Applied Numerical Methods for Engineers Using MATLAB and C

1. NUMERICAL COMPUTATION Motivation and Objectives / Number Representation / Machine Precision / Round-Off Error / Truncation Error / Random Number Generation / Numerical Software / Applications / Chapter Summary / Problems 2. LINEAR ALGEBRAIC SYSTEMS Motivation and Objectives / Gauss-Jordan Elimination / Gaussian Elimination / LU Decomposition / Ill-Conditioned Systems / Iterative Methods / Applications / Chapter Summary / Problems 3. EIGENVALUES AND EIGENVECTORS Motivation and Objectives / The Characteristic Polynomial / Power Methods / Jacobi"s Method / Householder Transformation / QR Method / Danilevsky"s Method / Polynomial Roots / Applications / Chapter Summary / Problems 4. CURVE FITTING Motivation and Objectives / Interpolation / Newton"s Difference Formula / Cubic Splines / Least Square / Two-Dimensional Interpolation / Applications / Chapter Summary / Problems 5. ROOT FINDING Motivation and Objectives / Bracketing Methods / Contraction Mapping Method / Secant Method / Muller"s Method / Newton"s Method / Polynomial Roots / Nonlinear Systems of Equations / Applications / Chapter Summary / Problems 6. OPTIMIZATION Motivation and Objectives / Local and Global Minima / Line Searches / Steepest Descent Method / Conjugate-Gradient Method / Quasi-Newton Methods / Penalty Functions / Simulated Annealing / Applications / Chapter Summary / Problems 7. DIFFERENTIATION AND INTEGRATION Motivation and Objectives / Numerical Differentiation / Noise-Corrupted Data / Newton-Cotes Integration Formulas / Romberg Integration / Gauss Quadrature / Improper Integrals / Multiple Integrals / Applications / Chapter Summary / Problems 8. ORDINARY DIFFERENTIAL EQUATIONS Motivation and Objectives / Euler"s Method / Runge-Kutta Methods / Step Size Control / Multi-Step Methods / Bulirsch-Stoer Extrapolation Methods / Stiff Differential Equations / Boundary Value Problems / Applications / Summary / Problems 9. PARTIAL DIFFERENTIAL EQUATIONS Motivation and Objectives / Elliptic Equations / One-Dimensional Parabolic Equations / Two-Dimensional Parabolic Equations / One-Dimensional Hyperbolic Equations / Two-Dimensional Hyperbolic Equations / Applications / Chapter Summary / Problems 10. DIGITAL SIGNAL PROCESSING Motivation and Objectives / Fourier Transform / Fast Fourier Transform (FFT) / Correlation / Convolution Digital Filters / Two-Dimensional FFT / System Identification / Applications / Chapter Summary / Problems / REFERENCES AND FURTHER READING / APPENDIX 1: NLIB USING MATLAB(R) / A Numerical Toolbox: NLIB / Main-Program Support / Linear Algebraic Systems / Eigenvalues and Eigenvectors / Curve Fitting / Root Finding / Optimization / Differentiation and Integration / Ordinary Differential Equations / Partial Differential Equations / Digital Signal Processing / APPENDIX 2: NLIB USING C / A Numerical Library: NLIB / NLIB Data Types / NLIB Core: nlib.c / Tabular Display: show.c / Graphical Display: draw.c / Linear Algebraic Systems: linear.c / Eigenvalues and Eigenvectors: eigen.c / Curve Fitting: curves.c / Root Finding: roots.c / Optimization: optim.c / Differentiation and Integration: integ.c / Ordinary Differential Equations: ode.c / Partial Differential Equations: pde.c / Digital Signal Processing: dsp.c / APPENDIX 3: VECTORS AND MATRICES / Vector and Matrix Notation / Basic Operations / Inverses / Eigenvalues and Eigenvectors / Vector Norms / APPENDIX 4: ANSWERS TO SELECTED PROBLEMS / INDEX