Still brief - but with the chapters that you wanted - Steven Chapra's new second edition is written for engineers and scientists who want to learn numerical problem solving. This text focuses on problem-solving (applications) rather than theory, using MATLAB, and is intended for Numerical Methods users; hence theory is included only to inform key concepts. The new second edition feature new material such as Numerical Differentiation and ODE's: Boundary-Value Problems.
Table of Contents
Part One Introduction
1. Mathematical Modeling Numerical Methods and Problem Solving
2. MATLAB Fundamentals
3. Programming with MATLAB
4. Roundoff and Trunication Errors
Part Two Roots and Optimization
5. Roots of Equations: Bracketing Methods
6. Roots of Equations: Open Methods
7. Optimization
Part Three Linear Systems
8. Linear Algebraic Equations and Matrices
9. Gauss Elimination
10. LU Decomposition
11. Matrix Inverse and Condition
12. Iterative Methods for Systems of Equations
Part Four Regression
13. Curve Fitting: Fitting a Straight Line
14. Curve Fitting: General Linear Least-Squares and Non-Linear Regression
Part Five Interpolation
15. Curve Fitting: Polynomial Interpolation
16. Curve Fitting: Splines
Part Six Integration and Differentiation
17. Numerical Intergration Formulas
18. Numerical Intergration Functions
19. Numerical Differentiation
Part Seven Ordinary Differential Equations
20. ODE's: Initial-Value Problems
21. ODE's: Adaptive Methods and Stiff Systems
22. ODE's: Boundary-Value Problems
Appendix A: Eigenvalues Appendix B: Fast Fourier Transform Appendix C: MATLAB Built-in Functions Appendix D: MATLAB M-File Functions Bibliography Index