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

Moscow Higher Technical School (MVTU) named after N.E. Bauman became the first state technical university in the country (MSTU named after N.E. Bauman).
One of the most important features of technical universities is the fundamental training of future engineers based on an in-depth and expanded cycle of mathematical, natural science and general engineering disciplines. This requires modern educational and methodological support that makes extensive use of advanced information technologies. In order to create such support, the scientific and pedagogical schools of the university and the Publishing House of Moscow State Technical University named after N.E. Bauman is preparing a series of textbooks on mathematics, mechanics, physics, computer science, electronics and other disciplines.
The series “Mathematics at a Technical University” contains 21 issues.
A large team of teachers from the departments of Applied Mathematics and Mathematical Modeling of Moscow State Technical University named after N.E. took part in writing a series of textbooks on mathematics. Bauman. Its members included both professional mathematicians - graduates of university mathematics departments, 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 demonstrative presentation of the material with the applied focus of numerous examples and problems discussed in the textbooks, which ensures close interdisciplinary connections between the course of higher mathematics and the natural sciences 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 IN THE SERIES "MATHEMATICS AT TECHNICAL UNIVERSITY"

I. Introduction to Analysis

Morozova V.D. Introduction to analysis: Proc. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 1996. -408 p. (Ser. Mathematics at a technical university; Issue I). The book is the first issue of the educational complex “Mathematics at a Technical University”, consisting of twenty-one issues. Introduces the reader to 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. The close connection between classical mathematical analysis with sections of modern mathematics (primarily 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.Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 1998.- 408 p. (Ser. Mathematics at a technical university; Issue II). The book is the second edition of the set of textbooks “Mathematics at a Technical University”. Introduces the reader to 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 that the author reads at MSTU. N.E. Bauman. For students of technical universities. May be useful for 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. Krischenko, V.N. Chetverikov. Differential calculus of functions of several variables: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 2000. - 456 p. (Ser. Mathematics at the Technical University; Issue V). The fifth issue examines in detail the fundamental concepts of limit and continuity of functions of many variables, properties of differentiable functions, questions of searching for absolute and conditional extrema of functions of many variables. The connection between the differential calculus of functions of many variables and differential geometry is reflected. Methods for solving systems of nonlinear equations are considered. The theoretical material is presented using linear and matrix algebra methods and illustrated with a selection of examples and problems. At the end of each chapter there are questions and tasks for independent solution. Download (7.43 MB, quality not very good)

VI. Integral calculus of functions of one variable

Zarubin V.S., Ivanova E.E., Kuvyrkin G.N. Integral calculus of functions of one variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house MSTU im. N.E. Bauman, 1999. - 528 p. (Ser. Mathematics at a technical university; Issue VI). The book is the sixth edition of the set of textbooks "Mathematics at a Technical University". Introduces the reader to the concepts of indefinite and definite integrals and methods for calculating them. Attention is paid to applications of the 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. Krischenko. - 2nd ed., stereotype. - M.: Publishing house of MSTU im. N.E. Bauman, 2003. -496 p. (Ser. Mathematics at a Technical University; Issue VII). The book is the seventh edition of the set of textbooks “Mathematics at a Technical University”. It introduces the reader to multiple, curvilinear and surface integrals and methods for calculating them. It pays attention to the applications of these types of integrals, and provides examples of physical, mechanical and technical content. In the final chapters elements of field theory and vector analysis are outlined. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers, graduate students and engineers. (Thank you very much 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 a technical university) The fundamentals of the theory of ordinary differential equations (ODE) are outlined 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, which lead to many applied problems. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N. E. Bauman. For students of technical universities and universities. May be useful for those interested in applied problems of the theory of differential equations. Download

IX. Rows

Vlasova E.A. Rows: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 3rd ed., corrected. - M.: Publishing house of MSTU im. N.E. Bauman, 2006. - 616 p. (Ser. Mathematics at a 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 introduces power series, Taylor series, trigonometric Fourier series and their applications, and Fourier integrals. The theory of series in Banach and Hilbert spaces is presented, and issues of functional analysis, the theory of measure and the Lebesgue integral are considered to the extent necessary for its study. The theoretical material is accompanied by detailed examples, drawings and a large number of tasks of varying levels of complexity. For students of technical universities. The textbook may be useful for teachers and graduate students. Download (djvu archived, 5.98 MB, 600dpi+OCR)

