Numerical Analysis & Implementation Environments

Course Code: 
Credit Points: 

Course Outline

  1. Introduction to Numerical Analysis.
  2. Introduction and basic elements of MATLAB and Octave.
  3. Representation of real numbers in finite precision and the floating-point model of arithmetic.
  4. Forward and backward stability of algorithms. Condition number of a numerical problem.
  5. Numerical linear algebra: Direct methods (LU, Cholesky and variants).
  6. Iterative methods for solving linear systems (Jacobi, Gauss-Seidel, Richardson).
  7. Brief introduction to projection methods for matrices with symmetric positive definite matrices (steepest descent and conjugate gradients).
  8. Numerical approximation of eigenvalue problems: Power method, inverse power method, shifted inverse power method. Brief description of the QR algorithm.
  9. Polynomial interpolation and representations (Lagrange, Newton, barycentric, Hermite), piecewise interpolating polynomials, splines. Brief introduction to Chebfun.
  10. Function and data-driven approximation. Least squares approximation and solving linear least squares problems. QR factorization by means of Householder reflectors.
  11. Methods for solving nonlinear equations (bisection, Newton, secant, regular falsi).
  12. Numerical integration with simple methods (rectangle, trapezoidal, Simpson).
  13. Finite difference methods for approximating derivatives and brief introduction to the numerical solution of differential equations.
  14. The role of Numerical Analysis in Computer Science and Engineering.

Startup Growth Lite is a free theme, contributed to the Drupal Community by More than Themes.