I am alone, but still I am. I cannot do everything, but I can still do something. And I won't refuse to do what little I can (c)

Moscow Higher Technical School (MVTU) named after N.E. Bauman State Technical University (MSTU named after N.E.Bauman) in the country.
One of the most important features of technical universities is the fundamental training of future engineers on the basis of an in-depth and extended cycle of mathematical, natural science and general engineering disciplines. This requires modern educational and methodological support, widely using advanced information technologies. In order to create such a provision, the scientific and pedagogical schools of the university and the publishing house of the Moscow State Technical University named after N.E. Bauman is preparing a series of textbooks in mathematics, mechanics, physics, computer science, electronics and other disciplines.
The series "Mathematics at the Technical University" contains 21 issues.
A large team of teachers from the departments of Applied Mathematics and Mathematical Modeling of the Moscow State Technical University named after N.E. Bauman. It consisted of both professional mathematicians - graduates of mathematics departments of universities, and university graduates who widely use mathematics in their scientific and teaching work. This combination of authors and editors of the series created the prerequisites for combining a rigorous and evidence-based presentation of the material with the applied orientation of numerous examples and problems considered in textbooks, which ensures close interdisciplinary connections of the course of higher mathematics with natural science and general engineering disciplines.
The structure of the textbooks provides for the possibility of several levels of study of this course, depending on the specific engineering specialty of the student and the requirements for the depth of his mathematical training.

BOOKS SERIES "MATHEMATICS IN TECHNICAL UNIVERSITY"

I. Introduction to Analysis

V.D. Morozova Introduction to Analysis: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 1996.-408 p. (Ser. Mathematics at the Technical University; Issue I). The book is the first issue of the educational complex "Mathematics at a Technical University", consisting of twenty-one issues. It acquaints the reader with the concepts of function, limit, continuity, which are fundamental in mathematical analysis and necessary at the initial stage of training a student of a technical university. It reflects the close connection of classical mathematical analysis with sections of modern mathematics (first of all, with the theory of sets of continuous mappings in metric spaces). For students of technical universities. May be useful for teachers and graduate students. Download (5.35 Mb)

II. Differential calculus of functions of one variable

Ivanova E.E. Differential calculus of functions of one variable: Textbook. for universities / Ed. V.S. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 1998, 408 p. (Ser. Mathematics at the Technical University; Issue II). The book is the second issue of a set of textbooks "Mathematics at a Technical University". It acquaints the reader with the concepts of derivative and differential, with their use in the study of functions of one variable. Much attention is paid to geometric applications of differential calculus and its application to solving nonlinear equations, interpolation and numerical differentiation of functions Examples and tasks of physical, mechanical and technical content are given. The content of the textbook corresponds to the course of lectures, which the author reads at the M. N.E. Bauman. For students of technical universities. May be useful to teachers and graduate students. Download (4.7 Mb)

III. Analytic geometry

IV. Linear algebra

V. Differential calculus of functions of several variables

A.N. Kanatnikov, A.P. Krishchenko, V.N. Chetverikov. Differential calculus of functions of several variables: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2000 .-- 456 p. (Ser. Mathematics at the Technical University; Issue V). In the fifth issue, the fundamental concepts of the limit and continuity of functions of many variables, the properties of differentiable functions, the issues of finding the absolute and conditional extrema of functions of many variables are considered in detail. The connection between the differential calculus of functions of several variables and differential geometry is reflected. Methods for solving systems of nonlinear equations are considered. The theoretical material is presented using the methods of linear and matrix algebra and illustrated by a series of examples and problems. At the end of each chapter there are questions and tasks to solve on your own. Download (7.43 Mb, the quality is not very good)

Vi. Integral calculus of functions of one variable

Zarubin B.C., Ivanova E.E., Kuvyrkin G.N. Integral calculus of functions of one variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house MSTU them. N.E. Bauman, 1999 .-- 528 p. (Ser. Mathematics at the Technical University; Issue VI). The book is the sixth issue of a set of textbooks "Mathematics at a Technical University". Introduces the reader to the concepts of indefinite and definite integrals and methods of calculating them. Attention is paid to applications of a definite integral, examples and problems of physical, mechanical and technical content are given. For students of technical universities. May be useful for teachers and graduate students. Download (6.01 Mb)

Vii. Multiple and curvilinear integrals. Elements of field theory

Gavrilov V.R., Ivanova B.B., Morozova V.D. Multiple and curvilinear integrals. Elements of field theory: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 2nd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2003.-496 p. (Ser. Mathematics at the Technical University; Issue VII). The book is the seventh issue of a set of textbooks "Mathematics at a Technical University". It acquaints the reader with multiple, curvilinear and surface integrals and methods for their calculation. It focuses on applications of these types of integrals, provides examples of physical, mechanical and technical content. In the final chapters the elements of field theory and vector analysis are outlined. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers, graduate students and engineers. (Many thanks for the links to this book. Imper) Download (7.4 MB)

VIII. Differential Equations

S.A. Agafonov, A.D. German, T.V. Muratova Differential Equations. - MSTU im. N.E. Bauman, 2004.-348 p. - (Mathematics at the Technical University) The foundations of the theory of ordinary differential equations (ODEs) are presented and the basic concepts of first-order partial differential equations are given. Numerous examples from mechanics and physics are given. A separate chapter is devoted to second-order linear ODEs, to which many applied problems lead. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E.Bauman. For students of technical universities and universities. It can be useful for those interested in applied problems of the theory of differential equations. Download

IX. Ranks

Vlasova E.A. Series: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Corrected. - M .: Publishing house of MSTU im. N.E. Bauman, 2006 .-- 616 p. (Ser. Mathematics at the Technical University; Issue IX). ISBN 5-7038-2884-8 The book introduces the reader to the basic concepts of the theory of numerical and functional series. The book presents power series, Taylor series, trigonometric Fourier series and their applications, as well as Fourier integrals. The theory of series in Banach and Hilbert spaces is presented, and in the volume necessary for its study, questions of functional analysis, measure theory and the Lebesgue integral are considered. The theoretical material is accompanied by detailed examples, figures and a large number of tasks of various levels of complexity. For students of technical universities. The textbook can be useful for teachers and graduate students. Download (djvu in the archive, 5.98 Mb, 600dpi + OCR)

