Course Details

# Applied Mathematics

NAB023 course is part of 1 study plan

NPC-SIK Summer Semester 1st year

Course Guarantor

Institute

Language of instruction

Czech

Credits

4 credits

Semester

summer

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

Lecture

13 weeks, 2 hours/week, elective

Syllabus

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.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

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.