Demidovich mathematical analysis download pdf. Problems and exercises in mathematical analysis for college students. Ed. Demidovich B.P.

M.: 2005 . - 560 s.

The collection includes over 4,000 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 answers are included in the appendix. For students of physical and mechanical-mathematical specialties of higher education educational institutions

Format: pdf (2005 , 560s.)

Size: 5 MB

Watch, download:drive.google

Format: pdf (1998 , 14th ed., revised, 624 pp.)

Size: 13 MB

Watch, download:drive.google

Format: djvu/zip (1997 , 13th ed., revised, 624 pp.)

Size: 5, 8MB

/Download file

● i-stres.narod.ru - Here you can find solutions to problems from the collection of math. analysis B.P. Demidovich . The numbers of the posted problems correspond to the 2003 edition. ("AST", "Astrel")

● truba.nnov.ru - People's solution book - 115 solved problems from Demidovich's collection.

Tasks and exercises mathematical analysis for colleges and universities. Under. ed. Demidovich B.P. M., 2001 Tutorial for higher education students tech. educational institutions. (Each paragraph contains a little theory, examples of problem solving and tasks.) The book can be downloaded on the website in 10 separate chapters, each 600-800 Kb.) Then unzipped into separate files gif format and can be viewed in any standard program like a set of photographs. (located on the website 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. Concept of function 26
§ 4. Graphic image functions.... 35
§ 5. Limit of a function 47
§ 6. O-symbolism 72
§ 7. Continuity of function 77
§ 8. Inverse function. Parametrically defined functions 87
§ 9. Uniform continuity of a function... 90
§ 10. Functional equations 94
Division II. Differential calculus of functions of one variable 96
§ 1. Derivative of an explicit function 96
§ 2. Derivative inverse function. Derivative of a function defined parametrically. Derivative of a function specified implicitly. . . .114
§ 3. Geometric meaning of the derivative 117
§ 4. Differential of a function 120
§ 5. Derivatives and differentials of higher orders 124
§ 6. Theorems of Rolle, Lagrange and Cauchy.... 134
§ 7. Increasing and decreasing functions. Inequalities 140
§ 8. Direction of concavity. Inflection points. . 144
§ 9. Disclosure of uncertainties 147
§ 10. Taylor formula 151
§eleven. Extremum of the function. The largest and smallest values of a function 156
§ 12. Construction of graphs of functions using characteristic points 161
§ 13. Problems for maximum and minimum functions. . . 164
§ 14. Tangency of curves. Circle of curvature. Evolute 167
§ 15. Approximate solution of equations.... 170
Division 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 on integration of functions 201
Division IV. Definite integral 204
§ 1. The definite integral as the limit of a 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 arc lengths 234
§ 7. Calculation of volumes 236
§ 8. Calculation of 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
Section V. Rows 246
§ 1. Number series. Tests for the convergence of series of constant sign 246
§ 2. Tests 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 products 307
§ 10. Stirling formula 314
§ 11. Approximation of continuous functions by polynomials 315
PART TWO
FUNCTIONS OF SEVERAL VARIABLES
Section VI. Differential calculus of functions of several variables 318
§ 1. Limit of a function. Continuity 318
§ 2. Partial derivatives. Function differential 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. Integrals depending on a parameter. . 379
§ 1. Proper integrals depending on the 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 surface areas.... 419

§ 5. Applications of double integrals to mechanics 421
§ 6. Triple integrals 424
§ 7. Calculation of volumes using 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. Grnia formula 452
§ 13. Physical Applications curvilinear integrals. "456
§ 14. Surface integrals 460
§ 15. Stokes formula 464
§ 16. Ostrogradsky formula 466
§ 17. Elements of field theory 471
Answers480