X. Theory of functions of a complex variable

V.D. Morozova The theory of functions of a complex variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Corrected. - M .: Publishing house of MSTU im. N.E. Bauman, 2009 .-- 520 p. (Ser. Mathematics at the Technical University; Issue X.) ISBN 978-5-7038-3189-2 The book is devoted to the theory of functions of one complex variable. It pays attention to issues related to conformal mappings, as well as the application of the theory to the solution of applied problems. Examples and problems from physics, mechanics and various branches of technology are given. For students of technical universities. It can be useful for teachers, graduate students and engineers. Download (djvu in the archive, 4.85 Mb, 600dpi + OCR)

XI. Integral transformations and operational calculus

Volkov I.K., Kanatnikov A.N. Integral transformations and operational calculus: Textbook. for universities. 2nd ed. - M .: Publishing house of MSTU im. N.E. Bauman, 2002.228 p. (Ser. Mathematics at the Technical University; Issue XI). The elements of the theory of integral transformations are stated. The main classes of integral transformations, which play an important role in solving problems of mathematical physics, electrical engineering, and radio engineering, are considered. The theoretical material is illustrated by a large number of examples. A separate section is devoted to operational calculus, which is of great practical importance. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman. For students of technical universities and universities, graduate students and researchers who use analytical methods in the study of mathematical models. Download (6.75 Mb) NEW - Volume XI, a little combed by the Guest (3.28 Mb)

XII. Differential equations of mathematical physicistsand

Martinson L.K., Malov Yu.I. Differential equations of mathematical physics: Textbook. for universities. 2nd ed. / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2002 .-- 368 p. (Ser. Mathematics at the Technical University; Issue XII). Various formulations of problems in mathematical physics for partial differential equations and the main analytical methods for their solution are considered, the properties of the solutions obtained are analyzed. A large number of linear and nonlinear problems are presented, the solution of which leads to the study of mathematical models of various processes in physics, chemistry, biology, ecology, etc. The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers, graduate students and engineers. Download (2.5 Mb)

XIII. Approximate Methods of Mathematical Physics

Vlasova E.A., Zarubin B.C., Kuvyrkin G.N. Approximate methods of mathematical physics: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2001.-700 p. (Ser. Mathematics at the Technical University; Issue XIII). The book is the thirteenth issue of the series of textbooks "Mathematics at a Technical University." Mathematical models of physical processes, elements of applied functional analysis and approximate analytical methods for solving problems of mathematical physics, as well as numerical methods of finite differences, finite and Examples of the use of these methods in applied problems are considered.The content of the textbook corresponds to the courses of lectures that the authors give at the Bauman Moscow State Technical University For students of technical universities It may be useful for teachers, graduate students and engineers. Download (4.9 Mb)

XIV. Optimization methods

A.V. Attetkov, SV. Galkin, B.C. Zarubin. Optimization methods: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 2nd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2003. -440 p. (Ser. Mathematics at the Technical University; Issue XIV). The book is devoted to one of the most important areas of training for a graduate of a technical university - the mathematical theory of optimization. The theoretical, computational and applied aspects of finite-dimensional optimization methods are considered. Much attention is paid to the description of algorithms for the numerical solution of problems of unconditional minimization of functions of one and several variables, methods of conditional optimization are presented. Examples of solving specific problems are given, a visual interpretation of the results obtained is given, which will contribute to the development of students' practical skills in applying optimization methods. The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers, graduate students and engineers. Download (2.1 Mb)

XV. Calculus of variations and optimal control

Vanko V.I., Ermoshina O.V., Kuvyrkin G.N. Calculus of variations and optimal control: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Corrected. - M .: Publishing house of MSTU im. N.E. Bauman, 2006. -488 p. (Ser. Mathematics at the Technical University; Issue XV). Along with the presentation of the foundations of the classical calculus of variations and elements of the theory of optimal control, direct methods of the calculus of variations and methods of transformation of variational problems, leading, in particular, to dual variational principles, are considered. The textbook is completed with examples from physics, mechanics and engineering, which show the effectiveness of the calculus of variations and optimal control methods for solving applied problems. The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For undergraduate and graduate students of technical universities, as well as for engineers and researchers specializing in applied mathematics and mathematical modeling. Download (1.8 Mb)

XVI. Probability theory

Probability theory: Textbook. for universities. - 3rd ed., Rev. / A.V. Pechinkin, O. I. Teskin, G.M. Tsvetkova and others; Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E.Bauman, 2004.-456 p. (Ser. Mathematics at the Technical University; Issue XVI). A distinctive feature of this book is a balanced combination of mathematical rigor in the presentation of the foundations of the theory of probability with the applied focus of problems and examples illustrating theoretical provisions. Each chapter of the book is completed by a set of a large number of check questions, typical examples and tasks for independent solution. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman. Download (2.87 Mb)

XVII. Math statistics

Mathematical statistics: Textbook. for universities / VB Goryainov, IV Pavlov, GM Tsvetkova, OI Teskin; Ed. B.C. Zarubina, A.P. Krishchenko. - M .: IED-vo MGTU im. N.E. Bauman, 2001.424 p. (Ser. Mathematics at the Technical University; Issue XVII). This book introduces the reader to the basic concepts of mathematical statistics and some of its applications. Its distinctive feature is a balanced combination of mathematical rigor with applied tasks. Each chapter of the book ends with a large set of sample examples, checklists, and self-help tasks. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman for students of technical universities. It can be useful for teachers, graduate students and engineers. (Many thanks to M128K145 for the link to the book) Download (4.2 Mb)

