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