Moscow: 2005 ... - 560 p.
The collection includes over 4000 problems and exercises on the most important sections of mathematical analysis: introduction to analysis, differential calculus of functions of one variable, indefinite and definite integrals, series, differential calculus of functions of several variables, integrals depending on a parameter, multiple and curvilinear integrals. Almost all problems have been answered! The appendix contains the answers. For students of physical and mechanical-mathematical specialties of higher educational institutions
Format: pdf (2005 , 560s.)
The size: 5 Mb
Watch, download:drive.google
Format: pdf (1998 , 14th ed., Rev., 624s.)
The size: 13 Mb
Watch, download:drive.google
Format: djvu / zip (1997 , 13th ed., Rev., 624s.)
The size: 5, 8Mb
/ Download file
● i-stres.narod.ru - Here you can find solutions to problems from the collection of mat. analysis B.P. Demidovich ... The numbers of the laid out problems correspond to the 2003 edition. ("AST", "Astrel")
● truba.nnov.ru - People's Reshebnik - 115 solved tasks from Demidovich's collection.
Objectives and exercises for mathematical analysis for technical colleges. Under. ed. Demidovich B.P. M., 2001 Tutorial for students of higher. tech. educational institutions. (Each paragraph contains a little theory, examples of solving problems and tasks.) The book can be downloaded from the site in 10 separate chapters, each 600-800 Kb.) Then it is unzipped into separate files gif format and can be viewed in any standard program like a set of photos. (located on the site math.reshebnik.ru )
TABLE OF CONTENTS
PART ONE FUNCTIONS OF ONE INDEPENDENT VARIABLE
Section I. Introduction to Analysis 7
§ I. Real numbers 7
§ 2. Sequence theory 12
§ 3. The concept of a function 26
§ 4. Graphic image functions .... 35
§ 5. Limit of a function 47
§ 6. O-symbolism 72
§ 7. Continuity of a function 77
§ 8. Inverse function. Functions Defined Parametrically 87
§ 9. Uniform continuity functions ... 90
§ 10. Functional equations 94
Section II. Differential calculus of functions of one variable 96
§ 1. Derivative explicit function 96
§ 2. Derivative inverse function... Derivative of a parametrically defined function. Derivative of an implicit function. ... ... .114
§ 3. The geometric meaning of the derivative 117
§ 4. Differential of function 120
§ 5. Derivatives and differentials of higher orders 124
§ 6. Theorems of Rolle, Lagrange and Cauchy .... 134
§ 7. Increase and decrease of a function. Inequalities 140
§ 8. Direction of concavity. Inflection points. ... 144
§ 9. Disclosure of uncertainties 147
§ 10. Taylor's formula 151
§eleven. Extremum function. Largest and Smallest Function Values 156
§ 12. Construction of graphs of functions by characteristic points 161
§ 13. Problems for maximum and minimum functions. ... ... 164
§ 14. Tangency of curves. Circle of curvature. Evolution 167
§ 15. Approximate solution of equations .... 170
Section III. Indefinite Integral 172
§ 1. The simplest indefinite integrals... 172
§ 2. Integration of rational functions ... 184
§ 3. Integration of some irrational functions 187
§ 4. Integration of trigonometric functions 192
§ 5. Integration of various transcendental functions 198
Section 6. Various examples function integration 201
Section IV. Definite Integral 204
§ 1. The definite integral as the limit of the sum. ... 204
§ 2. Calculation definite integrals using undefined 208
§ 3. Mean value theorems 219
§ 4. Improper integrals 223
§ 5. Calculation of areas 230
§ 6. Calculation of the lengths of arcs 234
§ 7. Calculation of volumes 236
§ 8. Calculation of the areas of surfaces of revolution 239
§ 9. Calculation of moments. Center of gravity coordinates 240
§ 10. Problems from mechanics and physics 242
§eleven. Approximate calculation of definite integrals 244
Division V. Ranks 246
§ 1. Number series. Convergence criteria for series of constant signs 246
§ 2. Criteria for the convergence of alternating series 259
§ 3. Actions on rows 267
§ 4. Functional series 268
§ 5. Power series 281
§ 6. Fourier series 294
§ 7. Summation of series 300
§ 8. Finding definite integrals using series 305
§ 9. Infinite works 307
§ 10. Stirling's formula 314
§ 11. Approximation continuous functions polynomials 315
PART TWO