XVIII. Random processes

Volkov I.K., Zuev SM., Tsvetkova G.M. Random processes: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 1999.-448 p. (Ser. Mathematics at the Technical University; Issue XVIII). The book is the eighteenth edition of the educational complex "Mathematics at a Technical University" and introduces the reader to the basic concepts of the theory of random processes and some of its many applications. According to the authors, this textbook should be a link between rigorous mathematical research, on the one hand, and practical problems - on the other hand, it should help the reader to master the applied methods of the theory of random processes. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers and graduate students. Download (2.87 Mb)

XIX. Discrete Math

Belousov A.I., Tkachev SB. Discrete mathematics: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2004.-744 p. (Ser. Mathematics at the Technical University; Issue XIX). The nineteenth issue of the series "Mathematics at a Technical University" presents the theory of sets and relations, elements of modern abstract algebra, graph theory, classical concepts of the theory of Boolean functions, as well as the foundations of the theory of formal languages, which includes theories of finite automata, regular languages, context-free languages In the analysis of graphs and automata, special attention is paid to algebraic methods. The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers, graduate students and engineers. Download (5.8 Mb)

XX. Operations research

Volkov I.K., Zagoruiko E.A. Operations Research: Textbook for Universities / Ed. V.S. Zarubina, A.P. Krishchenko. - M .: IED-vo MGGU im. N.E. Bauman. 2000 - 436 p (Ser Mathematics at the Technical University. Issue XX). Operations research accumulates those mathematical methods that are used to make informed decisions in various areas of human activity. In the educational literature, this discipline has not yet found its full reflection, although it is necessary for a modern engineer to master its methods. The book focuses on the formulation of operations research tasks, methods for their solution and criteria for choosing alternatives. Methods of linear and integer programming, optimization on networks, Markov decision-making models, elements of game theory and simulation are considered. A significant number of examples will help in studying the material. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman for students of technical universities. It can be useful for teachers, graduate students and engineers. Download (2Mb)

XXI. Mathematical modeling in engineering

Zarubin B.C. Mathematical modeling in technology: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 2nd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2003.-496 p. (Ser. Mathematics at the Technical University; Issue XXI, final). The book is an additional, twenty-first issue of the set of textbooks "Mathematics at a Technical University", completing the edition of the series. It is devoted to the application of mathematics to solving applied problems arising in various fields of technology. It includes a subject index to the entire complex of textbooks. The content of the textbook corresponds to the course " Fundamentals of Mathematical Modeling ", read by the author at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers, graduate students and engineers. Download (4, 3 Mb)

NEW Panov V.F. Ancient and Young Mathematics / Ed. B.C. Zarubin. - 2nd ed., Rev. - M .: Publishing house of MSTU im. N.E.Bauman, 2006 .-- 648 s: ill. ISBN 5-7038-2890-2 The book is an addition to the set of textbooks of the series "Mathematics at a Technical University" and introduces the reader to the main fragments of the history of the formation of modern mathematics. It is based on lectures on the courses "Introduction to the specialty" and "History of mathematics", read by the author to students of the Moscow State Technical University named after NE Bauman, studying in the specialty "Applied Mathematics". The first part of the book focuses on the biographies of the creators of mathematics and those thinkers whose ideas had a decisive influence on the development of this science. The second part presents the history of some basic mathematical concepts and ideas. For students of technical universities and mathematics teachers, as well as anyone interested in the history of science Download (djvu / rar, 4.69 Mb)

All books in one archive (thanks

Multiple and curvilinear integrals. Elements of field theory. Gavrilov V.R., Ivanova E.E., Morozova V.D.

2nd ed., Erased. - M .: Publishing house of MSTU im. N.E. Bauman, 2003.- 496 p. (Ser. Mathematics at the Technical University. Issue VII).

The book is the seventh issue of the set of textbooks "Mathematics at the Technical University". It acquaints the reader with multiple, curvilinear and surface integrals and methods for calculating them. It focuses on the applications of these types of integrals, provides examples of physical, mechanical and technical content. The final chapters outline elements of field theory and vector analysis.

For students of technical universities. It can be useful for teachers, graduate students and engineers.

