Table of Contents

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

7 Roots of Polynomials

8 Case Studies: Roots of Equations

Part 3 Linear Algebraic Equations

9 Gauss Elimination

10 LU Decomposition and Matrix Inversion

11 Special Matrices and Gauss-Seidel

12 Case Studies: Linear Algebraic Equations

Part 4 Optimization

13 One-Dimensional Unconstrained Optimization

14 Multidimensional Unconstrained Optimization

15 Constrained Optimization

16 Case Studies: Optimization

Part 5 Curve Fitting

17 Least-Squares Regression

18 Interpolation

19 Fourier Approximation

20 Case Studies: Curve Fitting

Part 6 Numerical Differentiation and Integration

21 Newton-Cotes Integration Formulas

22 Integration of Equations

23 Numerical Differentiation

24 Case Studies: 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 Case Studies: Ordinary Differential Equations

Part 8 Partial Differential Equations

29 Finite Difference: Elliptic Equations

30 Finite Difference: Parabolic Equations

31 Finite-Element Method

32 Case Studies: Partial Differential Equations

Appendix A The Fourier Series

Appendix B Getting Started with Matlab

Bibliography

Index

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