Numerical analysis

1. Mathematical preliminaries and error analysis

2. Solutions of equations in one variable

3. Interpolation and polynomial approximation

4. Numerical differentiation and integration

5. Initial-value problems for ordinary differential equations

6. Direct methods for solving linear systems

7. Iterative techniques in matrix algebra

8. Approximation theory

9. Approximating eigenvalues

10. Numerical solutions of nonlinear systems of equations

11. Boundary-value problems for ordinary differential equations

12. Numerical solutions to partial differential equations.