X. Theory of functions of a complex variable

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

XI. Integral transformations and operational calculus

Volkov I.K., Kanatnikov A.N. Integral transformations and operational calculus: Proc. 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 presented. The main classes of integral transformations that play an important role in solving problems in mathematical physics, electrical engineering, and radio engineering are considered. The theoretical material is illustrated with a large number of examples. A separate section is devoted to operational calculus, which has important applied significance. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities and universities, graduate students and researchers using analytical methods in the study of mathematical models. Download(6.75 MB) NEW-- Volume XI slightly combed by Guest (3.28 MB)

XII. Differential equations of mathematical physics And

Martinson L.K., Malov Yu.I. Differential equations of mathematical physics: Textbook. for universities. 2nd ed. / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 2002. - 368 p. (Ser. Mathematics at the Technical University; Issue XII). Various formulations of problems of mathematical physics for partial differential equations and the main analytical methods for solving them are considered, and the properties of the resulting solutions 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 that the authors give at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers, graduate students and engineers. Download (2.5 MB)

XIII. Approximate methods of mathematical physics

Vlasova E.A., Zarubin V.S., Kuvyrkin G.N. Approximate methods of mathematical physics: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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.” It consistently presents 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 boundary elements. 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 Moscow State Technical University named after N.E. For students of technical universities. Download(4.9 MB)

XIV. Optimization methods

A.V. Attetkov, S.V. Galkin, B.S. Zarubin. Optimization methods: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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 dedicated to one of the most important areas of training for a graduate of a technical university - the mathematical theory of optimization. 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, and methods of conditional optimization are outlined. Examples of solving specific problems are given, a visual interpretation of the results obtained is given, which will help students develop practical skills in applying optimization methods. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May 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: Proc. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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 for transforming variational problems, leading, in particular, to dual variational principles, are considered. The textbook is completed with examples from physics, mechanics and technology, which show the effectiveness of the methods of the calculus of variations and optimal control for solving applied problems. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For undergraduate and graduate students of technical universities, as well as for engineers and scientists specializing in the field of 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. Krischenko. - 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 the balanced combination of mathematical rigor in presenting the fundamentals of probability theory with the applied focus of problems and examples illustrating theoretical principles. Each chapter of the book ends with a set of a large number of test questions, typical examples and problems for independent solution. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. Download (2.87 Mb)

XVII. Math statistics

Mathematical statistics: Textbook. for universities / V. B. Goryainov, I. V. Pavlov, G. M. Tsvetkova, O. I. Teskin.; Ed. B.C. Zarubina, A.P. Krischenko. - M.: Ied-vo MSTU 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 an applied focus on problems. Each chapter of the book ends with a large set of typical examples, test questions and problems for independent solution. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May 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 S.M., Tsvetkova G.M. Random processes: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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 issue 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 master the applied methods of the theory of random processes. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May 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. Krischenko. - 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” outlines 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 fundamentals of the theory of formal languages, which includes the theories of finite automata, regular languages, and context-free languages and store automata. 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 that the authors give at MSTU. N.E. Bauman. For students of technical universities. May 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. Krischenko. - M.: Publishing house of Moscow State Humanitarian University named after. N.E. Bauman. 2000 - 436 s (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. This discipline has not yet been fully reflected in educational literature, although it is necessary for a modern engineer to master its methods. The book focuses on the formulation of operations research problems, methods for solving them, and criteria for selecting alternatives. Methods of linear and integer programming, optimization on networks, Markov decision-making models, elements of game theory and simulation modeling are considered. A significant number of examples will help when studying the material. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers, graduate students and engineers. Download (2MB)

XXI. Mathematical modeling in technology

Zarubin B.S. Mathematical modeling in technology: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 2nd ed., stereotype. - M.: Publishing house of MSTU im. N.E. Bauman, 2003. -496 p. (Ser. Mathematics at a technical university; Issue XXI, final). The book is an additional, twenty-first edition of the set of textbooks “Mathematics in a Technical University”, completing the publication 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 set of textbooks. The content of the textbook corresponds to the course “ Fundamentals of Mathematical Modeling", read by the author at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers, graduate students and engineers. Download (4, 3 MB)

NEW Panov V.F. Mathematics Ancient and Young/Ed. B.C. Zarubina. - 2nd ed., revised - M.: Publishing house of MSTU im. N. E. Bauman, 2006. - 648 p.: ill. ISBN 5-7038-2890-2 The book is an addition to the set of textbooks in the “Mathematics at a Technical University” series 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”, given by the author to students of MSTU. N. E. 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 provides a history of some basic mathematical concepts and ideas. For students of technical universities and mathematics teachers, as well as everyone interested in the history of science Download (djvu/rar, 4.69 Mb)