Format: djvu

The size: 7, 4 Mb

Download: yandex.disk

TABLE OF CONTENTS
Foreword 5
Basic symbols 11
1. Double integrals 15
1.1. Problems leading to the concept of a double integral 15
1.2. Definition of a double integral 17
1.3. Conditions for the existence of a double integral 24
1.4. Classes of integrable functions 27
1.5. Double Integral Properties 29
1.6. Mean value theorems for double integrals 36
1.7. Computing the double integral 40
1.8. Curvilinear coordinates on plane 62
1.9. Change of variables in a double integral 65
1.10. Surface area 79
1.11. Improper Double Integrals 84
Questions and tasks 93
2. Triple integrals 97
2.1. The problem of calculating body weight 97
2.2. Definition of a triple integral 98
2.3. Properties of the triple integral 102
2.4. Computing the triple integral 105
2.5. Change of variables in the triple integral 113
2.6. Cylindrical and spherical coordinates 118
2.7. Applications of double and triple integrals 128
Questions and Tasks 149
3. Multiple Integrals 153
3.1. Jordan Measure 153
3.2. Integral over a measurable set 164
3.3. Darboux sums and criteria for the integrability of a function 168
3.4. Properties of integrable functions and multiple integrals 179
3.5. Reduction of a multiple integral to a repeated one 183
3.6. Change of variables in multiple integrals 190
3.7. Multiple Improper Integrals 201
Questions and tasks 205
4. Numerical Integration 208
4.1. Using One-Dimensional Quadrature Formulas 208
4.2. Cubature Formulas 219
4.3. Multidimensional Cubature Formulas 231
4.4. Statistical Test Method 237
4.5. Computing Multiple Integrals by the Monte Carlo Method 247
Questions and tasks 253
5. Curvilinear Integrals 254
5.1. Curvilinear integral of the first kind 254
5.2. Calculation of a curvilinear integral of the first kind 257
5.3. Mechanical applications of the curvilinear integral of the first kind 265
5.4. Curvilinear integral of the second kind 274
5.5. Existence and calculation of a curvilinear integral of the second kind 279
5.6. Properties of a curvilinear integral of the second kind. 285
5.7. Green's Formula 288
5.8. Conditions for the independence of the curvilinear integral from the path of integration 296
5.9. Calculating the Curvilinear Integral of the Total Differential 306
E.5.1. Curvilinear integral in a multiply connected region 310
Questions and Tasks 314
6. Surface Integrals 319
6.1. About defining a surface in space 319
6.2. One-sided and two-sided surfaces 323
6.3. Surface area 327
6.4. Surface integral of the first kind 334
6.5. Applications of the surface integral of the first kind 341
6.6. Surface integral of the second kind 347
6.7. The physical meaning of a surface integral of the second kind 353
6.8. Stokes Formula 356
6.9. Conditions for the independence of a curvilinear integral of the second kind from the path of integration in space. 362
6.10. Formula Ostrogradsky - Gauss 364
Questions and tasks 371
7. Elements of field theory 375
7.1. Scalar field 375
7.2. Scalar field gradient 380
7.3. Vector field 383
7.4. Vector lines 390
7.5. Vector Field Flow and Divergence 397
7.6. Vector field circulation and rotor 407
7.7. The Simplest Types of Vector Fields 417
E.7.1. Vortex-free field in a multiply connected region 424
D.7.2. Vector potential of the solenoidal field 430
Questions and Tasks 435
8. Fundamentals of Vector Analysis 438
8.1. Hamilton Operator 438
8.2. Properties of the Hamilton Operator 444
8.3. Differential operations of the second order 448
8.4. Integral formulas 452
8.5. Inverse field theory problem 463
D.8.1. Differential Operations in Orthogonal Curvilinear Coordinates 465
Questions and Tasks 479
Recommended reading list 481
Index 484

Field theory and series

3rd semester 2013-14, spec. RL, OE, RT (specialists)

MODULE 1. Series Theory

Types of classroom activities and independent work	weeks	Labor intensity,clock	Note
Workshops
Homework current
House. task "Rows"
Linear control modulo

MODULE 2. Field theory

Types of classroom activities and independent work	The timing or implementation, weeks	Labor intensity,clock	Note
Workshops
Homework current
House. task "Multiple and curvilinear integrals"
Linear control modulo

MODULE 3. TFKP

Types of classroom activities and independent work	The timing or implementation, weeks	Labor intensity,clock	Note
Workshops
Homework current
House. task "TFKP"
Linear control modulo

Lectures

MODULE 1. Series Theory

Lecture 1. Number series and its convergence. Sufficient criteria for the convergence of positive numerical series.

OL-2 1-1.7; OL-4 Ch.16 §1-6.

Lecture2 . Alternating numerical series. Absolute and conditional convergence. Alternating numeric series. Leibniz's sign.

OL-2 1.8-1.9; OL-3 Ch.16 §7-8.

Lecture 3. Functional rows. Uniform convergence. Power series. Abel's theorem.

OL-2 2.1-2.5; OL-4 ch.16 §9-13.

Lecture4 . Basic properties of power series. Taylor series. Power series applications.

OL-2 2.5–2.8; OL-4 ch.16 §14-17.

Lecture5 . Orthogonality of the system of functions. Generalized Fourier series.

OL-2 3.1–3.3; DL-1 ch.5 §14.8.

Lecture6 . Expansion of functions in trigonometric Fourier series on a segment. Dirichlet conditions for the expansion of functions in a Fourier series. Connection of the order of smallness of the Euler - Fourier coefficients with the differentiability of a periodic function.

OL-2 3.6–3.9; OL-4 chap. 17 § 1-5.

Lectures 7– 8. Derivation of the Fourier integral by a formal transition from the trigonometric series at. The complex form of writing the Fourier integral. Integral Fourier transform and its main properties. Dirac delta function. Fourier integral of the Dirac delta function.

MODULE 2. Field theory

Lecture9 . Double integral. Double integral properties. Change of variables in a double integral.

OL-1 1.1-1.7, 1.9; OL-4 Ch. 14 § 1–3, 6.

Lecture10 ... Triple integral. Properties of the triple integral.

OL-1 2.1-2.4; OL-4 chap. 14 § 11, 12.

Lecture11 . Curvilinear integral of the second kind. Curvilinear integral properties.

OL-1 5.4-5.6; OL-4 Ch. 3 § 1–2.

Lecture12 . Green's formula. The condition for the independence of the curvilinear integral from the path of integration in a simply connected domain.

OL-1 5.7–5.8; OL-4 Ch.15 § 3-4.

Lecture13 . Calculation of the curvilinear integral of the total differential. Integral over the surface. Surface integral properties.

OL-1 5.9, 6.1–6.4; OL-4 Chapter 15 § 4.

Lecture14 . Surface integral of the second kind. Scalar field, vector field. Ostrogradsky - Gauss formula. Divergence.

OL-1 6.6-6.10, 7.1-7.5; OL-4 ch. 15 § 5,6,8.

Lecture15 . Stokes formula. Vortex (rotor) of a vector field and its properties. Potential vector field, Laplace field.

OL-1 6.8, 7.3–7.7; OL-4 ch. 15 § 7.

Lecture16 . Hamilton operator. Vector differential operations of the second order.

OL-1 8.1–8.4; OL-4 Chapter 15 § 9.

Lectures17 . Curvilinear Orthogonal Coordinates (COOC). Lame coefficients. Differential operations in KOOK.

OL-1 D.8.1; DL-1 Ch. 6 §3.

MODULE 3. TFKP

Lecture 18 . Complex function of complex variable. Functional series in S. Basic transcendental functions of a complex variable and their properties. Euler's formulas. The main transcendental functions of a complex variable and their properties. Euler's formulas.

OL-3 3.1 3.3–3.5; OL-5 Ch. 1 §1–2.

