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.