Educational and methodological manual for a student . Part III . — Togliatti: TSU, 2007. — 122 pages . Scientific Editor D. t. n. , Professor Zibrov P. F. Differential Equations . Differential equations of order I. Equations with divisible variables. Homogeneous differential equations. Equations in total differentials. Linear differential equations of order I. Bernoulli's Equations . Differential equations of the second order, allowing a decrease in the order. Uniform linear differential equations of order II with constant coefficients. Inhomogeneous linear differential equations of order II with constant coefficients. Systems of Differential Equations . Multiple integrals . Dual Integral . Cylindrical body volume. Calculation of double integrals in Cartesian coordinates. Calculation of double integrals in polar coordinates. Applications of double integrals to mechanical problems. Calculation of areas and volumes using double integrals. Calculation of surface area. Triple Integral . Mass of heterogeneous body. Calculation of triple integrals in Cartesian coordinates. Calculations of triple integrals in cylindrical coordinates. Calculation of triple integrals in spherical coordinates. Application of triple integrals. Curvilinear and surface integrals . Curvilinear integrals . Curvilinear integral of the first type (along the length of the arc). Curvilinear integral of the second type (by coordinates). Green's Formula . Conditions for the independence of the curvilinear integral from the path of integration. Relationship between curvilinear integrals of the first and second types . Surface integrals. Surface integrals of the first type . The concept of a two-sided surface . Surface integral of the second type (by projections). Connection of surface integrals of I and II types . The Ostrohradsky formula . Basic Concepts of Field Theory .