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

Appendix C – Getting Starte dwith Mathcad

Bibliography

Index