All books in one archive (Thank you

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, watch	Note
Practical lessons
Homework is current
House. task "Ranks"
Frontier control by module

MODULE 2. Field theory

Types of classroom activities and independent work	Deadlines for carrying out or fulfillment, weeks	Labor intensity, watch	Note
Practical lessons
Homework is current
House. task “Multiple and curvilinear integrals”
Frontier control by module

MODULE 3. TFKP

Types of classroom activities and independent work	Deadlines for carrying out or fulfillment, weeks	Labor intensity, watch	Note
Practical lessons
Homework is current
House. task "TFKP"
Frontier control by module

Lectures

MODULE 1. Series theory

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

OL-2 1-1.7; OL-4 ch.16 §1–6.

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

OL-2 1.8-1.9; OL-3 ch.16 §7–8.

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

OL-2 2.1-2.5; OL-4 chapter 16 §9-13.

Lecture4 . Basic properties of power series. Taylor series. Applications of power series.

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 chapter 5 §14.8.

Lecture6 . Expansion of functions into a trigonometric Fourier series on an interval. Dirichlet conditions for decomposability of functions in Fourier series. Relationship between the order of smallness of the Euler-Fourier coefficients and the differentiability of a periodic function.

OL-2 3.6–3.9; OL-4 chapter 17 § 1–5.

Lectures 7– 8. Derivation of the Fourier integral by formally passing from the trigonometric series at . Complex form of writing the Fourier integral. Integral Fourier transform and its basic properties. Dirac delta function. Fourier integral of the Dirac delta function.

MODULE 2. Field theory

Lecture9 . Double integral. Properties of double integral. Changing variables in a double integral.

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

Lecture10 . Triple integral. Properties of triple integral.

OL-1 2.1-2.4; OL-4 chapter 14 § 11, 12.

Lecture11 . Curvilinear integral of the second kind. Properties of a curvilinear integral.

OL-1 5.4-5.6; OL-4 chapter 3 § 1–2.

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

OL-1 5.7–5.8; OL-4 chapter 15 § 3–4.

Lecture13 . Calculation of the curvilinear integral of the total differential. Surface integral. Properties of the surface integral.

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 chapter 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 chapter 15 § 7.

Lecture16 . Hamilton's cameraman. Second order vector differential operations.

OL-1 8.1–8.4; OL-4 chapter 15 § 9.

Lectures17 . Curvilinear orthogonal coordinates (COOC). Lamé coefficients. Differential operations in KOOC.

OL-1 D.8.1; DL-1 chapter 6 §3.

MODULE 3. TFKP

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

OL-3 3.1 3.3–3.5; OL-5 chapter 1 §1–2.

Lecture 19 . Limit of a function of a complex variable. Continuity and derivative of a function of a complex variable. Cauchy-Riemann conditions. Analyticity of a function in a region and at a point. Analyticity of basic elementary functions of a complex variable.

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

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

OL-3 5.1–5.5; OL-5 chapter 1 §4–5.

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

OL-3 6.1–6.6; OL-5 chapter 1 §6.

Lecture 22 . Classification of isolated singular points of an analytic function according to the type of its expansion into a Laurent series in the neighborhood of these points.

OL-3 7.2–7.4; OL-5 chapter 1 §7.

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

OL-3 8.1–8.4; OL-5 chapter 1 §8.

Lecture 25. Reserve.

PRACTICAL LESSONS

MODULE 1. Series theory

Lesson 1. Number series with positive terms.

OL-5 Auditorium 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.

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

Lesson 2. Numerical alternating series.

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

At home. 2471, 2473, 2481, 2482, 2484.

Actions on rows. Midterm control for module 1 (lectures 1–2, classes 1–9).

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

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

Lesson 3. Power series. Convergence interval.

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

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

Lesson 4. Expansion of a function into series.

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

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

Application of power series.

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

Houses: 2642, 2645, 2653.

Lesson 5. Fourier series.

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

At home. 2675, 2682, 2674.

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

At home. 2695, 2696, 2699.

Lesson 6. Interim control modulo 1 ( lectures1 -- 8 , seminars1 – 5 ).

MODULE 2. Field theory

Z activity 7. Setting limits and calculating double integrals in Cartesian coordinates.

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

Houses: 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 areas of plane figures.

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

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

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

OL-5 Auditorium: 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 Auditorium: 2240, 2241, 2255, 2257, 2260, 2268

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

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

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

Houses: 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 Room: 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 Auditorium: 2349, 2350, 2357, 2366; 2373, 2375, 2377.

