Diferensial tənliklərSyllabus

Subject code

İF-40168y

Credits

6

Student workload

180

Semester

Autumn semester

Academic year

2025-2026

Subject type

Mandatory

Form of education

Full-time

Language of instruction

Azerbaijani

In-class hours

a) 30 saat - mühazirə b) 30 saat - seminar

Out-of-class hours

a) 72 saat - sərbəst iş b) 48 saat - hazırlıq

The subject "differential equations" covers the theoretical foundations of differential equations with ordinary and special derivatives, their solution methods and their application in mathematical modeling of various natural, engineering and technical processes. within the scope of the subject, the basics of first and higher order differential equations, systems of differential equations, cauchy and boundary value problems, mathematical physics equations, harmonic functions and the theory of potentials are taught. at the end of the course, students are able to apply the methods of solving differential equations, build mathematical models of various processes and analyze the obtained results and use them to solve practical problems.

• lecture
• seminar
• presentations
• interactive discussion

1. 1

   CLO 1: One-order ordinary differential equations and systems of equations, methods of construction of solutions of n-order ordinary differential equations, existence, uniqueness and stability of solutions of cauchy and boundary problems for these equations must have knowledge.

2. 2

   CLO 2: Must be able to apply ordinary differential equations to mathematical modeling of various processes of natural science.

3. 3

   CLO 3: The classification of differential equations with special derivatives, mathematical physics equations expressing various processes of natural science should be derived.

4. 4

   CLO 4: He should know the formulation of cauchy and boundary value problems for mathematical physics equations, types of boundary conditions and their physical explanation.

5. 5

   CLO 5: He should study the correctness of cauchy and boundary value problems for mathematical physics equations.

6. 6

   CLO 6: Methods of solving cauchy problems for hyperbolic and parabolic type equations, harmonic functions and elements of potential theory should be acquired.

1. 1.
   An overview of ordinary differential equations and some issues related to them. one-order differential equations. concepts of general and special solution of the cauchy problem. custom solution.Lecture

   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.

2. 2.
   Differentiated and separable differential equations. one-order homogeneous equation.Lecture

   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.

3. 3.
   One-order linear differential equations. bernoulli's equation. complete differential equations.Lecture

   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.

4. 4.
   One-order linear differential equations. bernoulli's equation. complete differential equationsLecture

   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.

5. 5.
   High order linear differential equations. linear homogeneous and non-linear differential equations. the concept of linear dependence of a system of functions.Lecture

   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.

6. 6.
   Finding a particular solution of a two-order linear inhomogeneous differential equation by the method of variation of arbitrary constants. finding the general solution of a two-order linear homogeneous differential equation with constant coefficients. determining the special solution of a two-order linear inhomogeneous differential equation with constant coefficients by sampling method.Lecture

   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.

7. 7.
   A system of ordinary differential equations. system solution. a system of ordinary differential equations. system solution. existence and uniqueness of a solution to the cauchy problem. general and specific solution concepts.Lecture

   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.

8. 8.
   Bringing a system of ordinary differential equations to a higher order differential equation and vice versa, a higher order differential equation to a system of ordinary differential equations. interpretation of the system of ordinary differential equations.Lecture

   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.

9. 9.
   A system of linear differential equations. matrix representation of a system of linear differential equations. solving a system of linear differential equations with constant coefficients.Lecture

   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.

10. 10.
    Problems of stability and correctness of the system of differential equations.Lecture

    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.

11. 11.
    Elliptic, parabolic and hyperbolic type equations. sim's dance equation. initial and boundary conditionsLecture

    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.

12. 12.
    An overview of special differential equations. types of two-order differential equations.Lecture

    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.

13. 13.
    Solving the cauchy problem for the oscillation equation of an infinite string by the dalamber method. solving the mixed problem for the oscillation equation of a string by the fourier method.Lecture

    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.

14. 14.
    Equations of parabolic type. heat conduction equation. heat distribution in a finite rod. equations of elliptic type. poisson's equation. laplace's equation. solving the drixle problem for a circle.Lecture

    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.

1. G.n. aliyeva, "ordinary differential equations and series", azerbaijan-2017(opens in a new tab)
2. G.n. aliyeva, "ordinary differential equations and series", azerbaijan-2017(opens in a new tab)
3. William e. boyce, richard c. diprima, douglas b. meade, "elementary differential equations", usa-2021(opens in a new tab)