Lecture 19 . The limit of a function of a complex variable. Continuity and derivative of a function of a complex variable. Cauchy - Riemann conditions. Analyticity of the function in the area and at the point. Analyticity of the basic elementary functions of a complex variable.

OL-3 3.2, 4.1-4.3, 4.6; OL-5 Ch. 1 §2–3.

Lecture20 . Integral of a continuous function of a complex variable, Cauchy integral formula.

OL-3 5.1–5.5; OL-5 Ch. 1 §4-5.

Lecture21 . Expansion of an analytic function in a Taylor series and a Laurent series.

OL-3 6.1–6.6; OL-5 Ch. 1 §6.

Lecture 22 . Classification of isolated singular points of an analytic function by the form of its Laurent expansion in the vicinity of these points.

OL-3 7.2-7.4; OL-5 Ch. 1 §7.

Lectures 23 –2 4 . Residue of an analytic function at its isolated singular point. Deduction at infinity. Application of deductions.

OL-3 8.1–8.4; OL-5 Ch. 1 §8.

Lecture 25. Reserve.

WORKSHOPS

MODULE 1. Series Theory

Lesson 1. Number series with positive terms.

OL-5 Aud. 2411, 2412, 2413, 2401, 2402, 2407, 2409, 2508, 2416, 2417, 2420, 2422-2424; 2428, 2429, 2431, 2437, 2434, 2440, 2442, 2451, 2454, 2455, 2461, 2465, 2467.

Houses. 2414, 2415, 2403, 2410, 2509, 2418, 2419, 2421, 2425, 2426; 2427, 2430, 2435, 2439, 2441, 2443, 2450, 2454, 2456, 2459, 2462, 2466.

Lesson 2. Numeric alternating series.

OL-5 Aud. 2470, 2472, 2474, 2477, 2479, 2480, 2483.

Houses. 2471, 2473, 2481, 2482, 2484.

Actions above the rows. Mid-term control module 1 (lectures 1–2, lessons 1–9).

OL-5 Aud.: 2484 (a, b), 2495, 9493, 2501, 2504, 2407.

Numbers: 2494, 2496, 2497, 2500, 2505, 2506.

Lesson 3. Power series. Convergence interval.

OL-5 Aud. 2526, 2528, 2530, 2533, 2534, 2540, 2545, 2547, 2549, 2551, 2553, 2554, 2557, 2559, 2560, 2563.

Houses. 2527, 2529, 2531, 2538, 2546, 2548, 2550, 2552, 2556, 2558, 2561, 2563.

Lesson 4. Decomposition of a function into series.

OL-5 Aud .: 2592, 2594, 2596-2598, 2600, 2631, 2633, 2635, 2637, 2601, 2602, 2611, 2615, 2606, 2619, 2617.

Numbers: 2595, 2599, 2632, 2636, 2638, 2607, 2608, 2616, 2618, 2630.

Power series application.

OL-5 Aud .: 2644, 2646, 2648, 2654, 2657.

Numbers: 2642, 2645, 2653.

Lesson 5. Fourier series.

OL-5 Aud. 2671, 2672, 2673, 2681.

Houses. 2675, 2682, 2674.

OL-5 Aud. 2584, 2686, 2698, 2702, 2695.

Houses. 2695, 2696, 2699.

Lesson 6.Boundary control mod 1 ( lectures1 -- 8 , seminars1 – 5 ).

MODULE 2. Field theory

Z activity 7. Arrangement of limits and calculation of double integrals in Cartesian coordinates.

OL-5: Aud .: 2113, 2118, 2121, 2124, 2125, 2131, 2132, 2134, 2137, 2139, 2151.

Numbers: 2115, 2117, 2120, 2123, 2142, 2126, 2130, 2133, 2135, 2136, 2138, 2140, 2142, 2150, 2153, 2138, 2153.

Lesson 8.Calculation of double integrals in polar coordinates. Calculation of the areas of flat figures.

OL-5 Aud .: 2160, 2162, 2166, 2168, 2178, 2181, 2183.

Numbers: 2163, 2161, 2165, 2167, 2171, 2177, 2180.

Lesson 9. Calculation of volumes. Calculation of surface area.

OL-5 Aud .: 2194, 2196, 2198, 2202; 2213, 2215, 2219, 2220, 2231.

Houses: 2195, 2197, 2199, 2200, 2201; 2214, 2216, 2218, 2222.

Lesson 10. Calculation of triple integrals.

OL-5 Aud .: 2240, 2241, 2255, 2257, 2260, 2268

Numbers: 2250, 2253, 2256, 2242, 2262, 2263, 2247, 2264.

Lesson 11. Calculation of curvilinear integrals. Applications of curvilinear integrals.

OL-5 Aud .: 2312, 2323, 2327, 2328, 2332, 2337, 2344.

Numbers: 2313, 2315, 2316, 2324, 2329, 2335, 2338, 2345.

Calculation of the curvilinear integral of the total differential. Finding a function by its total differential.

OL-5 Aud .: 2318 (a, c, d), 2319 (a, c), 2322 (a, c), 2326 (a, c).

Houses: 2318 (a, d), 2319 (b, d), 2322 (b, d), 2326 (b, d).

Lesson 12. Surface integrals. Field theory.

OL-5 Aud .: 2349, 2350, 2357, 2366; 2373, 2375, 2377.

Numbers: 2365, 2351, 2356, 2357; 2372, 2374, 2376, 2380, 2385 (c).

Aud .: 2383, 2384, 2385.

Houses: OL-5 Ch. 7: 2389, 2391, 2386, 2388, 2394, 2398 (1)

Lesson 13. Midway control modulo 2 ( lectures9 –1 7 , seminars 7-12).

MODULE 3. TFKP

Lesson 14. Numerical and power series with complex members. Calculation of the values \u200b\u200bof elementary functions of a complex variable.

OL-5 Aud. 2485, 2487, 2488, 2490, 2492, 2566, 2567, 2570. OL-7: 59, 62, 64.

