Numerical Analysis (2 º Sem 2013/2014)
Program
- Introduction to scientific computing. Scientific computing software. Sources of error in numerical calculations;
- Numerical solution of nonlinear equations and systems of equations. Fixed point method. Newton?s method. Convergence and error estimates;
- Numerical linear algebra. Numerical methods for linear systems. Iterative methods of Jacobi and Gauss-Seidel. Gauss elimination method and matrix factorization. Numerical methods for eigenvalues and eigenvectors;
- Approximation, interpolation and numerical integration. Polynomial, rational and trigonometric interpolation. Least-squares approximation. Interpolatory integration and Gauss integration;
- Numerical methods for initial value problems. Euler and Runge-Kutta methods. Linear multistep methods.
- Numerical solution of nonlinear equations and systems of equations. Fixed point method. Newton?s method. Convergence and error estimates;
- Numerical linear algebra. Numerical methods for linear systems. Iterative methods of Jacobi and Gauss-Seidel. Gauss elimination method and matrix factorization. Numerical methods for eigenvalues and eigenvectors;
- Approximation, interpolation and numerical integration. Polynomial, rational and trigonometric interpolation. Least-squares approximation. Interpolatory integration and Gauss integration;
- Numerical methods for initial value problems. Euler and Runge-Kutta methods. Linear multistep methods.