As a result of studying the discipline, students should know:
? basic concepts and definitions of mathematical modeling, methods and algorithms;
? basic mathematical models of technical objects;
? basic methods for analyzing mathematical models.
As a result of discipline, students must be able to:
? use well-known mathematical models for modeling technical objects

Mathematical analysis
Linear algebra and geometry
Algorithms and data structures
Empirical methods of software engineering
System analysis

Introduction. Components of MZ - mathematical model, mathematical method and algorithm. General concepts. Software system (PS), definitions and basic characteristics. Examples of components of MF PS. Basic requirements for mathematical models. Features of the construction of mathematical models. Methods of obtaining mathematical models, their advantages and disadvantages. Classification of mathematical models. Hierarchy of mathematical models. The concept of the model of micro, macro and meta-level. Examples Elements of the theory of errors. Errors in calculations, algorithms, methods, mathematical models. Examples of elements of the theory of errors Fundamentals of mathematical modeling of technical objects. Elements of the theory of differential equations. Classification of differential equations in partial derivatives. Ordinary differential equations. The order of ZDR. Examples of the use of VDD in simulation tasks. The notion of a general and partial solution of the GDD. Cauchy conditions. Writing control work "Elements of the theory of differential equations" Differential equations in partial derivatives. Elliptic, hyperbolic, parabolic equation. Initial conditions. Boundary conditions. The critical tasks in the design of technical objects. Examples of DRs in partial derivatives. General concepts of mathematical method. Numerical and analytical methods. Advantages and disadvantages. Elements of the general theory of approximate methods. Correctness. Stability. Convergence. Examples of boundary-value problems in modeling problems. An overview of methods for solving marginal-boundary problems. Analytical, networking methods: advantages, disadvantages, conditions of applicability .. The concept of the problems of analysis, synthesis, optimization. General statement of tasks and examples of their solution. Algorithms. Algorithmic solvability. General empirical properties of algorithms. Alphabet Operators and Algorithms. Associative calculus. Elements of the theory of algorithms. Universal algorithmic systems. Examples of universal algorithmic systems: Turing machines. Examples of universal algorithmic systems: normal Markov algorithms. Thesis Church. Concepts of problems that do not have an algorithmic solution.

Literature to the theoretical course
1. Samarsky AA, Mikhailov AP Mathematical Modeling: Ideas. Methods. Examples - 2 ed., Corr. - M.: FIZMATLIT, 2005. - 320 p.
2. Gary M., Johnson D. Computing Machines and Challenged Tasks. - M.: World, 1982. - 439 pp.
3. Samarsky AA, Gulin A.V. Numerical methods of mathematical physics. - M.: Scientific World, 2003. - 316 p.
4 .. Introduction to Mathematical Modeling / Ed. P.V. Trusova - M.: Logos, 2005 - 440s.
5. Lavrenyuk S.P. Course of differential equations. - Lviv: View. NTL, 1997. - 115s.
6. Rudavsky Yu. K., Kostrobii P. P., Sukhorolsky MA, Tatsiy R. M. Equations of Mathematical Physics. Generalized solutions of boundary problems: teach. manual for studio tech special higher shut up Education / National University Lviv Polytechnic University. - L.: Vt. Nats. Lviv Polytechnic University, 2002.-236 pp.
7. Molchanov I.N., Nikolaenko L.D. Fundamentals of the finite element method. - Kyiv: Naukova Dumka, 1989. - 272 pp.
8. J. Hopcroft, R. Motwani, J. Ulman. Introduction to the theory of automata, languages ??and calculations - M.: Williams, 2002. - 528 p.
9. T. Corman, C. Leysson, R. Revelt, K. Stein. Algorithms: construction and analysis - 2nd ed. - M.: Williams, 2006. - P. 1296.
Literature for laboratory classes
1. Plis AI, Slivina N.A. Mathcad 2000. Mathematical Workshop. - M.: Izd.: Finances and Statistics., 2003. - 656 p.
2. Samarsky AA Introduction to numerical methods: study. allowance for high schools. - 2nd ed., Pererab. and add - M.: Publishing house "Science". Gl Ed. phys.-mate Lit., 1987. - 288 p.
Literature for practical classes
1. Prosvetov GI Linear algebra and analytic geometry: Problems and solutions: educational practice. allowance - 2nd ed., Additional. - M.: Publishing house "Alfa-Press", 2009. - 208 p.
2. Zorich M.A. Mathematical analysis. - M.: Phase; Science; Ch. I. - 1997. - 568 p.
3. Polovko AM, Ganichev IV MathCAD for the student. - St. Petersburg : Publishing house BHV-Petersburg, 2006. - 336 p.

Laboratory classes
25
Practical training
(solving tasks)
10
Abstract
(ind.
task)
5
Com current work
(lecturer employment
10
Total points
(PC)
50
Control measure (KZ)
50
Semester Assessment (PC + CP)
100