FUNCTIONS OF MULTIPLE VARIABLES
Section VI. Differential calculus of functions of several variables 318
§ 1. Limit of a function. Continuity 318
§ 2. Partial derivatives. Differential function 324
§ 3. Differentiation of implicit functions .... 338
§ 4. Change of variables 348
§ 5. Geometric applications 361
§ 6. Taylor's formula 367
§ 7. Extremum of a function of several variables 370
Section VII. Parameter-dependent integrals. ... 379
§ 1. Proper integrals depending on a parameter 379
§ 2. Improper integrals depending on a parameter. Uniform convergence of integrals 385
§ 3. Differentiation and integration of improper integrals under the integral sign,. 392
§ 4. Euler integrals 400
§ 5. Fourier integral formula 404
Section VIII. Multiple and curvilinear integrals. 406
§ 1. Double integrals 406
§ 2. Calculation of areas, 414
§ 3. Calculation of volumes 416
§ 4. Calculation of the areas of surfaces .... 419
§ 5. Applications of double integrals to mechanics 421
§ 6. Triple integrals 424
§ 7. Calculation of volumes by means of triple integrals 428
§ 8. Applications of triple integrals to mechanics 431
§ 9. Improper double and triple integrals 435
§ 10. Multiple integrals 439
§eleven. Curvilinear Integrals 443
§ 12. Formula Grnia 452
§ 13. Physical applications of curvilinear integrals. . "456
§ 14. Surface integrals 460
§ 15. Stokes formula 464
§ 16. Formula Ostrogradsky 466
§ 17. Elements of field theory 471
Replies480
DEMIDOVICH Boris Pavlovich
Boris Pavlovich Demidovich was born on March 2, 1906 in the family of a teacher at the Novogrudok city school. His father, Pavel Petrovich Demidovich (07/10/1871-7.03.1931), from the Belarusian peasants (the village of Nikolayevshchina, Stolbtsovsky district, Minsk province), managed to get a higher education, having graduated from the Vilnius Teachers' Institute in 1897. Throughout his life teaching (first in various cities of the Minsk and Vilna provinces, and then in Minsk itself), he enthusiastically studied family life, beliefs and rituals of Belarusians, wrote down works of Belarusian anonymous literature - gutarkas. In 1908, P.P. Demidovich was even elected a member of the Imperial Society of Lovers of Natural Science, Anthropology and Ethnography at Moscow University. B.P. Demidovich's mother, Olympiada Platonovna Demidovich (nee Plyshevskaya) (06.16.1876-19.10.1970), the daughter of a priest, was also a teacher before marriage, and after that she was only engaged in raising her children: in the family, besides Boris, there were his three sisters Zinaida, Evgenia, Zoya and younger brother Paul. After graduating from the 5th Minsk school in 1923, B.P. Demidovich entered the physics and mathematics department of the pedagogical faculty of the first university in Belarus, the Belarusian State University... After graduating from BSU in 1927, he was recommended for postgraduate studies at the Department of Higher Mathematics, but did not pass the exam in the Belarusian language and left to work in Russia.
B.P. Demidovich works as a mathematics teacher in secondary educational institutions of the Smolensk and Bryansk regions (7-year-old school in Pochinki, Bryansk 9-year school named after the III International, Bryansk Construction College), and then, accidentally reading an ad in the local chronicle, arrives at Moscow and in 1931 entered a one-year postgraduate study at the Research Institute of Mathematics and Mechanics at Moscow State University. Upon completion of this short-term targeted postgraduate study, B.P. Demidovich is awarded the qualification of a teacher of mathematics at higher educational institutions. He receives a distribution at the Transport and Economic Institute of the NKPS, and teaches there in the Department of Mathematics in 1932-33. In 1933, while maintaining his teaching load at the TEI NKPS, B.P. Demidovich was still enrolled as a senior researcher in the Bureau of Experimental Transport Construction of the NKPS and worked there until 1934.At the same time, in 1932, B.P. Demidovich became ( by competition) postgraduate student of the Mathematical Institute of Moscow State University. In graduate school at MI Moscow State University, B.P. Demidovich began to study under the guidance of A.N. Kolmogorov's theory of functions of a real variable.
