The training manual presents practical lessons on the integral calculus of functions of one independent variable and the integration of ordinary differential equations, multiple and curvilinear integrals.
Practical assignments are divided into the following topics:
The first practical lesson. Double integrals. Calculation
areas by means of a double integral.
The second practical lesson. Calculation of volumes and surfaces by means of a double integral. Applications of the double integral to the problems of mechanics.
The third practical lesson. Triple integral.
The fourth practical lesson. Calculation of static moments, coordinates of the center of gravity and moments of inertia of plane figures and bodies.
The fifth practical lesson. Curvilinear integrals.
The sixth practical lesson. The independence of the curvilinear integral with respect to the coordinates of the path of integration. Integration of differential equations, the left side of which is a complete differential.
Seventh practical lesson. Green's formula. Area computation by means of a curvilinear integral