Course Details

Mathematics 3 (G)

Academic Year 2024/25

BAA010 course is part of 1 study plan

BPC-GK Winter Semester 2nd year

Course Guarantor

Institute

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

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.