Course detail
Applied Mathematics
FAST-CA057Acad. year: 2018/2019
Basics of ordinary fifferential equations focussing on engineering applications – classic solution, Cauchy problem and boundary problems (their classification). Analytical methods for solving boudary problems in ordinary secod and fourth order differential equations.
Methods of solution of non-homogeneous boundary problems – Fourier method, Green´s function, variation of constants method. Solutions of non-linear differential equations with given boundary conditions. Sobolev spaces and generalized solutions and reason for using such notions. Variational methods of solutions.
Introduction to the theory of partial differential equations of two variables – classes and basic notions. Classic solution of a boundary problem (classes), properties of solutions.
Laplace and Fourier transform – basic properties.
Fourier method of solution of evolution equations, difussion problems, wave equation.
Laplace method used to solve evolution equations - heat transfer equation.
Equations used in the theory of elasticity.
Supervisor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
Understanding the notion of generalized solutions to ordinary differential equations. Getting acquainted with principles of the modern methods used to solve odrinary and partial differential equations in transport structures.
Prerequisites
Basics of the theory of one- and more-functions. Differentiation and integration of functions.
Co-requisites
Not applicable.
Recommended optional programme components
Not applicable.
Recommended or required reading
Not applicable.
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.
Assesment methods and criteria linked to learning outcomes
Successful completion of the scheduled tests and submission of solutions to problems assigned by the teacher for home work. Unless properly excused, students must attend all the workshops. The result of the semester examination is given by the sum of maximum of 70 points obtained for a written test and a maximum of 30 points from the seminar.
Language of instruction
Czech
Work placements
Not applicable.
Course curriculum
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.
Aims
Understanding the notion of generalized solutions to ordinary differential equations. Getting acquainted with principles of the modern methods used to solve odrinary and partial differential equations in transport structures.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Classification of course in study plans
- Programme N-P-E-SI (N) Master's
branch K , 1. year of study, summer semester, 4 credits, compulsory-optional
- Programme N-K-C-SI (N) Master's
branch K , 1. year of study, summer semester, 4 credits, compulsory-optional
- Programme N-P-C-SI (N) Master's
branch K , 1. year of study, summer semester, 4 credits, compulsory-optional
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
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
26 hours, compulsory
Teacher / Lecturer
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.