Course Details

Numerical methods 1

Academic Year 2025/26

DAB030 course is part of 24 study plans

​ DKA-V Summer Semester 1st year

​ DKC-V Summer Semester 1st year

​ DPA-V Summer Semester 1st year

​ DPC-V Summer Semester 1st year

​ DKA-E Summer Semester 1st year

​ DKC-E Summer Semester 1st year

​ DPA-E Summer Semester 1st year

​ DPC-E Summer Semester 1st year

​ DKA-K Summer Semester 1st year

​ DKC-K Summer Semester 1st year

​ DPA-K Summer Semester 1st year

​ DPC-K Summer Semester 1st year

​ DKA-M Summer Semester 1st year

​ DKC-M Summer Semester 1st year

​ DPA-M Summer Semester 1st year

​ DPC-M Summer Semester 1st year

​ DPC-S Summer Semester 1st year

​ DPA-S Summer Semester 1st year

​ DKC-S Summer Semester 1st year

​ DKA-S Summer Semester 1st year

​ DPC-GK Summer Semester 1st year

​ DPA-GK Summer Semester 1st year

​ DKC-GK Summer Semester 1st year

​ DKA-GK Summer Semester 1st year

Course Guarantor

prof. Ing. Jiří Vala, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech

Credits

4 credits

Semester

summer

Forms and criteria of assessment

course-unit credit

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/290139

Lecture

13 weeks, 3 hours/week, elective

Syllabus

  • 1. Errors in numerical calculations. Numerical methods for one nonlinear equation in one unknown
  • 2. Basic principles of iterative methods. The Banach fixed-point theorem.
  • 3. Norms of vectors and of matrices, eigenvalues and eigenvectors of matrices. Iterative methods for systems of linear algebraic equations – part I.
  • 4. Iterative methods for linear algebraic equations – part II. Iterative methods for systems of nonlinear equations.
  • 5. Direct methods for systems of linear algebraic equations, LU-decomposition. Systems of linear algebraic equations with special matrice – part I.
  • 6. Systems of linear algebraic equations with special matrices – part II. The methods based on the minimization of a quadratic form.
  • 7. Computing inverse matrices and determinants, the stability and the condition number of a matrix.
  • 8. Eigenvalues of matrices – the power method. Basic principles of interpolation.
  • 9. Polynomial interpolation.
  • 10. Interpolation by means of splines. Orthogonal polynoms.
  • 11. Approximation by the discrete least squares.
  • 12. Numerical differentiation, Richardson´s extrapolation. Numerical integration of functions in one variables – part I.
  • 13. Numerical integration of functions in one variables – part II. Numerical integration of functions in two variables.