The Hydrodynamics of The Hydrofoil

Posted on January 6, 2022 by The Mitr

 

In this post, we will see the book The Hydrodynamics Of The Hydrofoil by A. N. Panchenkov.

About the book

The results of the investigation in the area of the hydrofoil theory are systematized in this monograph. A great deal of attention is given to the mechanical-mathematical aspects of the hydrofoil theory and to the development of the effective methods for solving the basic equations in the hydrofoil theory.

The book considers the theory of steady motion of a wing with an arbitrary profile in a plane-parallel flow; the linear theory of thin hydrofoils in the two-dimensional and three-dimensional flows; the theory of a hydrofoil in an unsteady flow; problems of the interaction of hydrofoils and motion of hydrofoils near the interface of fluids with different densities.

The monograph is intended for scientists and engineer­ing personnel at scientific research and design organizations specializing in the area of hydrodynamics of the submerged hydrofoil, aerodynamics, and aerohydrodynamics.

The book was translated from Russian was published in 1970 by Defense Technical Information Center.

Credits to original uploaders.

You can get the book here (cleaned) and here.

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Contents

Abstract
Preface
Introduction
Table of Contents

PART I: THE THEORY OF THE SUBMERGED HYDROFOIL IN A PLANE- PARALLEL FLOW 1

CHAPTER I. LINEAR THEORY OF A THIN HYDROFOIL IN A PLANE-PARALLEL FLOW 1

CHAPTER II. THE THEORY OF THE SUBMERGED HYDROFOIL OF AN ARBITRARY PROFILE IN A PLANE-PARALLEL FLOW 31

CHAPTER III. THEORY OF THE HYDROFOIL IN A PLANE-PARALLEL FLOW OF FLUID OF FINITE DEPTH 61

CHAPTER IV. INTERACTION OF HYDROFOILS IN A PLANE PARALLEL FLOW 95

CHAPTER V. THEORY OF THE SUBMERGED HYDROFOIL IN A PLANE-PARALLEL UNSTEADY FLOW 147

CHAPTER VI. THE THEORY OF HYDROFOIL IN A PLANE-PARALLEL FLOW OF FLUIDS OF VARIOUS DENSITIES 175

PART TWO: THE THEORY OF THE SUBMERGED HYDROFOIL IN A THREE-DIMENSIONAL FLOW 210

CHAPTER VII. BASIC CONSIDERATIONS IN THE THEORY OF THE THEORY OF THE HYDROFOILS WITH FINITE SPAN 210

CHAPTER VIII. THE THEORY OF THE SUBMERGED HYDROFOIL IN THE THREE-DIMENSIONAL FLUID FLOW OF INFINITE DEPTH 232

CHAPTER IX. THE THEORY OF THE SUBMERGED HYDROFOIL IN A THREE-DIMENSIONAL FLUID FLOW OF FINITE DEPTH 368

CHAPTER X. INTERACTION OF SUBMERGED HYDROFOILS IN A THREE-DIMENSIONAL FLOW 392

CHAPTER XI. THE THEORY OF THE SUBMERGED HYDROFOIL
IN A THREE-DIMENSIONAL UNSTEADY STATE 414

CHAPTER XII. MOTION OF LIFTING SYSTEMS NEAR THE INTERFACE OF FLUIDS WITH DIFFERENT DENSITIES 464

REFERENCES 519

 

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Higher Mathematics – Suvorov

Posted on January 5, 2022 by The Mitr

In this post, we will see the book Higher Mathematics: Textbook for Technical Schools by I. Suvorov.

About the book

The book is divided into three parts. The first part deals with basic analytic geometry in the plane. The straight line and quadratic curves (conic sections) are treated in a condensed manner. The second part is on differential calculus in which limits and continuity, differentials and derivatives of elementary functions are treated with examples (mostly from physics). Problems of extrema are also treated in a separate chapter. The final part covers integral calculus – both indefinite and definite integrals are covered. The supplementary section covers differentiation of functions with several variables, expansion of functions using power series and problems and exercises.

The book was translated from Russian by M. V. Oak  and was edited by George Yankovsky. The book was published in 1965 by Peace Publishers.

Credits to original uploader.

You can get the book here.