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 (07/10/1871-03/7/1931), from Belarusian peasants (the village of Nikolaevshchina, Stolbtsovsky district, Minsk province), managed to obtain a higher education, graduating from the Vilna Teachers' Institute in 1897. Teaching all his life (first in various cities of the Minsk and Vilna provinces, and then in Minsk itself), he enthusiastically studied the family life, beliefs and rituals of the Belarusians, and wrote down works of Belarusian anonymous literature - gutarkas. In 1908, P.P. Demidovich was even elected as a member of the Imperial Society of Lovers of Natural History, Anthropology and Ethnography at Moscow University. B.P. Demidovich’s mother, Olympiada Platonovna Demidovich (nee Plyshevskaya) (06/16/1876-10/19/1970), the daughter of a priest, was also a teacher before her marriage, and after that she was only involved in raising her children: in the family, besides Boris, there were also his three sisters Zinaida, Evgeniya, Zoya and his younger brother Pavel. Having graduated 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 study at the Department of Higher Mathematics, but did not pass the exam in Belarusian language and leaves for work in Russia.
Four years B.P. Demidovich works as a mathematics teacher in secondary educational institutions of the Smolensk and Bryansk regions (7-year school in Pochinki, Bryansk 9-year school named after the III International, Bryansk Construction College), and then, having accidentally read an advertisement in the local newsreel, comes to Moscow and entered in 1931 a one-year graduate school at the Research Institute of Mathematics and Mechanics at Moscow State University. Upon completion of this short-term target postgraduate study, B.P. Demidovich is awarded the qualification of a teacher of mathematics at technical colleges. He receives an assignment to the Transport-Economic Institute of the NKPS, and teaches there in the Mathematics department 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) graduate student at the Mathematical Institute of Moscow State University. In graduate school at the Moscow State University, B.P. Demidovich began studying under the guidance of A.N. Kolmogorov's theory of functions of a real variable.
However, A.N. Kolmogorov, seeing that B.P. Demidovich is more interested in problems of ordinary differential equations, advised him to devote himself to studying the qualitative theory of ordinary differential equations under the guidance of V.V. Stepanova. The development of qualitative methods in the theory of ordinary differential equations at Moscow State University is inextricably linked with the organization organized in 1930 by V.V. Stepanov with a special seminar on this topic, active participant which becomes B.P. Demidovich. Carrying out general supervision of his studies, V.V. Stepanov assigned him his young colleague, who was then just finishing writing his doctoral dissertation, V.V., as a direct scientific consultant. Nemytsky. Between V.V. Nemytsky and his essentially first graduate student B.P. Demidovich began the closest creative friendship for the rest of his life. After graduating from graduate school at MI Moscow State University in 1935, B.P. Demidovich works for one semester at the Department of Mathematics at the Institute of Leather Industry named after. L.M. Kaganovich, and from February 1936, at the invitation of L.A. Tumarkin, is enrolled as an assistant in 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 remained its permanent employee. In 1935 at MI Moscow State University B.P. Demidovich defends his candidate's thesis "On the existence of an integral invariant on a system of periodic orbits." She was highly praised by official opponent A.Ya. Khinchin; N.N. Luzin recommended publishing its main results in DAN USSR, A.A. Markov gave a positive review of its detailed publication in the Mathematical Collection (although formally, for a candidate’s thesis, the presence of publications was then optional). The Qualification Commission of the People's Commissariat of Education of the RSFSR awards B.P. Demidovich in 1936 received the academic degree of Candidate of Physical and Mathematical Sciences, and in 1938 he was awarded the academic title of Associate Professor of the Department of Mathematical Analysis of the Faculty of Mechanics and Mathematics of Moscow State University. In 1963 B.P. Demidovich, at a meeting of the Academic Council of the Faculty of Mechanics and Mathematics of Moscow State University, based on the totality of his main works, defended his doctoral dissertation under the general title “Limited solutions of differential equations” (official opponents V.V. Nemytsky, B.M. Levitan, V.A. Yakubovich, “advanced enterprise" - Department of Ordinary Differential Equations of Matmekha Leningrad State University, head of the department V.A. Pliss). In the same year, the Higher Attestation Commission awarded him the academic degree of Doctor of Physical and Mathematical Sciences, and in 1965 confirmed him with the academic title of professor of the Department of Mathematical Analysis of Mekhmat MSU. In 1968, the Presidium of the Supreme Soviet of the RSFSR awarded B.P. Demidovich received the honorary title "Honored Scientist of the RSFSR". 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, we can highlight five main directions of its scientific activity:
· 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 dynamic systems.
Review of results in these areas and full list his scientific publications (he has about sixty of them) are listed in the same personalities. Along with scientific and pedagogical activities at Moscow State University, B.P. Demidovich taught part-time at a number of leading universities in Moscow (Moscow Higher Technical School named after N.E. Bauman, Military Engineering Academy named after F.E. Dzerzhinsky, etc.). High professionalism and rich teaching experience are reflected in the books he wrote, in particular, the well-known University Problem Book on Mathematical Analysis (the number of editions of which in our country alone is already in the second dozen with a total circulation of over 1,000,000 copies), translated into many foreign languages, as well as manuals on sustainability, which are always popular with readers.
B.P. gave a lot of strength and energy. Demidovich educated his students and followers, heading after the death of V.V. Stepanova and V.V. Nemytsky at the Faculty of Mechanics and Mathematics of Moscow State University, the above-mentioned research seminar on the qualitative theory of ordinary differential equations (together with A.F. Filippov and M.I. Elshin). He was often invited to join the Organizing Committees of both scientific conferences and school competitions. He actively collaborated with the editors of various mathematical journals (Differential Equations, Russian Journal of Mathematics), as well as with the mathematical editors of TSB. Distinguished by his great diligence, responsibility and conscientiousness, Boris Pavlovich was a little withdrawn by nature: this was partly explained by the sad fact that in 1933 he was arrested, and then (1937) illegally repressed under the notorious article “58-note” , 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 great success left his studies 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 a constant workload at his main job and part-time, studying at home in the evenings in cramped living conditions, he never refused to help his 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 4,000 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; rows; differential calculus of functions of several variables; integrals depending on a parameter; multiple and curvilinear integrals. Answers have been provided for almost all problems. The appendix contains (tables.
For students of physical and mechanical-mathematical specialties of higher educational institutions.