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

Room: 2383, 2384, 2385.

At home: OL-5 chapter 7: 2389, 2391, 2386, 2388, 2394, 2398(1)

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

MODULE 3. TFKP

Lesson 14. Numerical and power series with complex terms. Calculation of values ​​of elementary functions of a complex variable.

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

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

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

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

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

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

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

At home. 167, 169, 171, 173, 251, 253, 257.

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

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

At home. 266, 268, 270, 272, 274.

Zeros of an analytical function. Isolated singular points and their classification.

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

At home. 277, 291, 293, 295, 297, 301, 305, 307.

Isolated singular points and residues at them. Application of residues to the calculation of contour integrals.

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

At home. 319, 321, 323, 325, 327, 339, 347, 351, 353.

Lesson 16. Interim control modulo 3 ( lectures 18–24, seminars 14–15).

Lesson 17. Reserve.

Control activities

MODULE 1. Series theory

1.Homework “Rows” (7th week) .

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

MODULE 2. Field theory

3.Homework “Multiple and curvilinear integrals” (13th week).

4. Midterm control on the module (13th week).

MODULE 3. TFKP

5.Homework “TFKP” (16th week).

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

Literature

Basic literature (RL)

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. Theory of functions of a complex variable. – M.: Publishing house of MSTU im. N.E. Bauman, 2000. – 520 p.

4. Piskunov N.S. Differential and integral calculus for colleges. v.2. – M.: Nauka, 1985. – 560 p.

5. Problems and exercises in mathematical analysis for college students. Ed. B.P. Demidovich. – M.: Nauka, 1970. – 472 p.

6. Krasnov M.L., Kiselev L.I., Makarenko G.I. Functions of a complex variable. Operational calculus. Theory of stability. 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. Course of mathematical analysis. – M.: Higher School, 1981. – 584s.

3. Sveshnikov A.G., Tikhonov A.M. Theory of functions of a complex variable. – M.: Nauka, 1967. – 304 p.

Methodical manuals (MP)

7. Serzhantova M.M., Loginova L.A., Poznyakova L.V. Field theory: Textbook \Ed. Sergeantova M.M. – M.: MSTU Publishing House, 1992. – 58 p., ill.

1. Vanko V.I., Galkin S.V., Morozova V.D. Guidelines 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., Heresko T.A. Methodological guide for doing homework on TFKP, Moscow Higher Technical School, 1976. – 41 p.

3. Golenko K.A., Heresko T.A., Shchetinina N.N. Methodological instructions for preparing for tests in the course of higher mathematics, Moscow Higher Technical School, 1986. – 36 p.

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 a technical university. Issue VII).

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

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

Format: djvu

Size: 7.4 MB

Download: yandex.disk

TABLE OF CONTENTS
Preface 5
Basic designations 11
1. Double integrals 15
1.1. Problems leading to the concept of double integral 15
1.2. Definition of double integral 17
1.3. Conditions for the existence of a double integral 24
1.4. Classes of integrable functions 27
1.5. Properties of double integral 29
1.6. Mean value theorems for double integrals 36
1.7. Calculation of double integral 40
1.8. Curvilinear coordinates on a plane 62
1.9. Changing 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. Problem of calculating body mass 97
2.2. Definition of triple integral 98
2.3. Properties of triple integral 102
2.4. Triple integral calculation 105
2.5. Changing variables in a 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 integrability of a function 168
3.4. Properties of integrable functions and multiple integral 179
3.5. Reducing a multiple integral to a repeated one 183
3.6. Changing variables in a multiple integral 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. Calculation of multiple integrals using 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 a curvilinear integral from the path of integration 296
5.9. Calculating the Curvilinear Integral of a Total Differential 306
D.5.1. Curvilinear integral in a multiply connected domain 310
Questions and tasks 314
6. Surface integrals 319
6.1. On defining a surface in space 319
6.2. Single-sided and double-sided surfaces 323
6.3. Surface area 327
6.4. Surface integral of the first kind 334
6.5. Applications of surface integral of the first kind 341
6.6. Surface integral of the second kind 347
6.7. Physical meaning of the 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. Ostrogradsky - Gauss formula 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
D.7.1. Irrotation-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. Second order differential operations 448
8.4. Integral formulas 452
8.5. Inverse problem of field theory 463
D.8.1. Differential operations in orthogonal curvilinear coordinates 465
Questions and tasks 479
List of recommended literature 481
Subject index 484

