Course detail
Mathematics 3
FAST-BAA003Acad. year: 2025/2026
Double and triple integrals. Their calculation, transformation, physical and geometric interpretation.
Curvilinear integral in a scalar field, its calculation and application. Divergence and rotation of a vector field. Curvilinear integral in a vector field, its calculation and application. Independence of a curvilinear integral on the integration path. Green`s theorem.
Existence and uniqueness of solutions to first order differential equations. n-th order homogeneous linear differential equations with constant coefficients. Solutions to non-homogeneous linear differential equations with special-type right-hand sides. Variation-of-constants method.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Offered to foreign students
Entry knowledge
Rules for evaluation and completion of the course
Aims
They should learn the basic facts on selected first-order differential equations, on existence and uniqueness of solutions, be able to find analytical solutions to separated, linear, 1st-order homogeneous, and exact differential equations, calculate the solution of a non-homogeneous linear nth-order differential equation with special right-hand sides as well as using the general method of the variation of constants, understand the structure of solutions to non-homogeneous nth-order linear differential equations.
Knowledge of double and triple integrals, their calculation and application. Knowledge of curvilinear integral in a scalar and vector field, their calculation and application. Knowledge of basic facts on existence, uniqueness and analytical methods of solutions on selected first-order differential equations and nth-order linear differential equations.
Study aids
Prerequisites and corequisites
Basic literature
Jirásek, F., Čipera, S., Vacek, M.,Sbírka řešených příkladů z matematiky II, SNTL Praha 1986. (CS)
Recommended reading
Classification of course in study plans
- Programme BPA-SI Bachelor's 2 year of study, winter semester, compulsory
- Programme BPC-SI Bachelor's
specialization VS , 2 year of study, winter semester, compulsory
- Programme BPC-EVB Bachelor's 2 year of study, winter semester, compulsory
- Programme BKC-SI Bachelor's 2 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- 1. Definition of double integral, basic properties and calculation.
- 2. Transformations and applications of double integral.
- 3. Definition of triple integral, basic properties and calculation.
- 4. Transformations and applications of triple integral.
- 5. Notion of a curve. 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. Green`s theorem and its application.
- 8. Independence of a curvilinear integral on the integration path.
- 9. Basics of ordinary differential equations.
- 10. First order differential equations - separable, linear, exact equations.
- 11. N-th order homogeneous linear differential equations with constant coefficients.
- 12. Solutions to non-homogeneous linear differential equations.
- 13. Variation-of-constants method. Applications in technology.
Exercise
Teacher / Lecturer
Syllabus
- 1. Quadrics and integration revision.
- 2. Double integral calculation.
- 3. Double integral transformations.
- 4. Double integral applications.
- 5. Triple integral calculation.
- 6. Transformations and applications of triple integral.
- 7. Curvilinear integral in a scalar field and its applications.
- 8. Curvilinear integral in a vector field and its applications.
- 9. Green`s theorem. Independence of a curvilinear integral on the integration path. Potential.
- 10. First order differential equations - separable, linear.
- 11. Exact equation. N-th order homogeneous linear differential equations with constant coefficients.
- 12. Solutions to non-homogeneous linear differential equations with special-type right-hand sides.
- 13. Variation-of-constants method. Seminar evaluation.