Course Details

Mathematics 3

Academic Year 2025/26

BAA003 course is part of 4 study plans

​ BPA-SI Winter Semester 2nd year

​ BPC-SI / VS Winter Semester 2nd year

​ BPC-EVB Winter Semester 2nd year

​ BKC-SI Winter Semester 2nd year

Course Guarantor

doc. Ing. Vladislav Kozák, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech, English

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

To offer to students of all faculties

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289589

Lecture

13 weeks, 2 hours/week, elective

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

13 weeks, 2 hours/week, compulsory

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.