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Contents

A. BASIC ANALYTIC GEOMETRY IN THE PLANE

Chapter I. Method of Coordinates 11

Chapter II. The Straight Line 22

Chapter III. Quadric Curves 39

B. ELEMENTS OF DIFFERENTIAL CALCULUS

Chapter IV. Theory of Limits 73

Chapter V. Function and Its Continuity 95

Chapter VI. Derivative Function 115

Chapter VII. Derivatives of Elementary Functions 128

Chapter VIII. Studying Functions with the Aid of Their Derivatives 154

Chapter IX. Differential 176

C. ELEMENTS OF INTEGRAL CALCULUS

Chapter X. Indefinite Integral 185

Chapter XI. The Definite Integral and Its Applications 205

D. SUPPLEMENT

Chapter XII. Differentiation of Functions of Several Variables 233

Chapter XIII. Expansion of a Function in a Power Series 240

E. PROBLEMS AND EXERCISES 258

F. A SHORT HISTORICAL NOTE 314

Index 317

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Generalized Functions (Vols. 1-6) – Gelfand, Shilov, Graev, Vilenkin, Pyatetskii-Shapiro

Posted on January 4, 2022 by The Mitr

In this post we will see the six volume set of Generalized Functions by I. M. Gelfand, G. E. Shilov, M. I. Graev, N. Ya. Vilenkin, I. I. Pyatetskii-Shapiro.

About the books

The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green’s function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel′fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory.

Volume 1 Properties And Operations is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.

Volume 2 Spaces Of Fundamental And Generalized Functions is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley–Wiener theorem.

In Volume 3 Theory Of Differential Equations, applications of generalized functions to the Cauchy problem for systems of partial differential equations with constant coefficients are considered. The book includes the study of uniqueness classes of solutions of the Cauchy problem and the study of classes of functions where the Cauchy problem is well posed. The last chapter of this volume presents results related to spectral decomposition of differential operators related to generalized eigenfunctions.

The main goal of Volume 4  Applications Of Harmonic Analysis is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces E⊂H⊂E′, where H is a Hilbert space, E′ is dual to E, and inclusions E⊂H and H⊂E′ are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.

The unifying idea of Volume 5 Integral Geometry And Representation Theory in the series is the application of the theory of generalized functions developed in earlier volumes to problems of integral geometry, to representations of Lie groups, specifically of the Lorentz group, and to harmonic analysis on corresponding homogeneous spaces. The book is written with great clarity and requires little in the way of special previous knowledge of either group representation theory or integral geometry; it is also independent of the earlier volumes in the series. The exposition starts with the definition, properties, and main results related to the classical Radon transform, passing to integral geometry in complex space, representations of the group of complex unimodular matrices of second order, and harmonic analysis on this group and on most important homogeneous spaces related to this group. The volume ends with the study of representations of the group of real unimodular matrices of order two.

The unifying theme of Volume 6 Representation Theory And Automorphic Forms is the study of representations of the general linear group of order two over various fields and rings of number-theoretic nature, most importantly over local fields (p-adic fields and fields of power series over finite fields) and over the ring of adeles. Representation theory of the latter group naturally leads to the study of automorphic functions and related number-theoretic problems. The book contains a wealth of information about discrete subgroups and automorphic representations, and can be used both as a very good introduction to the subject and as a valuable reference.

 

The books were translated by Eugene Saletan (Vol. 1), Morris Friedman, Amiel Feinstein, Christian Peltzer (Vol. 2), Meinhard Meyet (Vol. 3), Amiel Feinstein (Vol. 4), Eugene Saletan (Vol. 5), K. A. Hirsch (Vol. 6). The series was published between 1964-1969.  Vol 1 (1964) 1968 (Vol 2) 1967 (Vol 3), 1964 (Vol 4), 1966 (Vol 5), 1969 (Vol 6).

Credits to the original uploaders.

Volume 1 here.

Volume 2 here.

Volume 3 here.

Volume 4 here.

Volume 5 here.

Volume 6 here.

PS: I am not posting contents as it would make the post very long. If you want please post them in comments so that others can benefit.

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A Course on Mathematical Analysis – Khinchin

Posted on January 3, 2022 by The Mitr

In this post, we will see the book A Course on Mathematical Analysis by  A. Ya. Khinchin.