Collection of problems and exercises in mathematical analysis: Textbook. - 13th ed., rev. - M.: Publishing house Mosk. University, CheRo, 1997. - 624 p.
ISBN 5-211-03645-Х
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

Division I. Introduction to Analysis
§ 1. Real numbers
§ 2. Sequence theory
§ 3. Concept of function
§ 4. Graphic representation of a function
§ 5. Limit of a function
§ 6. O-symbolism
§ 7. Continuity of a function
§ 8. Inverse function. Parametrically defined functions
§ 9. Uniform continuity of a function
§ 10. Functional equations

Division II. Differential calculus of functions of one variable
§ 1. Derivative of an explicit function
§ 2. Derivative of the inverse function. Derivative of a function defined parametrically. Derivative of a function specified implicitly
§ 3. Geometric meaning of the derivative
§ 4. Differential of a function
§ 5. Derivatives and differentials of higher orders
§ 6. Theorems of Rolle, Lagrange and Cauchy
§ 7. Increasing and decreasing functions. Inequalities
§ 8. Direction of concavity. Inflection points
§ 9. Disclosure of uncertainties
§ 10. Taylor's formula.
§ 11. Extremum of a function. Largest and smallest values of a function
§ 12. Plotting function graphs using characteristic points
§ 13. Problems involving maximum and minimum functions
§ 14. Tangency of curves. Circle of curvature. Evolute
§ 15. Approximate solution of equations

Division 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 on integration of functions

Division IV. Definite integral
§ 1. The definite integral as the limit of a sum
§ 2. Calculation of definite integrals using indefinite integrals
§ 3. Theorems on mean values
§ 4. Improper integrals
§ 5. Calculation of areas
§ 6. Calculation of arc lengths
§ 7. Calculation of volumes
§ 8. Calculation of 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

Division V Rows
§ 1. Number series. Signs of convergence of series of constant sign
§ 2. Tests for the convergence of alternating series
§ 3. Actions on series
§ 4. Functional series
§ 5. Power series
§ 6. Fourier series
§ 7. Summation of series
§ 8. Finding definite integrals using series
§ 9. Infinite products
§ 10. Stirling formula
§ 11. Approximation of continuous functions by polynomials

PART TWO
FUNCTIONS OF SEVERAL VARIABLES

Section VI. Differential calculus of functions of several variables
§ 1. Limit of a function. Continuity
§ 2. Partial derivatives. Function differential
§ 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. Integrals depending on a parameter
§ 1. Proper integrals depending on the 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. Fourier integral formula

Section VIII. Multiple and curvilinear integrals
§ 1. Double integrals
§ 2. Calculation of areas
§ 3. Calculation of volumes
§ 4. Calculation of surface areas
§ 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. Ostrogradsky's formula
§ 17. Elements of field theory

Download the book Collection of problems and exercises in mathematical analysis - Demidovich B.P. - 1997

Publication date: 04/17/2010 07:44 UTC

Tags: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :: :.

M.: 2005 . - 560 s.

Format: pdf (2005 , 560s.)

