Errors, Computer Arithmetic, Error method and algorithm, Linear Systems, Method of Gauss, Gauss-Jordan, factorization LU, Method Choleski, Iterative method of Jacobi, Gauss, Gauss-seidel, SOR, Nonlinear equations and systems, partition method, fixed point, Newton-Raphson, secant, Interpolation and Approximation of Lagrange, Newton, Hermite, functions, spline, Numerical Differentiation and Integration type Lagrange, Taylor, Richardson, rule rectangle, trapezoid, Simpson, type Newton-Cotes, Numerical solution of ordinary differential equations, partial differential equations.
The purpose of this course is to provide a complete knowledge of numerical methods for solving problems that appear in Science and Technology.
More precisely the aim of this course is the comprehension of the basic numerical methods for approximating solutions of various mathematical problems using a computer.
Emphasis is also given on the theoretical/mathematical background of these methods for their full comprehension.
After the successful completion of this course, the student should be able to:
- understand the floating point arithmetic and floating point numbers.
- understand, calculate and estimate the error that occurs from approximate solutions of problems.
- approximate solutions of systems of linear and non-linear equations, using basic arithmetic methods.
- approximate solutions of non-linear equations, using basic arithmetic methods.
- describe the behavior of functions in one variable using suitable interpolation polynomials.
- approximate the derivative and the integral functions in one variable, using arithmetic differentiation and integration methods.
- apply basic arithmetic methods for solving simple differential equations.