Diferensial tənliklərTopics

In the subject, the general understanding, formulation and use of ordinary differential equations in applied problems are studied. basic forms of one-order differential equations, concepts of general and special solutions are explained. also, the formulation of the cauchy problem and the determination of the specific solution are investigated.

In the subject, the general form and solution methods of one-order differential equations separated and separated into their variables are studied. integrating an equation by separation of variables and finding a general solution are explained. also, the solution of one-order homogeneous differential equations by appropriate substitution is investigated.

The general form and solution methods of one-order linear differential equations are studied in the subject. the transformation of bernoulli's equation into a linear equation by suitable substitution is explained. the determination and solution of complete differential equations by integration are also investigated.

In the subject, the structure of one-order linear differential equations and the main methods used in their solution are studied. the transformation of bernoulli's equation into a linear differential equation by special substitution is explained. also, the recognition of complete differential equations, checking the completeness condition and finding the general solution are investigated.

In the subject, the general structure and main properties of high order linear differential equations are studied. the differences between linear homogeneous and linear non-homogeneous differential equations and the principles of constructing their solutions are explained. also, concepts of linear dependence and linear independence of a system of functions are investigated in connection with the solution of differential equations.

In the subject, finding the special solution of a two-order linear inhomogeneous differential equation by the method of variation of arbitrary constants is studied. the construction of the general solution of linear homogeneous differential equations with constant coefficients through the characteristic equation is explained. also, the determination of the particular solution for linear inhomogeneous equations with constant coefficients by the sampling method according to the form of the right-hand side is investigated.

In the subject, the system of ordinary differential equations, its solution and the general structure of the system of ordinary differential equations are studied. the methods of finding the solution of the system, general and special solution concepts are explained. also, the conditions for the formulation of the cauchy problem, existence and uniqueness of the solution are investigated.

In the subject, the rules of transformation of the system of normal differential equations into a differential equation of higher order are studied. it is explained how to write a high-order differential equation in the form of a system of normal differential equations by introducing new variables. geometrical and applied interpretation of normal systems is also investigated.

In the subject, the general structure of the system of linear differential equations and the concept of solution are studied. the writing of the system in the form of a matrix and the application of matrix methods are explained. also, the solution of the system of linear differential equations with constant coefficients by means of characteristic roots and eigenvectors is investigated.

In the subject, the stability of the solution of the system of differential equations and its dependence on the initial conditions are studied. the concepts of stable and unstable solutions and their role in the analysis of system behavior are explained. also, the correct formulation of the problem, the existence of the solution, its uniqueness and continuous dependence on the data are investigated.

The main features of elliptic, parabolic and hyperbolic types of special differential equations are studied in the subject. the equation of motion of a string is explained as an example of an equation of hyperbolic type, and its physical meaning is explored. also, the role of initial and boundary conditions in establishing the solution of the problem is considered.

In the subject, the main concepts of differential equations with special derivatives, their difference from ordinary differential equations and fields of application are studied. the general form and main properties of two-order special differential equations are explained. the rules for dividing these equations into elliptic, parabolic and hyperbolic types are also investigated.

In the subject, the formulation of the cauchy problem for the oscillation equation of an infinite string and its solution with the dalamber formula are studied. the formulation of the mixed problem including initial and boundary conditions for a finite string is explained. also, finding the solution of the oscillation equation of the string in the form of a series by means of the fourier method is investigated.

Parabolic type equations and their main example, the heat transfer equation, are studied in the subject. the issue of heat distribution in a finite rod is explained on the basis of initial and boundary conditions. elliptic-type equations, poisson and laplace equations, methods of solving the drixle problem for a circle are also investigated.