However, A.N. Kolmogorov, seeing that B.P. Demidovich was more interested in the problems of ordinary differential equations, advised him to devote himself to the study of the qualitative theory of ordinary differential equations under the guidance of V.V. Stepanov. The development at Moscow State University of qualitative methods in the theory of ordinary differential equations is inextricably linked with the organization organized in 1930 by V.V. Stepanov special seminar on this topic, active participant which becomes B.P. Demidovich. Carrying out the general management of his studies, V.V. Stepanov assigned him, as a direct scientific adviser, his young colleague, who was then just completing his doctoral dissertation, V.V. Nemytsky. Between V.V. Nemytskiy and his essentially first graduate student B.P. Demidovich struck up the closest creative friendship for life. After completing his postgraduate studies at the Moscow State University in 1935, B.P. Demidovich has been working for one semester at the Department of Mathematics at the Institute of the Leather Industry. L.M. Kaganovich, and since February 1936, at the invitation of L.A. Tumarkin, is credited as an assistant of the Department of Mathematical Analysis of the Faculty of Mechanics and Mathematics of Moscow State University. From that time until the end of his days, he remains her permanent employee. In 1935, at MI MSU B.P. Demidovich defends his Ph.D. thesis"On the existence of an integral invariant on a system of periodic orbits". It was highly appreciated by the official opponent A.Ya. Khinchin; N.N. Luzin recommended publishing its main results in DAN SSSR, A.A. Markov gave a positive review for its detailed publication in the Mathematical Collection (although formally, publications on the candidate's dissertation were not mandatory at that time). The Qualification Commission of the People's Commissariat of Education of the RSFSR awards B.P. Demidovich in 1936, the degree of candidate of physical and mathematical sciences, and in 1938 he approved him in the academic rank of associate professor of the Department of Mathematical Analysis of Mechanics and Mathematics of Moscow State University. In 1963 B.P. Demidovich, at a meeting of the Academic Council of Mechmatics of Moscow State University, on the basis of his main works, he defended his doctoral dissertation under the general title "Limited solutions of differential equations" (official opponents V.V. Nemytsky, B.M. Levitan, V.A. enterprise "- Department of Ordinary Differential Equations of Matmeh Leningrad State University, Head of Department VA Pliss). In the same year, the Higher Attestation Commission awarded him the degree of Doctor of Physical and Mathematical Sciences, and in 1965 approved him in the academic rank of Professor of the Department of Mathematical Analysis of Mechmatics at Moscow State University. In 1968, the Presidium of the Supreme Soviet of the RSFSR assigned B.P. Demidovich the honorary title "Honored Scientist of the RSFSR". The scientific heritage of B.P. Demidovich is analyzed in great detail in the personalities indicated in the footnote. Repeating the conclusion of the authors of these personalities, five main directions of its scientific activities:
· dynamic systems with integral invariants;
· Periodic and almost-periodic solutions of ordinary differential equations;
Correct and completely correct (according to Demidovich) differential systems;
· limited solutions ordinary differential equations;
· Stability of ordinary differential equations, in particular, orbital stability of dynamical systems.
Review of results in these areas and full list of his scientific publications (he has about sixty) is given in the same personalities. Along with scientific and pedagogical activities at Moscow State University, B.P. Demidovich taught concurrently at a number of leading universities in Moscow (MVTU named after N.E.Bauman, Military Engineering Academy named after F.E.Dzerzhinsky, etc.). High professionalism and rich pedagogical experience are reflected in the books written by him, in particular, the well-known University problem book on mathematical analysis (the number of publications of which only in our country is already in the second ten with a total circulation of over 1,000,000 copies), translated into many foreign languages, as well as a sustainability guide that has been popular with readers.
B.P. gave a lot of strength and energy. Demidovich to educate his students and followers, heading after the death of V.V. Stepanov and V.V. Nemytskiy at the Mekhmat Moscow State University, the aforementioned research seminar on the qualitative theory of ordinary differential equations (together with A.F. Filippov and M.I. Elshin). He was often invited to the Organizing Committees of both scientific conferences and school Olympiads. He actively collaborated with the editors of various mathematical journals (" Differential Equations", RZh" Mathematics "), as well as with the mathematical edition of" TSB. " then (1937) and illegally repressed under the notorious article "58 -prim", his younger brother Pavel Pavlovich Demidovich is a young, talented physicist ("much more talented than me," he stressed), who graduated from the pedagogical faculty of BSU in 1931 and for great success in his studies, left at the university for further specialization in the field of wave mechanics. Everyone who knew B.P. Demidovich, noting his sensitivity and responsiveness, treated him with deep respect and sincere sympathy. Having a large family (four children), with constant workload at his main job and part-time, studying at home in the evenings in cramped living conditions, he never refused to help colleagues, whether it was conducting classes with students or participating in Sunday work. B.P. died. Demidovich April 23, 1977 suddenly (diagnosis: acute cardiovascular failure). It happened on Saturday, at home. And the day before, on Thursday, he, as usual, gave his next lecture ...
Collection of problems and exercises on mathematical analysis - Demidovich B.P. - 1997
The collection includes over 4000 problems and exercises on the most important sections of mathematical analysis: introduction to analysis; differential calculus of functions of one variable; indefinite and definite integrals; ranks; differential calculus of functions of several variables; integrals depending on a parameter; multiple and curvilinear integrals. Almost all problems have been answered. Placed in the application (tables.
For students of physical and mechanical and mathematical specialties of higher educational institutions.
Collection of problems and exercises in mathematical analysis: Textbook. - 13th ed., Rev. - M .: Publishing house of Moscow. University, CheRo, 1997 .-- 624 p.
ISBN 5-211-03645-X
UDC 517 (075.8)
BBK 22.161
D30
Free download e-book v convenient format, watch and read:
- fileskachat.com, fast and free download.
