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