interpolation 19 Fourier Approximation 20 Engineering Applications: Curve Fitting Part 6 Numerical Differentiation and Integration 21 Newton-Cotes Integration Formulas 22 Integration of Equations 23 Numerical Differentiation 24 Engineering Applications: Numerical Integration and Differentiation Part 7 Ordinary Differential Equations 25 Runge-Kutta Methods 26 Stiffness and Multistep Methods 27 Boundary-Value and Eigenvalue Problems 28 Engineering Applications: Ordinary Differential Equations Part 8 Partial Differential Equations 29 Finite Difference: Elliptic Equations 30 Finite Difference: Parabolic Equations 31 Finite-Element Method 32 Engineering Applications: Partial Differential Equations Appendix A The Fourier Series Appendix B Getting Started with Matlab Bibliography Index