Size: 5 MB

Watch, download:drive.google

Format: pdf (1998 , 14th ed., revised, 624 pp.)

Size: 13 MB

Watch, download:drive.google

Format: djvu/zip (1997 , 13th ed., revised, 624 pp.)

Size: 5, 8MB

/Download file

● truba.nnov.ru - People's solution book - 115 solved problems from Demidovich's collection.

Problems and exercises in mathematical analysis for college students. Under. ed. Demidovich B.P. M., 2001 Textbook for higher education students. tech. educational institutions. (Each paragraph contains a little theory, examples of problem solving and problems.) The book can be downloaded on the website 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 website 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. Concept of function 26
§ 4. Graphic representation of the function.... 35
§ 5. Limit of a function 47
§ 6. O-symbolism 72
§ 7. Continuity of function 77
§ 8. Inverse function. Parametrically defined functions 87
§ 9. Uniform continuity of a function... 90
§ 10. Functional equations 94
Division 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 function defined parametrically. Derivative of a function specified implicitly. . . .114
§ 3. Geometric meaning of the derivative 117
§ 4. Differential of a function 120
§ 5. Derivatives and differentials of higher orders 124
§ 6. Theorems of Rolle, Lagrange and Cauchy.... 134
§ 7. Increasing and decreasing functions. Inequalities 140
§ 8. Direction of concavity. Inflection points. . 144
§ 9. Disclosure of uncertainties 147
§ 10. Taylor formula 151
§eleven. Extremum of the function. The largest and smallest values of a function 156
§ 12. Construction of graphs of functions using characteristic points 161
§ 13. Problems for maximum and minimum functions. . . 164
§ 14. Tangency of curves. Circle of curvature. Evolute 167
§ 15. Approximate solution of equations.... 170
Division 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 on integration of functions 201
Division IV. Definite integral 204
§ 1. The definite integral as the limit of a sum. . 204
§ 2. Calculation of definite integrals using indefinite integrals 208
§ 3. Mean value theorems 219
§ 4. Improper integrals 223
§ 5. Calculation of areas 230
§ 6. Calculation of arc lengths 234
§ 7. Calculation of volumes 236
§ 8. Calculation of 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
Section V. Rows 246
§ 1. Number series. Tests for the convergence of series of constant sign 246
§ 2. Tests 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 products 307
§ 10. Stirling formula 314
§ 11. Approximation of continuous functions by polynomials 315
PART TWO
FUNCTIONS OF SEVERAL VARIABLES
Section VI. Differential calculus of functions of several variables 318
§ 1. Limit of a function. Continuity 318
§ 2. Partial derivatives. Function differential 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. Integrals depending on a parameter. . 379
§ 1. Proper integrals depending on the parameter 379

§ 2. Improper integrals depending on a parameter. Uniform convergence of integrals 385

§ 5. Applications of double integrals to mechanics 421
§ 6. Triple integrals 424
§ 7. Calculation of volumes using 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. Grnia formula 452
§ 13. Physical applications of curvilinear integrals. "456
§ 14. Surface integrals 460
§ 15. Stokes formula 464
§ 16. Ostrogradsky formula 466
§ 17. Elements of field theory 471
Answers480

