Course detail
Mathematics 3 (G)
FAST-BAA010Acad. year: 2020/2021
Double and triple integral and their applications. Transformations of double and triple integrals.
Curve integrals in scalar and vector fields, basic properties ans calculation. Independence of the curve integral of the path of integration. Green`s Theorem.
Ordinary differential equations (DE) of the first order, existence and uniqueness of the solution. DE with separable variables, homogeneous, linear and exact DE. Orthogonal and isogonal trajectories, envelope of the family of curves. Linear DE of n-th order, general solution, basic properties of solutions. Linear DE with constant coefficients.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Basics of integral calculus of functions of one variable and the basic interpretations.
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
2. Transformations of double integrals. Physical and geometric applications of double integrals.
3. Calculation and transformations of triple integrals.
4. Physical and geometric applications of triple integrals.
5. Curvilinear integral in a scalar field and its applications.
6. Vector field. Divergence and rotation of a vector field. Curvilinear integral in a vector field and its applications.
7. Independence of a curvilinear integral on the integration path.
8. Green`s theorem and its application.
9. Basics of ordinary differential equations. First order differential equations - separable, homogeneous.
10. First order differential equations - linear, exact equations. Orthogonal and isogonal trajectories.
11. Structure of the set of solutions to an n-th order linear differential equation. Linear independence of solutions, Wronskian.
12. Homogeneous linear differential equations with constant coefficients. Solutions to non-homogeneous linear differential equations.
13. Solutions to non-homogeneous linear differential equations. Variation-of-constants method.
Work placements
Aims
They should learn the basics of line integrals in scalar and vector fields and their aplications. They should know how to calculate simple line integrals.
They should be acquainted with selected first-order differential equations (DE) focussing on problems of existence and uniqueness of their solutions, know how to find analytical solutions to separated, linear, 1st-order homogeneous, exact DE's, calculate non-homogeneous linear nth-order DE's with a special right-hand side and using the variation of constants method. They should understand the structure of solutions of nth-order non-homogeneous linear DE's with issues of orthogonal and isogonal trajectories.
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
- Programme BPC-GK Bachelor's 2 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
Exercise
Teacher / Lecturer
Syllabus