Outline

1. Introduction, errors, and FLOPS
   Chapter 1 3 lectures
   $\bullet$ Approximation and Error $\bullet$ Computer arithmetic

2. Nonlinear Equations
   Chapter 2 4 lectures
   $\bullet$ Introduction and scalar equations $\bullet$ Nonlinear system of equations

3. Numerical solution of Linear systems
   Chapter 3 4 lectures
   $\bullet$Solving linear systems $\bullet$Error analyses and accuracy $\bullet$iterative methods

4. Eigenvalue Problem
   Chapter 4

5. Interpolation Chapter 5 3 lectures
   $\bullet$ Polinomial interpolation $\bullet$ Piecewise polyunomial interpolation

6. Numerical Integration
   Chapter 6 3 lectures
   

7. Numerical solution of the ODE's
   Chapter 7 4 lectures
   $\bullet$ Numerical quadrature $\bullet$ Numerical differentiation

   $\bullet$ Introduction and Euler's method $\bullet$ Accuracy and stability $\bullet$ Implicit method and stiff equations $\bullet$ Runge-Kutta and Taylor methods

8. Least squares
   Chapter 8 3 lectures

28 lectures including 3 midterms and one matlab lab