PART ONE
FUNCTIONS OF ONE INDEPENDENT VARIABLE
Section I. Introduction to Analysis
§ 1. Real numbers
§ 2. Sequence theory
§ 3. The concept of a function
§ 4. Graphic representation of a function
§ 5. Limit of a function
§ 6. O-symbolism
§ 7. Continuity of a function
§ 8. Inverse function. Functions specified parametrically
§ 9. Uniform continuity of a function
§ 10. Functional equations
Section II. Differential calculus of functions of one variable
§ 1. Derivative of an explicit function
§ 2. Derivative of the inverse function. Derivative of a parametrically defined function. The derivative of an implicit function
§ 3. Geometric meaning of the derivative
§ 4. Differential of a function
§ 5. Derivatives and differentials of higher orders
§ 6. Rolle's, Lagrange's and Cauchy's theorems
§ 7. Increase and decrease of a function. Inequalities
§ 8. Direction of concavity. Inflection points
§ 9. Disclosure of uncertainties
§ 10. Taylor's formula.
§ 11. Extremum of a function. Largest and Smallest Function Values
§ 12. Plotting a function from characteristic points
§ 13. Problems for maximum and minimum functions
§ 14. Tangency of curves. Circle of curvature. Evolution
§ 15. Approximate solution of equations
Section III Indefinite integral
§ 1. The simplest indefinite integrals
§ 2. Integration of rational functions
§ 3. Integration of some irrational functions
§ 4. Integration of trigonometric functions
§ 5. Integration of various transcendental functions
§ 6. Various examples for the integration of functions
Section IV. Definite integral
§ 1. The definite integral as the limit of the sum
§ 2. Calculation of definite integrals using indefinite
§ 3. Mean theorems
§ 4. Improper integrals
§ 5. Calculation of areas
§ 6. Calculation of arc lengths
§ 7. Calculation of volumes
§ 8. Calculation of the areas of surfaces of revolution
§ 9. Calculation of moments. Center of gravity coordinates
§ 10. Problems from mechanics and physics
§ 11. Approximate calculation of definite integrals
Section V. The ranks
§ 1. Number series. Convergence criteria for series of constant signs
§ 2. Criteria for the convergence of alternating series
§ 3. Actions on rows
§ 4. Functional series
§ 5. Power series
§ 6. Fourier series
§ 7. Summation of series
§ 8. Finding definite integrals using series
§ 9. Endless works
§ 10. Stirling's formula
§ 11. Approximation of continuous functions by polynomials
PART TWO
FUNCTIONS OF MULTIPLE VARIABLES
Section VI. Differential calculus of functions of several variables
§ 1. Limit of a function. Continuity
§ 2. Partial derivatives. Differential function
§ 3. Differentiation of implicit functions
§ 4. Change of variables
§ 5. Geometric applications
§ 6. Taylor's formula
§ 7. Extremum of a function of several variables
Section VII. Parameter-dependent integrals
§ 1. Eigen integrals depending on a parameter
§ 2. Improper integrals depending on a parameter. Uniform convergence of integrals
§ 3. Differentiation and integration of improper integrals under the integral sign
§ 4. Euler integrals
§ 5. The Fourier integral formula
Section VIII. Multiple and Curvilinear Integrals
§ 1. Double integrals
§ 2. Calculation of areas
§ 3. Calculation of volumes
§ 4. Calculation of the areas of surfaces
§ 5. Applications of double integrals to mechanics
§ 6. Triple integrals
§ 7. Calculation of volumes using triple integrals
§ 8. Applications of triple integrals to mechanics
§ 9. Improper double and triple integrals
§ 10. Multiple integrals
§ 11. Curvilinear integrals
§ 12. Green's formula.
§ 13. Physical applications of curvilinear integrals
§ 14. Surface integrals
§ 15. Stokes formula
§ 16. Formula Ostrogradsky
§ 17. Elements of field theory
Download the book Collection of problems and exercises in mathematical analysis - Demidovich B.P. - 1997
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Tasks and exercises in mathematical analysis for technical colleges. Ed. Demidovich B.P.
M .: 2004 - 496s. M .: 1968 - 472s.
This collection contains over 3000 problems and covers all sections of the university course in higher mathematics. The collection contains basic theoretical information, definitions and formulas for each section of the course, as well as solutions of especially important typical tasks... The book is intended for students of technical colleges, as well as for those engaged in self-education. The collection was formed as a result of many years of teaching by the authors of higher mathematics in higher technical institutions in Moscow. The collection contains tasks and examples of mathematical analysis in relation to maximum program general course of higher mathematics of higher technical educational institutions. The collection covers all sections of the university course in higher mathematics (with the exception of analytical geometry). Special attention focuses on the most important sections of the course that require strong skills (finding limits, differentiation techniques, plotting functions, integration techniques, applying definite integrals, series, solving differential equations).
Format: pdf(2004, 496s.)
The size: 11 Mb
Watch, download: drive.google
Format: pdf(1968, 472s.)
