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 Started with Mathcad
Bibliography
Index