• 1. Basics of ordinary differential equations focussing on engineering applications – classic solution, Cauchy problem and boundary problems (classes).
• 2. Analytical methods used to solve boundary problems in ordinary secod and fourth order differential equations.
• 3. Methods of solution of non-homogeneous boundary problems – Fourier method,
• 4. Green´s function, variation of constants method.
• 5. Solutions of non-linear differential equations with given boundary conditions.
• 6. Sobolev spaces and generalized solutions and reason for using such notions.
• 7. Variational methods of solutions.
• 8. Introduction to the theory of partial differential equations of two variables – classes and basic notions.
• 9. Classic solution of a boundary problem (classes), properties of solutions.
• 10. Laplace and Fourier transform – basic properties.
• 11. Fourier method used to solve evolution equations, difussion problems, wave equation.
• 12. Laplace method used to solve evolution equations – heat transfer equation.
• 13. Equations used in the theory of elasticity.

Related directly to the above listed topics of lectures.

• 1. Basics of ordinary differential equations focussing on engineering applications – classic solution, Cauchy problem and boundary problems (classes).
• 2. Analytical methods used to solve boundary problems in ordinary secod and fourth order differential equations.
• 3. Methods of solution of non-homogeneous boundary problems – Fourier method,
• 4. Green´s function, variation of constants method.
• 5. Solutions of non-linear differential equations with given boundary conditions.
• 6. Sobolev spaces and generalized solutions and reason for using such notions.
• 7. Variational methods of solutions.
• 8. Introduction to the theory of partial differential equations of two variables – classes and basic notions.
• 9. Classic solution of a boundary problem (classes), properties of solutions.
• 10. Laplace and Fourier transform – basic properties.
• 11. Fourier method used to solve evolution equations, difussion problems, wave equation.
• 12. Laplace method used to solve evolution equations – heat transfer equation.
• 13. Equations used in the theory of elasticity.