The size: 8 Mb
Watch, download: drive.google
TABLE OF CONTENTS
Foreword 6
Chapter I. Introduction to Analysis 7
§ 1, Concept of a function 7
§ 2. Graphs elementary functions 12
§ 3. Limits 17
§ 4. Infinitely small and infinitely large 28
§ 5. Continuity of functions 31
Chapter II. Differentiating Functions 37
§ 1. Direct calculation of derivatives 37
§ 2. Tabular differentiation 41
§ 3. Derivatives of functions that are not explicitly given 51
§ 4. Geometric and mechanical applications of the derivative 54
§ 5. Higher-order derivatives 60
§ 6. Differentials of the first and higher orders 65
§ 7. Mean theorems 69
§ 8. Taylor's formula 71
§ 9. L'Hôpital-Bernoulli rule for disclosure of uncertainties 72
Chapter III. Extrema of a function and geometric applications of the derivative 77
§ 1. Extrema of a function of one argument 77
§ 2. Direction of concavity. Inflection points 85
§ 3. Asymptotes 87
§ 4. Construction of graphs of functions by characteristic points 89
§ 5. The differential of the arc. Curvature 94
Chapter IV. Indefinite integral 100
§ 1. Direct integration 100
§ 2. Substitution method 107
§ 3. Integration by parts, 110
§4. Simplest Integrals Containing a Square Trinomial 112
§ 5, Integration of rational functions 116
§ 6. Integration of some irrational functions 121
§ 7. Integration of trigonometric functions 124
S 8> Integration hyperbolic functions 129
§ 9. Application of trigonometric and hyperbolic substitutions to find integrals of the form \ Ux,> jax + bx + c) dx t
where R is a rational function 130
| 10. Integration of various transcendental functions 131
| 11. Application of reduction formulas 132
§ 12. Integration different functions 132
Chapter V- The Definite Integral 135
§ 1. The definite integral as the limit of the sum 135
§ 2. Calculation of definite integrals by means of indefinite ones 137
§ 3. Improper integrals 140
§ 4. Change of variable in a definite integral 144
§ 5. Integration by parts 146
§ 6. Mean value theorem 147
§ 7. Areas of flat figures 149
§ 8. Length of an arc of a curve 154
§ 9. Volumes of bodies 157
§ 10, Surface area of revolution 161
§eleven. Moments. Centers of gravity. Gulden's Theorems 163
§ 12. Applications of definite integrals to the solution of physical problems 168
Chapter VI. Functions of several variables 174
§ 1. Basic concepts of 17F
§ 2. Continuity 178
§ 3. Partial derivatives 179
§ 4. Total differential of a function 182
§ 5. Differentiation of complex functions 185
§ 6. Derivative in this direction and the gradient of the function 189
§ 7. Derivatives and differentials of higher orders ... 192
§ 8. Integration of total differentials 198
§ 9. Differentiation of Implicit Functions 200
§ 10. Change of variables 207
§eleven. Tangent Plane and Normal to Surface 213
§ 12. Taylor's formula for a function of several variables 217
§ 13. Extremum of a function of several variables 219
§ 14. Problems of finding the largest and smallest values of functions 225
§ 15. Singular points of plane curves 227
§ 16 Envelope 229
§17. Space Curve Arc Length 231
§ 18. Vector functions of scalar argument 231
§ 19. The natural trihedron of the space curve 235
§ 20. Curvature and torsion of a space curve 239
Chapter VII. Multiple and Curvilinear Integrals 242
§ 1. Double integral in rectangular coordinates 242
§ 2. Change of variables in a double integral 248
§ 3. Calculation of the areas of figures 251
§ 4. Calculation of the volumes of bodies 253
§ 5. Calculation of the areas of surfaces 255
% 6. Applications of the double integral to mechanics 256
§ 7, Triple Integrals 258
§ 8. Improper integrals depending on a parameter.
Improper Multiple Integrals 264
§ 9. Curvilinear integrals 268
§ 10. Surface integrals 279
8 11. Formula Ostrogradskiy-Gauss 282
& 12. Elements of field theory 283
Chapter VIII. Rows 288
§ 1. Number series 288
§ 2. Functional series 300
& 3. Taylor Series 307
§ 4. Fourier series 315
Chapter IX. Differential Equations 319
§ 1. Verification of solutions. Compilation of differential equations for families of curves. Initial conditions 319
§ 2- Differential equations of the 1st order 322
§ 3. Differential equations of the 1st order with separable variables. Orthogonal paths 324
§ 4, Homogeneous differential equations of the 1st order 327
§ 5. Linear differential equations of the 1st order. Bernoulli's Equation 329
§ 6. Equations in total differentials. Integrating Factor 332
§ 7. Differential equations of the 1st order, not solved
with respect to the derivative, 334
§ S. The Lagrange and Clairaud Equations 337
§9. Mixed differential equations of the 1st order 339
§ 10. Differential equations of higher orders 343
§ 11. Linear differential equations 347
§ 12. Linear differential equations of the second order
with constant coefficients 349
§ 13, Linear differential equations with constants
coefficients of the order of higher than 2nd 355
§ 14. Euler's equations 356
§ 15. Systems of differential equations 358
§ 16. Integration of differential equations using
power series 360
§ 17. Problems for the Fourier method 362
Chapter X. Approximate Calculations 366
§ 1. Actions with approximate numbers 366
§ 2. Interpolation of functions 371
§ 3. Calculation of real roots of equations 375
§ 4. Numerical integration of functions 382
§ 5, Numerical Integration of Ordinary Differential Equations 385
§ 6. Approximate calculation of the Fourier coefficients 394
Answers, solutions, instructions 396
Applications 484
I- Greek alphabet 484
II. Some Constants 484
W. Reciprocals, degrees, roots, logarithms 485
IV. Trigonometric Functions 487
V. Exponential, hyperbolic and trigonometric functions488
Vi. Some curves 489
Moscow: 2005 ... - 560 p.
