- Description:
-
1. Matrices, eigenvalues and eigenvectors, spectrum.
2. Norm, norms of matrices, condition number, Gershgorin Theorem.
3. Symmetric matrices, positive definite matrices.
4. Cholesky decomposition. Variational principle.
5. Iterative methods. Sparse matrices. Conditioning.
6. Ordinary linear differential equations - basic properties.
7. Boundary value problems for second order differential equations; eigenvalues and eigenfunctions.
8. Function spaces, dot product of functions. Eigenspaces.
7. Solvability of boundary value problems for second order linear differential equations.
8. Differential operators, operator equations, eigenvalues and eigenfunctions. Solvability of operator equations.
9. Variational principle. Stable and unstable solutions.
10. Variational methods (Ritz, finite elements).
11. Laplace and Poisson Equation.
12. Wave equation.
13. Backup.
- Recommended literature:
-
!F. Bubeník: Mathematics for Engineers. CVUT, 2014, ISBN 978-80-01-03792-8.
!F. Bubeník: Problems to Mathematics for Engineers, CVUT 2014, ISBN 978-80-01-05621-9
?K. Rektorys: Solving Ordinary and Partial Boundary Value Problems in Science and Engineering (Applied and Computational Mechanics), CRC Press; 1 edition (1998), ISBN 978-0849325526
?Sherman Stein, Anthony Barcellos, Calculus and Analytic Geometry 5th ed., Mcgraw-Hill 1992, ISBN 978-0070611757
Abbreviations used:
Semester:
- W ... winter semester (usually October - February)
- S ... spring semester (usually March - June)
- W,S ... both semesters
Mode of completion of the course:
- A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
- GA ... Graded Assessment (a grade is awarded for this course)
- EX ... Examination (a grade is awarded for this course)
- A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)
Weekly load (hours per week):
- P ... lecture
- C ... seminar
- L ... laboratory
- R ... proseminar
- S ... seminar