Houses. 2486, 2489, 2491, 2564, 2555. OL-5: 60, 63, 65.

Calculation of the values \u200b\u200bof elementary functions of a complex variable. Checking the analyticity of functions and finding derivatives. Finding an analytical function by its real or imaginary part.

OL-6 Aud. 66 (a, b, d) 70, 104, 106, 114, 117 (a, b, f), 140, 142, 148.

Houses. 66 (c, e, f) 69, 105, 115, 117 (c, d, e), 141, 145, 147.

Integral Cauchy formula. Expansion of an analytic function in Taylor and Laurent series.

OL-6 Aud. 168, 170, 172, 174, 250, 252, 258.

Houses. 167, 169, 171, 173, 251, 253, 257.

Lesson 15. Expansion of analytic functions in Taylor and Laurent series.

OL-6 Aud. 265, 267, 269, 271, 273, 275.

Houses. 266, 268, 270, 272, 274.

The zeros of the analytic function. Isolated special points and their classification.

OL-6 Aud. 276, 278, 290, 292, 294, 302, 304 306.

Houses. 277, 291, 293, 295, 297, 301, 305, 307.

Isolated singular points and deductions therein. Application of residues to the calculation of contour integrals.

OL -6 Aud. 316, 318, 322, 324, 328, 338, 348, 350, 352.

Houses. 319, 321, 323, 325, 327, 339, 347, 351, 353.

Lesson 16. Midway control mod 3 ( lectures 18-24, seminars 14-15).

Lesson 17. Reserve.

Control activities

MODULE 1. Series Theory

1. Homework "Rows" (7th week) .

2.Rubezhny control by module (7th week).

MODULE 2. Field theory

3. Homework "Multiple and Curvilinear Integrals" (13th week).

4.Rubezhny control by module (13th week).

MODULE 3. TFKP

5. Homework "TFKP" (16th week).

6.Rubezhny control by module (16th week).

Literature

Basic literature (OL)

1. Gavrilov V.R., Ivanova E.E. Morozova V.D. Multiple and curvilinear integrals. Elements of field theory. - M .: Publishing house of MSTU im. N.E. Bauman, 2001 .-- 492 p.

2. Vlasova E.A. Rows. - M .: Publishing house of MSTU im. N.E. Bauman, 2000 .-- 612 p.

3. Morozova V.D. The theory of functions of a complex variable. - M .: Publishing house of MSTU im. N.E. Bauman, 2000 .-- 520 p.

4. Piskunov NS Differential and integral calculus for technical colleges. vol. 2. - M .: Nauka, 1985 .-- 560 p.

5. Tasks and exercises in mathematical analysis for technical colleges. Ed. B.P. Demidovich. - M.: Science, 1970. - 472 p.

6. Krasnov M.L., Kiselev L.I., Makarenko G.I. Complex variable functions. Operational calculus. Stability theory. Tasks and exercises. - M .: Nauka, 1981 .-- 215 p.

Further reading (DL)

1. Ilyin V.A., Poznyak E.G. Fundamentals of Mathematical Analysis: Part 2. - M .: Nauka, 1980.- 448 p.

4. Kudryavtsev L. D. The course of mathematical analysis. - M .: Higher school, 1981. - 584p.

3. Sveshnikov A.G., Tikhonov A.M. The theory of functions of a complex variable. - Moscow: Nauka, 1967 .-- 304 p.

Teaching aids (MP)

7. Serzhantova M.M., Loginova L.A., Poznyakova L.V. Field theory: Textbook \\ Ed. Sergeant M.M. - M .: Publishing house of MSTU, 1992. - 58 p., Ill.

1. Vanko V.I., Galkin S.V., Morozova V.D. Methodical instructions for independent work of students in the sections "Theory of functions of a complex variable" and "Operational calculus", MVTU, 1988. - 28 p.

2. Shostak R.Ya., Kogan S.M., Kheresko T.A. Methodological guide for homework on TFKP, MVTU, 1976. - 41 p.

3. Golenko K.A., Kheresko T.A., Shchetinina N.N. Methodical instructions for preparation for tests on the course of higher mathematics, MVTU, 1986. - 36 p.

Book series

Recommended by the Ministry of General and Vocational EducationOf the Russian Federation as a textbook for students of higher technical educational institutions

Moscow
Publishing house MSTU im. N.E.Bauman

1. V.D. Morozova Introduction to Analysis: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 1996.-408 p. (Ser. Mathematics at the Technical University; Issue I).
   The book is the first issue of the educational complex "Mathematics at a Technical University", consisting of twenty-one issues. It acquaints the reader with the concepts of function, limit, continuity, which are fundamental in mathematical analysis and necessary at the initial stage of training a student of a technical university. It reflects the close connection of classical mathematical analysis with sections of modern mathematics (first of all, with the theory of sets of continuous mappings in metric spaces).
   For students of technical universities. It can be useful for teachers and graduate students.
   Download
2. Ivanova E.E. Differential calculus of functions of one variable: Textbook. for universities / Ed. V.S. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 1998, 408 p. (Ser. Mathematics at the Technical University; Issue II).
   The book is the second issue of a set of textbooks "Mathematics at a Technical University". It acquaints the reader with the concepts of derivative and differential, with their use in the study of functions of one variable. Much attention is paid to geometric applications of differential calculus and its application to solving nonlinear equations, interpolation and numerical differentiation of functions Examples and tasks of physical, mechanical and technical content are given.
   The content of the textbook corresponds to the course of lectures given by the author at the Moscow State Technical University. N.E. Bauman. For students of technical universities. May be useful to teachers and graduate students.
   Download
3. Kanatnikov A.N., Krishchenko A.P. Analytic geometry. 2nd ed. - M., Publishing house of MSTU im. Bauman, 2000, 388 p. (Ser. Mathematics at the Technical University; Issue III.)
   The book introduces the basic concepts of vector algebra and its applications, the theory of matrices and determinants, systems of linear equations, curves and surfaces of the second order.
   The material is presented to the extent necessary at the initial stage of training a student of a technical university.
   The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E.Bauman.
   Download Edition 2 Edition 3
4. Kanatnikov A.N., Krishchenko A.P. Linear Algebra: Textbook. for universities. 3rd ed., Stereotype. / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2002 .-- 336 p. (Ser. Mathematics at the Technical University; Issue IV).
   Description: The book is the fourth issue of the series "Mathematics at a Technical University" and contains a presentation of the basic course on linear algebra, in addition to the basic concepts of tensor algebra and iterative methods for the numerical solution of systems of linear algebraic equations.
   Download
5. A.N. Kanatnikov, A.P. Krishchenko, V.N. Chetverikov. Differential calculus of functions of several variables: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2000 .-- 456 p. (Ser. Mathematics at the Technical University; Issue V).
   In the fifth issue, the fundamental concepts of the limit and continuity of functions of many variables, the properties of differentiable functions, the issues of finding the absolute and conditional extrema of functions of many variables are considered in detail. The connection between the differential calculus of functions of several variables and differential geometry is reflected. Methods for solving systems of nonlinear equations are considered.
   The theoretical material is presented using the methods of linear and matrix algebra and illustrated by a series of examples and problems. At the end of each chapter there are questions and tasks to solve on your own.
   
