Shoichiro Nakamura, Ohio State University, Columbus

Published September, 1995 by Prentice Hall PTR (ECS Professional)

Copyright 1996, 496 pp.
Cloth
ISBN 0-13-051518-3
$82.00

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    Numerical Methods

Featuring a disk containing MATLAB scripts of functions and examples, this book explores using MATLAB for numerical methods and graphic visualization.

Offers a complete tutorial of MATLAB, covering numerical methods with MATLAB and advanced three-dimensional graphics with colors.

1. MATLAB Primer.

Tutorials on Command Window. Array Variables. Unique Aspect of Numbers in MATLAB. Mathematical Functions of MATLAB. Functions that do Chores. Developing a Program as M-file. How to Write User's Own Functions. Saving and Loading of Data. How to Make Hard Copies.

2. Graphics with MATLAB.

Simple Plotting. How to Take Hard Copy of Graphs. Contour of Two-dimensional Functions. Triangular Grid and Contours. Curvilinear Grid and Contours. Mesh and Surface Plotting. MATLAB as a Drawing Tool. Interactive Graphics. M-files.

3. Linear Algebra.

Matrices and Vectors. Matrix and Vector Operations in MATLAB. Inverse Matrix. Linear Equations. Unsolvable Problems. Determinant. Ill-conditioned Problems. Gauss Elimination. Gauss- Jordan Elimination and Matrix Inversion. LU Decomposition. Iterative Solution. Matrix Eigenvalues.

4. Polynomials and Interpolation.

MATLAB Commands for Polynomials. Linear Interpolation. Polynomial Interpolation with Power Seriesi Form. Lagrange Interpolation Polynomial. Error of Interpolation Polynomials. Differentiation and Integration of Lagrange Interpolation Formula. Interpolation with Chebyshev and Legendre Points. Cubic Hermite Interpolation. Two Dimensional Interpolation. Transfinite Interpolation. M-files.

5. Numerical Integration.

Trapezoidal Rule. Simpson's Rules. Other Quadratures. Numerical Integration with Infinite Limits or Singularities. MATLAB Commands for Integrations. Numerical Integration on a Two-dimensional Domain. M-files.

6. Numerical Differentiation.

Derivatives of Interporation Polynomials. Difference Approximations. Taylor Expansion Method. Algorithms to Automate Derivation. Difference Approximation for Partial Derivatives. Numerical Evaluation of High Order Derivatives. M-files.

7. Roots of Nonlinear Equations.

Graphical Method. Bisection Method. Newton Iteration. Secant Method. Successive Substitution Method. Simultaneous Nonlinear Equations. M-files.

8. Curve Fitting to Measured Data.

Line Fitting. Nonlinear Curve Fitting with a Power Function. Curve Fitting with a Higher Order Polynomial. Curve Fitting by a Linear Combination of Known Functions.

9. Spline Functions and Nonlinear Interpolation.

C-spline Interpolation. Cubic B-spline. Interpolation with a Nonlinear Function. M-files.

10. Initial Value Problems of Ordinary Differential Equations.

First Order ODEs. Euler Methods. Runge-Kutta Methods. Shooting Method. Method of Lines.

11. Boundary Value Problems of Ordinary Differential Equations.

Introduction. Boundary Value Problems for Rods and Slabs. Solution of Tridiagonal Equation. Variable Coefficients and Nonuniform Grid Spacing. Cylinders and Spheres. Nonlinear Ordinary Differential Equations.

Appendix A. Colors.
Appendix B. Drawing of Three-Dimensional Objects.
Appendix C. Moview.
Appendix D. Image Processing.
Appendix E. Graphical User Interface.