The collection includes over 4000 problems and exercises on the most important sections of mathematical analysis: introduction to analysis, differential calculus of functions of one variable, indefinite and definite integrals, series, differential calculus of functions of several variables, integrals depending on a parameter, multiple and curvilinear integrals. Almost all problems have been answered! The appendix contains the answers. For students of physics and mechanics and mathematics specialties of higher educational institutions
Format: pdf (2005 , 560s.)
The size: 5 Mb
Watch, download:drive.google
Format: pdf (1998 , 14th ed., Rev., 624s.)
The size: 13 Mb
Watch, download:drive.google
Format: djvu / zip (1997 , 13th ed., Rev., 624s.)
The size: 5, 8Mb
/ Download file
● i-stres.narod.ru - Here you can find solutions to problems from the collection of mat. analysis B.P. Demidovich ... The numbers of the laid out problems correspond to the 2003 edition. ("AST", "Astrel")
● truba.nnov.ru - People's Reshebnik - 115 solved tasks from Demidovich's collection.
Tasks and exercises in mathematical analysis for technical colleges. Under. ed. Demidovich B.P. M., 2001 Textbook for students of higher. tech. educational institutions. (Each paragraph contains a little theory, examples of solving problems and tasks.) The book can be downloaded from the site in 10 separate chapters, each 600-800 KB.) Then it is unzipped into separate gif files and viewed in any standard program as a set of photographs. (located on the site math.reshebnik.ru )
TABLE OF CONTENTS
PART ONE FUNCTIONS OF ONE INDEPENDENT VARIABLE
Section I. Introduction to Analysis 7
§ I. Real numbers 7
§ 2. Sequence theory 12
§ 3. The concept of a function 26
§ 4. Graphic representation of a function .... 35
§ 5. Limit of a function 47
§ 6. O-symbolism 72
§ 7. Continuity of a function 77
§ 8. Inverse function. Functions Defined Parametrically 87
§ 9. Uniform continuity of a function ... 90
§ 10. Functional equations 94
Section II. Differential calculus of functions of one variable 96
§ 1. Derivative of an explicit function 96
§ 2. Derivative of the inverse function. Derivative of a parametrically defined function. Derivative of an implicit function. ... ... .114
§ 3. The geometric meaning of the derivative 117
§ 4. Differential of function 120
§ 5. Derivatives and differentials of higher orders 124
§ 6. Theorems of Rolle, Lagrange and Cauchy .... 134
§ 7. Increase and decrease of a function. Inequalities 140
§ 8. Direction of concavity. Inflection points. ... 144
§ 9. Disclosure of uncertainties 147
§ 10. Taylor's formula 151
§eleven. Extremum function. Largest and Smallest Function Values 156
§ 12. Construction of graphs of functions by characteristic points 161
§ 13. Problems for maximum and minimum functions. ... ... 164
§ 14. Tangency of curves. Circle of curvature. Evolution 167
§ 15. Approximate solution of equations .... 170
Section III. Indefinite Integral 172
§ 1. The simplest indefinite integrals ... 172
§ 2. Integration of rational functions ... 184
§ 3. Integration of some irrational functions 187
§ 4. Integration of trigonometric functions 192
§ 5. Integration of various transcendental functions 198
§ 6. Various examples for the integration of functions 201
Section IV. Definite Integral 204
§ 1. The definite integral as the limit of the sum. ... 204
§ 2. Calculation of definite integrals using indefinite 208
§ 3. Mean value theorems 219
§ 4. Improper integrals 223
§ 5. Calculation of areas 230
§ 6. Calculation of the lengths of arcs 234
§ 7. Calculation of volumes 236
§ 8. Calculation of the areas of surfaces of revolution 239
§ 9. Calculation of moments. Center of gravity coordinates 240
§ 10. Problems from mechanics and physics 242
§eleven. Approximate calculation of definite integrals 244
Division V. Ranks 246
§ 1. Number series. Convergence criteria for series of constant signs 246
§ 2. Criteria for the convergence of alternating series 259
§ 3. Actions on rows 267
§ 4. Functional series 268
§ 5. Power series 281
§ 6. Fourier series 294
§ 7. Summation of series 300
§ 8. Finding definite integrals using series 305
§ 9. Infinite works 307
§ 10. Stirling's formula 314
§ 11. Approximation of continuous functions by polynomials 315
PART TWO
FUNCTIONS OF MULTIPLE VARIABLES