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 (07/10/1871-03/7/1931), from Belarusian peasants (the village of Nikolaevshchina, Stolbtsovsky district, Minsk province), managed to obtain a higher education, graduating from the Vilna Teachers' Institute in 1897. Teaching all his life (first in various cities of the Minsk and Vilna provinces, and then in Minsk itself), he enthusiastically studied the family life, beliefs and rituals of the Belarusians, and wrote down works of Belarusian anonymous literature - gutarkas. In 1908, P.P. Demidovich was even elected as a member of the Imperial Society of Lovers of Natural History, Anthropology and Ethnography at Moscow University. B.P. Demidovich’s mother, Olympiada Platonovna Demidovich (nee Plyshevskaya) (06/16/1876-10/19/1970), the daughter of a priest, was also a teacher before her marriage, and after that she was only involved in raising her children: in the family, besides Boris, there were also his three sisters Zinaida, Evgeniya, Zoya and his younger brother Pavel. Having graduated 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 graduate school in the department of higher mathematics, but failed the exam in the Belarusian language and left to work in Russia.
Four years B.P. Demidovich works as a mathematics teacher in secondary educational institutions of the Smolensk and Bryansk regions (7-year school in Pochinki, Bryansk 9-year school named after the III International, Bryansk Construction College), and then, having accidentally read an advertisement in the local newsreel, comes to Moscow and entered in 1931 a one-year graduate school at the Research Institute of Mathematics and Mechanics at Moscow State University. Upon completion of this short-term target postgraduate study, B.P. Demidovich is awarded the qualification of a teacher of mathematics at technical colleges. He receives an assignment to the Transport-Economic Institute of the NKPS, and teaches there in the Mathematics department 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) graduate student at the Mathematical Institute of Moscow State University. In graduate school at the Moscow State University, B.P. Demidovich began studying 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 problems of ordinary differential equations; he advised him to devote himself to studying the qualitative theory of ordinary differential equations under the guidance of V.V. Stepanova. The development of qualitative methods in the theory of ordinary differential equations at Moscow State University is inextricably linked with the organization organized in 1930 by V.V. Stepanov with a special seminar on this topic, in which B.P. became an active participant. Demidovich. Carrying out general supervision of his studies, V.V. Stepanov assigned him his young colleague, who was then just finishing writing his doctoral dissertation, V.V., as a direct scientific consultant. Nemytsky. Between V.V. Nemytsky and his essentially first graduate student B.P. Demidovich began the closest creative friendship for the rest of his life. After graduating from graduate school at MI Moscow State University in 1935, B.P. Demidovich works for one semester at the Department of Mathematics at the Institute of Leather Industry named after. L.M. Kaganovich, and from February 1936, at the invitation of L.A. Tumarkin, is enrolled as an assistant in 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 remained its permanent employee. In 1935 at MI Moscow State University B.P. Demidovich defends his candidate's thesis "On the existence of an integral invariant on a system of periodic orbits." She was highly praised by official opponent A.Ya. Khinchin; N.N. Luzin recommended publishing its main results in DAN USSR, A.A. Markov gave a positive review of its detailed publication in the Mathematical Collection (although formally, for a candidate’s thesis, the presence of publications was then optional). The Qualification Commission of the People's Commissariat of Education of the RSFSR awards B.P. Demidovich in 1936 received the academic degree of Candidate of Physical and Mathematical Sciences, and in 1938 he was awarded the academic title of Associate Professor of the Department of Mathematical Analysis of the Faculty of Mechanics and Mathematics of Moscow State University. In 1963 B.P. Demidovich, at a meeting of the Academic Council of the Faculty of Mechanics and Mathematics of Moscow State University, based on the totality of his main works, defended his doctoral dissertation under the general title “Limited solutions of differential equations” (official opponents V.V. Nemytsky, B.M. Levitan, V.A. Yakubovich, “advanced enterprise" - Department of Ordinary Differential Equations of Matmekha Leningrad State University, head of the department V.A. Pliss). In the same year, the Higher Attestation Commission awarded him the academic degree of Doctor of Physical and Mathematical Sciences, and in 1965 confirmed him with the academic title of professor of the Department of Mathematical Analysis of Mekhmat MSU. In 1968, the Presidium of the Supreme Soviet of the RSFSR awarded B.P. Demidovich received the honorary title "Honored Scientist of the RSFSR". 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, we can distinguish five main areas of his scientific activity:
· 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 dynamic systems.
An overview of the results in these areas and a complete list of his scientific publications (he has about sixty of them) are given in the same personalities. Along with scientific and pedagogical activities at Moscow State University, B.P. Demidovich taught part-time at a number of leading universities in Moscow (Moscow Higher Technical School named after N.E. Bauman, Military Engineering Academy named after F.E. Dzerzhinsky, etc.). High professionalism and rich teaching experience are reflected in the books he wrote, in particular, the well-known University Problem Book on Mathematical Analysis (the number of editions of which in our country alone is already in the second dozen with a total circulation of over 1,000,000 copies), translated into many foreign languages, as well as manuals on sustainability, which are always popular with readers.
B.P. gave a lot of strength and energy. Demidovich educated his students and followers, heading after the death of V.V. Stepanova and V.V. Nemytsky at the Faculty of Mechanics and Mathematics of Moscow State University, the above-mentioned research seminar on the qualitative theory of ordinary differential equations (together with A.F. Filippov and M.I. Elshin). He was often invited to join the Organizing Committees of both scientific conferences and school Olympiads. He actively collaborated with the editors of various mathematical journals (Differential Equations, Russian Journal of Mathematics), as well as with the mathematical editors of TSB. Distinguished by his great diligence, responsibility and conscientiousness, Boris Pavlovich was a little withdrawn by nature: this was partly explained by the sad fact that in 1933 he was arrested, and then (1937) illegally repressed under the notorious article “58-note” , 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, was 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 a constant workload at his main job and part-time, studying at home in the evenings in cramped living conditions, he never refused to help his 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...

