Course Details

Mathematics 3 (G)

Academic Year 2025/26

BAA010 course is part of 1 study plan

​ BPC-GK Winter Semester 2nd year

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289944

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 1. Definition of double and triple integrals their basic properties. Calculation of double integrals.
  • 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.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Basic properties of double and triple integrals. Calculation of double integrals.
  • 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. First order differential equations - separable, homogeneous.
  • 10. First order differential equations - linear, exact equations. Orthogonal and isogonal trajectories.
  • 11. Homogeneous linear differential equations with constant coefficients.
  • 12. Solutions to non-homogeneous linear differential equations.
  • 13. Variation-of-constants method. Seminar evaluation.