Section VI. Differential calculus of functions of several variables 318
§ 1. Limit of a function. Continuity 318
§ 2. Partial derivatives. Differential function 324
§ 3. Differentiation of implicit functions .... 338
§ 4. Change of variables 348
§ 5. Geometric applications 361
§ 6. Taylor's formula 367
§ 7. Extremum of a function of several variables 370
Section VII. Parameter-dependent integrals. ... 379
§ 1. Proper integrals depending on a parameter 379
§ 2. Improper integrals depending on a parameter. Uniform convergence of integrals 385
§ 3. Differentiation and integration of improper integrals under the integral sign,. 392
§ 4. Euler integrals 400
§ 5. Fourier integral formula 404
Section VIII. Multiple and curvilinear integrals. 406
§ 1. Double integrals 406
§ 2. Calculation of areas, 414
§ 3. Calculation of volumes 416
§ 4. Calculation of the areas of surfaces .... 419
§ 5. Applications of double integrals to mechanics 421
§ 6. Triple integrals 424
§ 7. Calculation of volumes by means of triple integrals 428
§ 8. Applications of triple integrals to mechanics 431
§ 9. Improper double and triple integrals 435
§ 10. Multiple integrals 439
§eleven. Curvilinear Integrals 443
§ 12. Formula Grnia 452
§ 13. Physical applications of curvilinear integrals. . "456
§ 14. Surface integrals 460
§ 15. Stokes formula 464
§ 16. Formula Ostrogradsky 466
§ 17. Elements of field theory 471
Replies480
DEMIDOVICH Boris Pavlovich
Boris Pavlovich Demidovich was born on March 2, 1906 in the family of a teacher at the Novogrudok city school. His father, Pavel Petrovich Demidovich (07/10/1871-7.03.1931), from the Belarusian peasants (the village of Nikolayevshchina, Stolbtsovsky district, Minsk province), managed to get a higher education, having graduated from the Vilnius Teachers' Institute in 1897. Throughout his life teaching (first in various cities of the Minsk and Vilna provinces, and then in Minsk itself), he enthusiastically studied family life, beliefs and rituals of Belarusians, wrote down works of Belarusian anonymous literature - gutarkas. In 1908, P.P. Demidovich was even elected a member of the Imperial Society of Lovers of Natural Science, Anthropology and Ethnography at Moscow University. B.P. Demidovich's mother, Olympiada Platonovna Demidovich (nee Plyshevskaya) (06.16.1876-19.10.1970), the daughter of a priest, was also a teacher before marriage, and after that she was only engaged in raising her children: in the family, besides Boris, there were his three sisters Zinaida, Evgenia, Zoya and his younger brother Pavel. After graduating from the 5th Minsk school in 1923, B.P. Demidovich entered the physics and mathematics department of the pedagogical faculty of the first university in Belarus, created in 1921 - the Belarusian State University. After graduating from BSU in 1927, he was recommended for postgraduate studies at the Department of Higher Mathematics, but did not pass the exam in the Belarusian language and left to work in Russia.
B.P. Demidovich works as a mathematics teacher in secondary educational institutions of the Smolensk and Bryansk regions (7-year-old school in Pochinki, Bryansk 9-year school named after the III International, Bryansk Construction College), and then, accidentally reading an ad in the local chronicle, arrives at Moscow and in 1931 entered a one-year postgraduate study at the Research Institute of Mathematics and Mechanics at Moscow State University. Upon completion of this short-term targeted postgraduate study, B.P. Demidovich is awarded the qualification of a teacher of mathematics at higher educational institutions. He receives a distribution at the Transport and Economic Institute of the NKPS, and teaches there in the Department of Mathematics in 1932-33. In 1933, while maintaining his teaching load at the TEI NKPS, B.P. Demidovich was still enrolled as a senior researcher in the Bureau of Experimental Transport Construction of the NKPS and worked there until 1934.At the same time, in 1932, B.P. Demidovich became ( by competition) postgraduate student of the Mathematical Institute of Moscow State University. In graduate school at MI Moscow State University, B.P. Demidovich began to study under the guidance of A.N. Kolmogorov's theory of functions of a real variable.
