Part One: Modeling, Computers, and Error Analysis

1 Mathematical Modeling and Engineering Problem Solving
2 Computers and Software
3 Approximations and Roundoff Errors
4 Truncation Errors and the Taylor Series Epilogue

Part Two: Roots of Equations

5 Bracketing Methods
6 Open Methods
7 Roots of Polynomials
8 Engineering Applications Roots of Equations

Part Three: Linear Algebraic Equations

9 Gauss Elimination
10 LU Decomposition and Matrix Inversion
11 Banded Systems and Gauss-Seidel
12 Engineering Applications Linear Algebraic Equations

Part Four: Optimization

13 Univaruiate Unconstrained Optimization
14 Multivariate Unconstrained Optimization
15 Constrained Optimization
16 Engineering Applications Optimization

Part Five: Curve Fitting

17 Least-Squares Regression
18 Interpolation
19 Fourier Approximation
20 Engineering Applications Curve Fitting

Part Six: Numerical Integration and Differentiation

21 Newton-Codes Integration
22 Integration of Equations
23 Numerical Differentiation
24 Engineering Applications Numerical Integration and Differentiation

Part Seven: Ordinary Differential Equations

25 One-Step Methods
26 Multi-Step Methods
27 Boundary-Value and Eigenvalue Problems
28 Engineering Applications Ordinary Differential Equations

Part Eight: Partial Differential Equations

29 Finite-Difference Elliptic Equations
30 Finite-Difference Parabolic Equations
31 Finite Element Method
32 Engineering Applications Partial Differential Equations