Book series

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

Moscow
Publishing house of MSTU named after. N. E. Bauman

1. Morozova V.D. Introduction to analysis: Proc. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 1996. -408 p. (Ser. Mathematics at a technical university; Issue I).
   The book is the first issue of the educational complex “Mathematics at a Technical University”, consisting of twenty-one issues. Introduces the reader to 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. The close connection between classical mathematical analysis with sections of modern mathematics (primarily 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
2. Ivanova E.E. Differential calculus of functions of one variable: Textbook. for universities / Ed. V.S.Zarubina, A.P.Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 1998.- 408 p. (Ser. Mathematics at a technical university; Issue II).
   The book is the second edition of the set of textbooks “Mathematics at a Technical University”. Introduces the reader to 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 that the author reads at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers and graduate students.
   Download
3. Kanatnikov A.N., Krischenko A.P. Analytic geometry. -2nd ed. - M., Publishing house of MSTU im. Bauman, 2000, 388 pp. (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 second-order surfaces.
   The material is presented to the extent necessary at the initial stage of training for a technical university student.
   The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman.
   Download Edition 2 Edition 3
4. Kanatnikov A.N., Krischenko A.P. Linear algebra: Textbook. for universities. 3rd ed., stereotype. / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 2002. - 336 p. (Ser. Mathematics at a technical university; Issue IV).
   Description: The book is the fourth issue in the series “Mathematics at a Technical University” and contains a presentation of a basic course in linear algebra. Additionally, the basic concepts of tensor algebra and iterative methods for numerical solution of systems of linear algebraic equations are included.
   Download
5. A.N. Kanatnikov, A.P. Krischenko, V.N. Chetverikov. Differential calculus of functions of several variables: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 2000. - 456 p. (Ser. Mathematics at the Technical University; Issue V).
   The fifth issue examines in detail the fundamental concepts of limit and continuity of functions of many variables, properties of differentiable functions, questions of searching for absolute and conditional extrema of functions of many variables. The connection between the differential calculus of functions of many variables and differential geometry is reflected. Methods for solving systems of nonlinear equations are considered.
   The theoretical material is presented using linear and matrix algebra methods and illustrated with a selection of examples and problems. At the end of each chapter there are questions and tasks for independent solution.
   