   Download
6. Zarubin B.C., Ivanova E.E., Kuvyrkin G.N. Integral calculus of functions of one variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house
   MSTU them. N.E. Bauman, 1999 .-- 528 p. (Ser. Mathematics at the Technical University; Issue VI).
   The book is the sixth issue of a set of textbooks "Mathematics at a Technical University". Introduces the reader to the concepts of indefinite and definite integrals and methods of calculating them. Attention is paid to applications of a definite integral, examples and problems of physical, mechanical and technical content are given.
   The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman.
   For students of technical universities. It can be useful for teachers and graduate students.
   Download
7. Gavrilov V.R., Ivanova B.B., Morozova V.D. Multiple and curvilinear integrals. Elements of field theory: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 2nd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2003.-496 p. (Ser. Mathematics at the Technical University; Issue VII).
   The book is the seventh issue of a set of textbooks "Mathematics at a Technical University". It acquaints the reader with multiple, curvilinear and surface integrals and methods for their calculation. It focuses on applications of these types of integrals, provides examples of physical, mechanical and technical content. In the final chapters the elements of field theory and vector analysis are outlined.
   The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman.
   For students of technical universities. It can be useful for teachers, graduate students and engineers.
   Download
8. S.A. Agafonov, A.D. German, T.V. Muratova Differential Equations. - MSTU im. N.E. Bauman, 2004.-348 p. - (Mathematics at the Technical University)
   The foundations of the theory of ordinary differential equations (ODE) are presented and the basic concepts of first-order partial differential equations are given. Numerous examples from mechanics and physics are given. A separate chapter is devoted to second-order linear ODEs, to which many applied problems lead. The content of the textbook corresponds to the course of lectures given by the authors at the M. N.E.Bauman. For students of technical universities and universities. It can be useful for those interested in applied problems of the theory of differential equations.
   Download
9. Vlasova E.A. Series: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Corrected. - M .: Publishing house of MSTU im. N.E. Bauman, 2006 .-- 616 p. (Ser. Mathematics at the Technical University; Issue IX). ISBN 5-7038-2884-8
   The book introduces the reader to the basic concepts of the theory of numerical and functional series. The book presents power series, Taylor series, trigonometric Fourier series and their applications, as well as Fourier integrals. The theory of series in Banach and Hilbert spaces is presented, and in the volume necessary for its study, questions of functional analysis, measure theory and Lebesgue integral are considered. The theoretical material is accompanied by detailed examples, figures and a large number of tasks of various levels of complexity.
   Download
10. V.D. Morozova The theory of functions of a complex variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Corrected. - M .: Publishing house of MSTU im. N.E. Bauman, 2009 .-- 520 p. (Ser. Mathematics at the Technical University; Issue X.) ISBN 978-5-7038-3189-2
    The book is devoted to the theory of functions of one complex variable. It pays attention to issues related to conformal mappings, as well as the application of the theory to the solution of applied problems. Examples and problems from physics, mechanics and various branches of technology are given.
    For students of technical universities. It can be useful for teachers, graduate students and engineers.
    Download
11. Volkov I.K., Kanatnikov A.N. Integral transformations and operational calculus: Textbook. for universities. 2nd ed. - M .: Publishing house of MSTU im. N.E. Bauman, 2002.228 p. (Ser. Mathematics at the Technical University; Issue XI).
    The elements of the theory of integral transformations are stated. The main classes of integral transformations, which play an important role in solving problems of mathematical physics, electrical engineering, and radio engineering, are considered. The theoretical material is illustrated by a large number of examples. A separate section is devoted to operational calculus, which is of great practical importance.
    The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman.
    For students of technical universities and universities, graduate students and researchers who use analytical methods in the study of mathematical models.
    Download
12. Martinson L.K., Malov Yu.I. Differential equations of mathematical physics: Textbook. for universities. 2nd ed. / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2002 .-- 368 p. (Ser. Mathematics at the Technical University; Issue XII).
    Various formulations of problems in mathematical physics for partial differential equations and the main analytical methods for their solution are considered, the properties of the solutions obtained are analyzed. A large number of linear and nonlinear problems are presented, the solution of which leads to the study of mathematical models of various processes in physics, chemistry, biology, ecology, etc.
    The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman.
    For students of technical universities. It can be useful for teachers, graduate students and engineers.
    Download
13. Vlasova B.A., Zarubin B.C., Kuvyrkin G.N. Approximate methods of mathematical physics: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 2001.-700 p. (Ser. Mathematics at the Technical University; Issue XIII).
    The book is the thirteenth issue of a series of textbooks "Mathematics at a Technical University." Mathematical models of physical processes, elements of applied functional analysis and approximate analytical methods for solving problems of mathematical physics, as well as numerical methods of finite differences, finite and Examples of the use of these methods in applied problems are considered.The content of the textbook corresponds to the courses of lectures that the authors give at the Bauman Moscow State Technical University For students of technical universities It may be useful for teachers, graduate students and engineers.
    Download
14. A.V. Attetkov, SV. Galkin, B.C. Zarubin. Optimization methods: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 2nd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2003. -440 p. (Ser. Mathematics at the Technical University; Issue XIV).
