Numerical analysis and graphic visualization with MATLAB Book

Preface.

1. MATLAB Primer.

Before Starting Calculations. How to Do Calculations. Branch Statements. Loops with for/end or while/end. Reading and Writing. Array Variables. Unique Aspect of Numbers in MATLAB. Mathematical Functions of MATLAB. Functions That Do Chores. Developing a Program as an M-File. How to Write Your Own Functions. Saving and Loading Data. How to Make Hard Copies.

2. Graphics with MATLAB.

Simple Plotting. Interactive Editing of Figures. How to Print or Record Graphs. Plotting of Two-Dimensional Functions. Triangular Grid and Contours. Curvilinear Grid and Contours. Plotting Curved Surfaces. MATLAB as a Drawing Board. Interactive Graphics. M-Files.

3. Linear Algebra.

Matrices and Vectors. Matrix and Vector Operations in MATLAB. Inverse Matrix. Linear Equations. Unsolvable Problems. The 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 Series. Lagrange Interpolation Polynomial. Error of Interpolation Polynomials. Differentiation and Integration of Lagrange Interpolation Formula. Interpolation with Chebyshev 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 Interpolation Polynomials. Difference Approximations. Taylor Expansion Method. Algorithms to Automate Derivations. 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 Equations. Variable Coefficients and Nonuniform Grids. Cylinders and Spheres. Nonlinear Ordinary Differential Equations.

Appendix A: Colors.

Appendix B: Drawing Three-Dimensional Objects.

Appendix C: Movies.

Appendix D: Image Processing.

Appendix E: Graphical User Interface.

Appendix F: Answer Key.

Subject Index.