   Download
6. Zarubin V.S., Ivanova E.E., Kuvyrkin G.N. Integral calculus of functions of one variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - M.: Publishing house
   MSTU im. N.E. Bauman, 1999. - 528 p. (Ser. Mathematics at a technical university; Issue VI).
   The book is the sixth edition of the set of textbooks "Mathematics at a Technical University". Introduces the reader to the concepts of indefinite and definite integrals and methods for calculating them. Attention is paid to applications of the definite integral, examples and problems of physical, mechanical and technical content are given.
   The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman.
   For students of technical universities. May 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. Krischenko. - 2nd ed., stereotype. - M.: Publishing house of MSTU im. N.E. Bauman, 2003. -496 p. (Ser. Mathematics at a Technical University; Issue VII).
   The book is the seventh edition of the set of textbooks “Mathematics at a Technical University”. It introduces the reader to multiple, curvilinear and surface integrals and methods for calculating them. It pays attention to the applications of these types of integrals, and provides examples of physical, mechanical and technical content. In the final chapters elements of field theory and vector analysis are outlined.
   The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman.
   For students of technical universities. May 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 a technical university)
   The fundamentals of the theory of ordinary differential equations (ODE) are outlined 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, which lead to many applied problems. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N. E. Bauman. For students of technical universities and universities. May be useful for those interested in applied problems of the theory of differential equations.
   Download
9. Vlasova E.A. Rows: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 3rd ed., corrected. - M.: Publishing house of MSTU im. N.E. Bauman, 2006. - 616 p. (Ser. Mathematics at a 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 introduces power series, Taylor series, trigonometric Fourier series and their applications, and Fourier integrals. The theory of series in Banach and Hilbert spaces is presented, and issues of functional analysis, the theory of measure and the Lebesgue integral are considered to the extent necessary for its study. The theoretical material is accompanied by detailed examples, drawings and a large number of tasks of varying levels of complexity.
   Download
10. Morozova V.D. Theory of functions of a complex variable: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 3rd ed., corrected. - M.: Publishing house of MSTU im. N.E. Bauman, 2009. - 520 p. (Ser. Mathematics at a Technical University; Issue X.) ISBN 978-5-7038-3189-2
    The book is devoted to the theory of functions of one complex variable. It focuses on issues related to conformal mappings, as well as the application of theory to solving applied problems. Examples and problems from physics, mechanics and various branches of technology are given.
    For students of technical universities. May be useful for teachers, graduate students and engineers.
    Download
11. Volkov I.K., Kanatnikov A.N. Integral transformations and operational calculus: Proc. 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 presented. The main classes of integral transformations that play an important role in solving problems in mathematical physics, electrical engineering, and radio engineering are considered. The theoretical material is illustrated with a large number of examples. A separate section is devoted to operational calculus, which has important applied significance.
    The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman.
    For students of technical universities and universities, graduate students and researchers using 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. Krischenko. - M.: Publishing house of MSTU im. N.E. Bauman, 2002. - 368 p. (Ser. Mathematics at the Technical University; Issue XII).
    Various formulations of problems of mathematical physics for partial differential equations and the main analytical methods for solving them are considered, and the properties of the resulting solutions 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 that the authors give at MSTU. N.E. Bauman.
    For students of technical universities. May be useful for teachers, graduate students and engineers.
    Download
13. Vlasova B.A., Zarubin B.S., Kuvyrkin G.N. Approximate methods of mathematical physics: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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.” It consistently presents 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 boundary elements. 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 Moscow State Technical University named after N.E. For students of technical universities.
    Download
14. A.V. Attetkov, S.V. Galkin, B.S. Zarubin. Optimization methods: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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 dedicated to one of the most important areas of training for a graduate of a technical university - the mathematical theory of optimization. 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, and methods of conditional optimization are outlined. Examples of solving specific problems are given, a visual interpretation of the results obtained is given, which will help students develop practical skills in applying optimization methods.
    The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May 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: Proc. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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 for transforming variational problems, leading, in particular, to dual variational principles, are considered. The textbook is completed with examples from physics, mechanics and technology, which show the effectiveness of the methods of the calculus of variations and optimal control for solving applied problems.
    The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For undergraduate and graduate students of technical universities, as well as for engineers and scientists specializing in the field of 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. Krischenko. - 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 the balanced combination of mathematical rigor in presenting the fundamentals of probability theory with the applied focus of problems and examples illustrating theoretical principles. Each chapter of the book ends with a set of a large number of test questions, typical examples and problems for independent solution. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman.
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17. Mathematical statistics: Textbook. for universities / V. B. Goryainov, I. V. Pavlov, G. M. Tsvetkova, O. I. Teskin.; Ed. B.C. Zarubina, A.P. Krischenko. - M.: Ied-vo MSTU 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 an applied focus on problems. Each chapter of the book ends with a large set of typical examples, test questions and problems for independent solution.
    The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers, graduate students and engineers.
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18. Volkov I.K., Zuev S.M., Tsvetkova G.M. Random processes: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 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 issue 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 master the applied methods of the theory of random processes.
    The content of the textbook corresponds to the course of lectures that the authors give at MSTU. 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. Krischenko. - 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” outlines 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 fundamentals of the theory of formal languages, which includes the theories of finite automata, regular languages, and context-free languages and store automata. 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 that the authors give at MSTU. N.E. Bauman.
    For students of technical universities. May 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. Krischenko. - M.: Publishing house of Moscow State Humanitarian University named after. N.E. Bauman. 2000 - 436 s (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. This discipline has not yet been fully reflected in educational literature, although it is necessary for a modern engineer to master its methods.
    The book focuses on the formulation of operations research problems, methods for solving them, and criteria for selecting alternatives. Methods of linear and integer programming, optimization on networks, Markov decision-making models, elements of game theory and simulation modeling are considered. A significant number of examples will help when studying the material. The content of the textbook corresponds to the course of lectures that the authors give at MSTU. N.E. Bauman. For students of technical universities. May be useful for teachers, graduate students and engineers.
    Download
21. Zarubin B.S. Mathematical modeling in technology: Textbook. for universities / Ed. B.C. Zarubina, A.P. Krischenko. - 2nd ed., stereotype. - M.: Publishing house of MSTU im. N.E. Bauman, 2003. -496 p. (Ser. Mathematics at a technical university; Issue XXI, final).
    The book is an additional, twenty-first edition of the set of textbooks “Mathematics in a Technical University”, completing the publication 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 set of textbooks. The content of the textbook corresponds to the course “ Fundamentals of Mathematical Modeling", read by the author at MSTU. N.E. Bauman.
    For students of technical universities. May be useful for teachers, graduate students and engineers.