Mathematical methods 3 for computer engineers

• Vector spaces and linear transformations Subspaces of Rn, base and dimension. General vector spaces, function spaces and norms. Matrix transformations, null spaces and column spaces. Application: Fourier series and solution of partial differential equations.
• Differential equations with solution methods.
• Numerical methods General numerics: Representations of floating point numbers in the computer, calculations with floating point numbers and various sources of error. Error magnification and condition. Convergence rate
• Direct methods:
  • Solution of linear equation systems, PA = LU factorization, least squares method
  • Interpolation with cubic splines, Bezier curves.
• Iterative methods:
  • Newton's multivariate method
  • Solution of linear equation systems (Jakobi, conjugate gradients)
  • Calculation of eigenvalues and eigenvectors (power method)
  • Solution of some types of differential equations, Runge-Kutta.

Knowledge

The candidate has a good knowledge of subspaces of Rn and linear transformations between finite-dimensional real vector spaces. The candidate has knowledge about general vector spaces and linear transformations. The candidate is familiar with common sources of error in numerical calculations. The candidate is accustomed with relevant IT applications of mathematics in the subject.

Skills

The candidate can complete induction proofs. The candidate can solve some types of first and second order difference equations. The candidate can solve linear and non-linear systems numerically. The candidate can solve problems with least squares method. The candidate can interpolate. The candidate can calculate eigenvalues and eigenvectors numerically. The candidate can solve some types of differential equations numerically.

General competence

The candidate can use mathematics to communicate engineering issues, with the main emphasis on information technology. The candidate understands that the level of precision in the mathematical language makes it suitable to structurize and solve engineering problems.

Lectures and exercises.

80% of the obligatory exercises need to be approved for exam admission.

The lectures may be given in English.