Problems and exercises in mathematical analysis for college students. Ed. Demidovich B.P.

M.: 2004 - 496 p. M.: 1968 - 472 p.

This collection contains over 3000 problems and covers all sections of the university course of higher mathematics. The collection contains the main theoretical information, definitions and formulas for each section of the course, as well as solutions to particularly important standard problems. The problem book is intended for university students, as well as for individuals engaged in self-education. The collection was formed as a result of many years of teaching by the authors of higher mathematics at higher technical institutions in Moscow. The collection contains problems and examples on mathematical analysis in relation to maximum program general course of higher mathematics at higher technical educational institutions. The collection covers all sections of the university course of higher mathematics (with the exception of analytical geometry). Special attention addressed to the most important sections of the course that require strong skills (finding limits, differentiation techniques, graphing functions, integration techniques, applications of definite integrals, series, solving differential equations).

Format: pdf(2004, 496 pp.)

Size: 11 MB

Watch, download: drive.google

Format: pdf(1968, 472 pp.)

Size: 8 MB

Watch, download: drive.google

TABLE OF CONTENTS
Preface 6
Chapter I. Introduction to Analysis 7
§ 1, Concept of function 7
§ 2. Graphs of elementary functions 12
§ 3. Limits 17
§ 4. Infinitely small and infinitely large 28
§ 5. Continuity of functions 31
Chapter II. Differentiation of 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 derivative 54
§ 5. Derivatives of higher orders 60
§ 6. Differentials of the first and higher orders 65
§ 7. Mean value theorems 69
§ 8. Taylor formula 71
§ 9. L'Hopital-Bernoulli rule for disclosing uncertainties 72
Chapter III. Extrema of the 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 using characteristic points 89
§ 5. Arc differential. Curvature 94
Chapter IV. Indefinite integral 100
§ 1. Direct integration 100
§ 2. Substitution method 107
§ 3. Integration by parts, 110
§4. The simplest integrals containing a quadratic trinomial 112
§ 5, Integration of rational functions 116
§ 6. Integration of some irrational functions 121
§ 7. Integration of trigonometric functions 124
S 8> Integration of hyperbolic functions 129
§ 9. Application of trigonometric and hyperbolic substitutions to find integrals of the form
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 - Definite integral 135
§ 1. The definite integral as the limit of the sum 135
§ 2. Calculation of definite integrals using indefinite integrals 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 plane figures 149
§ 8. Length of the 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 17F
§ 2. Continuity 178
§ 3. Partial derivatives 179
§ 4. Complete differential of a function 182
§ 5. Differentiation complex functions 185
§ 6. Derivative in a given direction and gradient of a 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 surface normal 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. Arc length of spatial curve 231
§ 18. Vector functions of a scalar argument 231
§ 19. Natural trihedron of a spatial curve 235
§ 20. Curvature and torsion of a spatial curve 239
Chapter VII. Multiple and curvilinear integrals 242
§ 1. Double integral in rectangular coordinates 242
§ 2. Change of variables in the double integral 248
§ 3. Calculation of the areas of figures 251
§ 4. Calculation of volumes of bodies 253
§ 5. Calculation of surface areas 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. Ostrogradsky-Gauss formula 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. Drawing up differential equations for families of curves. Initial conditions 319
§ 2-Differential equations of 1st order 322
§ 3. Differential equations of the 1st order with separable variables. Orthogonal trajectories 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 derivative, 334
§ S. Lagrange and Clairaut equations 337
§9. Mixed differential equations of 1st order 339
§ 10. Differential equations of higher orders 343
§ 11. Linear differential equations 347
§ 12. Linear differential equations of the 2nd order
with constant odds 349
§ 13, Linear differential equations with constants
coefficients of order 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 using 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 Fourier coefficients 394
Answers, solutions, directions 396
Applications 484
I- Greek alphabet 484
II. Some constants 484
W. Reciprocals, powers, roots, logarithms 485
IV. Trigonometric functions 487
V. Exponential, hyperbolic and trigonometric functions488
VI. Some curves 489