However, A.N. Kolmogorov, seeing that B.P. Demidovich was more interested in the problems of ordinary differential equations, advised him to devote himself to the study of the qualitative theory of ordinary differential equations under the guidance of V.V. Stepanov. The development at Moscow State University of qualitative methods in the theory of ordinary differential equations is inextricably linked with the organization organized in 1930 by V.V. Stepanov, a special seminar on this topic, in which B.P. Demidovich. Carrying out the general management of his studies, V.V. Stepanov assigned him, as a direct scientific adviser, his young colleague, who was then just completing his doctoral dissertation, V.V. Nemytsky. Between V.V. Nemytskiy and his essentially first graduate student B.P. Demidovich struck up the closest creative friendship for life. After completing his postgraduate studies at the Moscow State University in 1935, B.P. Demidovich has been working for one semester at the Department of Mathematics at the Institute of the Leather Industry. L.M. Kaganovich, and since February 1936, at the invitation of L.A. Tumarkin, is credited as an assistant of the Department of Mathematical Analysis of the Faculty of Mechanics and Mathematics of Moscow State University. From that time until the end of his days, he remains her permanent employee. In 1935, at MI MSU B.P. Demidovich defended his Ph.D. thesis "On the existence of an integral invariant on a system of periodic orbits". It was highly appreciated by the official opponent A.Ya. Khinchin; N.N. Luzin recommended publishing its main results in DAN SSSR, A.A. Markov gave a positive review for its detailed publication in the Mathematical Collection (although formally, publications on the candidate's dissertation were not mandatory at that time). The Qualification Commission of the People's Commissariat of Education of the RSFSR awards B.P. Demidovich in 1936, the degree of candidate of physical and mathematical sciences, and in 1938 he approved him in the academic rank of associate professor of the Department of Mathematical Analysis of Mechanics and Mathematics of Moscow State University. In 1963 B.P. Demidovich, at a meeting of the Academic Council of Mechmatics of Moscow State University, on the basis of his main works, he defended his doctoral dissertation under the general title "Limited solutions of differential equations" (official opponents V.V. Nemytsky, B.M. Levitan, V.A. enterprise "- Department of Ordinary Differential Equations of Matmeh Leningrad State University, Head of Department VA Pliss). In the same year, the Higher Attestation Commission awarded him the degree of Doctor of Physical and Mathematical Sciences, and in 1965 approved him in the academic rank of Professor of the Department of Mathematical Analysis of Mechmatics at Moscow State University. In 1968, the Presidium of the Supreme Soviet of the RSFSR assigned B.P. Demidovich the honorary title "Honored Scientist of the RSFSR". The scientific heritage of B.P. Demidovich is analyzed in great detail in the personalities indicated in the footnote. Repeating the conclusion of the authors of these personalities, five main directions of his scientific activity can be distinguished:
· Dynamic systems with integral invariants;
· Periodic and almost-periodic solutions of ordinary differential equations;
· Correct and completely correct (according to Demidovich) differential systems;
· Limited solutions of ordinary differential equations;
· Stability of ordinary differential equations, in particular, orbital stability of dynamical systems.
An overview of the results in these areas and a complete list of his scientific publications (he has about sixty) is given in the same persons. Along with scientific and pedagogical activities at Moscow State University, B.P. Demidovich taught concurrently at a number of leading universities in Moscow (MVTU named after N.E.Bauman, Military Engineering Academy named after F.E.Dzerzhinsky, etc.). High professionalism and rich pedagogical experience are reflected in the books written by him, in particular, the well-known University problem book on mathematical analysis (the number of publications of which only in our country is already in the second ten with a total circulation of over 1,000,000 copies), translated into many foreign languages, as well as a sustainability guide that has been popular with readers.
B.P. gave a lot of strength and energy. Demidovich to educate his students and followers, heading after the death of V.V. Stepanov and V.V. Nemytskiy at the Mekhmat Moscow State University, the aforementioned research seminar on the qualitative theory of ordinary differential equations (together with A.F. Filippov and M.I. Elshin). He was often invited to the Organizing Committees of both scientific conferences and school Olympiads. He actively collaborated with the editors of various mathematical journals ("Differential Equations", RZh "Mathematics"), as well as with the mathematical editorial board of "TSB". Distinguished by great diligence, responsibility and conscientiousness, Boris Pavlovich was a bit withdrawn by nature: this was partly due to the sad fact that in 1933 he was arrested, and then (1937) and illegally repressed under the notorious article "58 -prim" , his younger brother Pavel Pavlovich Demidovich is a young, talented physicist ("much more talented than me," he emphasized), who graduated from the pedagogical faculty of BSU in 1931 and for his great academic success left at the university for further specialization in the field of wave mechanics. Everyone who knew B.P. Demidovich, noting his sensitivity and responsiveness, treated him with deep respect and sincere sympathy. Having a large family (four children), with constant workload at his main job and part-time, studying at home in the evenings in cramped living conditions, he never refused to help colleagues, whether it was conducting classes with students or participating in Sunday work. B.P. died. Demidovich April 23, 1977 suddenly (diagnosis: acute cardiovascular failure). It happened on Saturday, at home. And the day before, on Thursday, he, as usual, gave his next lecture ...
