• 1. Errors in numerical calculations. Linear spaces and operators, fixed point theorems. Iterative methods for the analysis of nonlinear algebraic and selected further equations.
• 2. Iterative and coupled methods for the analysis of linear algebraic equations, relaxation methods, method of conjugated gradients.
• 3. Multiplicative decomposition of matrices. Numerical evaluation of eigenvalues and eigenvectors of matrices and of inverse matrices, algorithms for special matrices.
• 4. Condition numbers of systems of linear equations. Least squares method, pseudoinverse matrices.
• 5. Generalizations of methods from 3. and 4. to the analysis of systems of nonlinear equations.
• 6. Lagrange and Hermite interpolation of functions of 1 variable, namely polynoms and splines.
• 7. Approximation of functions of 1 variable using the least squares methos: linear and nonlinear approach.
• 8. Approximation of function of more variables.
• 9. Numerical differentiation. Finite difference method for the analysis of selected initial and boundary problems for ordinary differential equations.
• 10. Numerical quadrature. Finite element method for the analysis of selected initial and boundary problems for ordinary differential equations.
• 11. Time-dependent problems. Time discretization: Euler methods, Cranka-Nicholson method, Runge-Kutta methods, Newmark method.
• 12. Generalization of 9. and 10. for pro partial differential equations of evolution, e.g. heat transfer equations, fluid flow equations and equations of dynamics of building structures.
• 13. Sensitivity and inverse problems. Identification of uncertain material parameters from known measurement results. Selected engineering application, due to other courses.

Seminars follow the related lectures:

• 1. Errors in numerical calculations. Linear spaces and operators, fixed point theorems. Iterative methods for the analysis of nonlinear algebraic and selected further equations.
• 2. Iterative and coupled methods for the analysis of linear algebraic equations, relaxation methods, method of conjugated gradients.
• 3. Multiplicative decomposition of matrices. Numerical evaluation of eigenvalues and eigenvectors of matrices and of inverse matrices, algorithms for special matrices.
• 4. Condition numbers of systems of linear equations. Least squares method, pseudoinverse matrices.
• 5. Generalizations of methods from 3. and 4. to the analysis of systems of nonlinear equations.
• 6. Lagrange and Hermite interpolation of functions of 1 variable, namely polynoms and splines.
• 7. Approximation of functions of 1 variable using the least squares methos: linear and nonlinear approach.
• 8. Approximation of function of more variables.
• 9. Numerical differentiation. Finite difference method for the analysis of selected initial and boundary problems for ordinary differential equations.
• 10. Numerical quadrature. Finite element method for the analysis of selected initial and boundary problems for ordinary differential equations.
• 11. Time-dependent problems. Time discretization: Euler methods, Cranka-Nicholson method, Runge-Kutta methods, Newmark method.
• 12. Generalization of 9. and 10. for pro partial differential equations of evolution, e.g. heat transfer equations, fluid flow equations and equations of dynamics of building structures.
• 13. Sensitivity and inverse problems. Identification of uncertain material parameters from known measurement results. Selected engineering application, due to other courses.