    The book is devoted to one of the most important areas of training for a graduate of a technical university - the mathematical theory of optimization. The theoretical, computational and applied aspects of finite-dimensional optimization methods are considered. Much attention is paid to the description of algorithms for the numerical solution of problems of unconditional minimization of functions of one and several variables, methods of conditional optimization are presented. Examples of solving specific problems are given, a visual interpretation of the results obtained is given, which will contribute to the development of students' practical skills in applying optimization methods.
    The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For students of technical universities. It can be useful for teachers, graduate students and engineers.
    Download
15. Vanko V.I., Ermoshina O.V., Kuvyrkin G.N. Calculus of variations and optimal control: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Corrected. - M .: Publishing house of MSTU im. N.E. Bauman, 2006. -488 p. (Ser. Mathematics at the Technical University; Issue XV).
    Along with the presentation of the foundations of the classical calculus of variations and elements of the theory of optimal control, direct methods of the calculus of variations and methods of transformation of variational problems, leading, in particular, to dual variational principles, are considered. The textbook is completed with examples from physics, mechanics and engineering, which show the effectiveness of the calculus of variations and optimal control methods for solving applied problems.
    The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For undergraduate and graduate students of technical universities, as well as for engineers and researchers specializing in applied mathematics and mathematical modeling.
    Download
16. Probability theory: Textbook. for universities. - 3rd ed., Rev. / A.V. Pechinkin, O. I. Teskin, G.M. Tsvetkova and others; Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E.Bauman, 2004.-456 p. (Ser. Mathematics at the Technical University; Issue XVI).
    A distinctive feature of this book is a balanced combination of mathematical rigor in the presentation of the foundations of the theory of probability with the applied focus of problems and examples illustrating theoretical provisions. Each chapter of the book is completed by a set of a large number of check questions, typical examples and tasks for independent solution. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman.
    Download
17. Mathematical statistics: Textbook. for universities / VB Goryainov, IV Pavlov, GM Tsvetkova, OI Teskin; Ed. B.C. Zarubina, A.P. Krishchenko. - M .: IED-vo MGTU im. N.E. Bauman, 2001.424 p. (Ser. Mathematics at the Technical University; Issue XVII).
    This book introduces the reader to the basic concepts of mathematical statistics and some of its applications. Its distinctive feature is a balanced combination of mathematical rigor with applied tasks. Each chapter of the book ends with a large set of sample examples, checklists, and self-help tasks.
    The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman for students of technical universities. It can be useful for teachers, graduate students and engineers.
    Download
18. Volkov I.K., Zuev SM., Tsvetkova G.M. Random processes: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - M .: Publishing house of MSTU im. N.E. Bauman, 1999.-448 p. (Ser. Mathematics at the Technical University; Issue XVIII).
    The book is the eighteenth edition of the educational complex "Mathematics at a Technical University" and introduces the reader to the basic concepts of the theory of random processes and some of its many applications. According to the authors, this textbook should be a link between rigorous mathematical research, on the one hand, and practical problems - on the other hand, it should help the reader to master the applied methods of the theory of random processes.
    The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman. For students of technical universities. May be useful for teachers and graduate students.
    Download
19. Belousov A.I., Tkachev SB. Discrete mathematics: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 3rd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2004.-744 p. (Ser. Mathematics at the Technical University; Issue XIX).
    The nineteenth issue of the series "Mathematics at a Technical University" presents the theory of sets and relations, elements of modern abstract algebra, graph theory, classical concepts of the theory of Boolean functions, as well as the foundations of the theory of formal languages, which includes theories of finite automata, regular languages, context-free languages In the analysis of graphs and automata, special attention is paid to algebraic methods.
    The content of the textbook corresponds to the course of lectures, which the authors read at the Moscow State Technical University. N.E. Bauman.
    For students of technical universities. It can be useful for teachers, graduate students and engineers.
    Download
20. Volkov I.K., Zagoruiko E.A. Operations Research: Textbook for Universities / Ed. V.S. Zarubina, A.P. Krishchenko. - M .: IED-vo MGGU im. N.E. Bauman. 2000 - 436 p (Ser Mathematics at the Technical University. Issue XX).
    Operations research accumulates those mathematical methods that are used to make informed decisions in various areas of human activity. In the educational literature, this discipline has not yet found its full reflection, although it is necessary for a modern engineer to master its methods.
    The book focuses on the formulation of operations research tasks, methods for their solution and criteria for choosing alternatives. Methods of linear and integer programming, optimization on networks, Markov decision-making models, elements of game theory and simulation are considered. A significant number of examples will help in studying the material. The content of the textbook corresponds to the course of lectures given by the authors at the Moscow State Technical University. N.E. Bauman for students of technical universities. It can be useful for teachers, graduate students and engineers.
    Download
21. Zarubin B.C. Mathematical modeling in technology: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krishchenko. - 2nd ed., Stereotype. - M .: Publishing house of MSTU im. N.E. Bauman, 2003.-496 p. (Ser. Mathematics at the Technical University; Issue XXI, final).
    The book is an additional, twenty-first issue of the set of textbooks "Mathematics at a Technical University", completing the edition of the series. It is devoted to the application of mathematics to solving applied problems arising in various fields of technology. It includes a subject index to the entire complex of textbooks. The content of the textbook corresponds to the course " Fundamentals of Mathematical Modeling ", read by the author at the Moscow State Technical University. N.E. Bauman.
    For students of technical universities. It can be useful for teachers, graduate students and engineers.