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.

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.