About the book

This course of mathematical analysis is a text-book for students of mechanico-mathematicaland physico-mathematical faculties of our universities (and to some extent of pedagogical institutes as well) ; it is intended as the main text-book in the study of a science which appears in the curriculum under the heading of mathematical analysis and which deals with the theory of limits, infinite series and differential calculus with simple applications of these subjects.

The book was translated from Russian was published in 1957.

Credits to original uploader.

You can get the book here.

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Contents

Chapter 1. FUNCTIONS 1

§ 1. Variables 1
§ 2. Functions 3
§ 3. The region of definition of a function 6
§ 4. Functions and formulae 7
§ 5. The geometrical representation of functions 11
§ 6. Elementary functions 13

Chapter 2. ELEMENTARY THEORY OF LIMITS 18

§ 7. Infinitesimal quantities 18
§ 8. Operations with infinitesimal quantities 23
§ 9. Infinitely large quantities 26
§ 10. Quantities which tend to limits 29
§ 11. Operations with quantities which tend to limits 33
§ 12. Infinitesimal and infinitely large quantities of different orders 39

Chapter 3. THE DEVELOPMENT OF THE ACCURATE THEORY OF LIMIT TRANSITION 45

§ 13. The mathematical definition of a process 45
§ 14. The accurate concept of limits 47
§ 15. The development of the concept of limit transitions 52

Chapter 4. REAL NUMBERS 56

§ 16. Necessity of producing a general theory of real numbers 56
§ 17. Construction of a continuum 59
§ 18. Fundamental lemmas 69
§ 19. Final points in connection with the theory of limits 74

Chapter 5. CONTINUOUS FUNCTIONS 79

§ 20. Definition of continuity 79
§ 21. Operations with continuous functions 84
§ 22. Continuity of a composite function 85
§ 23. Fundamental properties of continuous functions 87
§ 24. Continuity of elementary functions 94

Chapter 6. DERIVATIVES 98

§ 25. Uniform and non-uniform variation of functions 98
§ 26. Instantaneous velocity of non-uniform movement 101
§ 27. Local density of a heterogeneous rod 106
§ 28. Definition of a derivative 108
§ 29. Laws of differentiation 110
§ 30. The existence of functions and their geometrical illustration 123

Chapter 7. DIFFERENTIALS 128

§ 31. Definition and relationship with derivatives 128
§ 32. Geometrical illustration and laws for evaluation 132
§ 33. Invariant character of the relationship between a derivative and a differential 134

Chapter 8. DERIVATIVES AND DIFFERENTIALS OF HIGHER ORDERS 136

§ 34. Derivatives of higher orders 136
§ 35. Differentials of higher orders and their relationship with derivatives 139

Chapter 9. MEAN VALUE THEOREMS 142

§ 36. Theorem on finite increments 142
§ 37. Evaluation of limits of ratios of infinitely small and infinitely large quantities 147
§ 38. Taylor’s formula 154
§ 39. The last term in Taylor’s formula 158

Chapter 10. APPLICATION OF DIFFERENTIAL CALCULUS TO ANALYSIS OF FUNCTIONS 164

§ 40. Increasing and decreasing of functions 164
§ 4l. Extrema 167

Chapter 11. INVERSE OF DIFFERENTIATION 175

§ 42. Concept of primitives 175
§ 43. Simple general methods of integration 182

Chapter 12. INTEGRAL 193

§ 44. Area of a curvilinear trapezium 193
§ 45. Work of a variable force 198
§ 46. General concept of an integral 201
§ 47. Upper and lower sums 204
§ 48. Integreability of functions 207

Chapter 13. RELATIONSHIP BETWEEN AN INTEGRAL AND A PRIMITIVE 213

§ 49. Simple properties of integrals 213
§ 50. Relationship between an integral and a primitive 218
§ 51. Further properties of integrals 223

Chapter 14. THE GEOMETRICAL AND MECHANICAL APPLICATIONS OF INTEGRALS 230

§ 52. Length of an arc of a plane curve 230
§ 53. Lengths of arcs of curves in space 241
§ 54. Mass, centre of gravity and moments of inertia of a material plane curve 242
§ 55. Capacities of geometrical bodies 247

Chapter 15. APPROXIMATE EVALUATION OF INTEGRALS 254

§ 56. Problematic set up 254
§ 57. Method of trapeziums 257
§ 58. Method of parabolas 262

Chapter 16. INTEGRATION OF RATIONAL FUNCTIONS 265

§ 59. Algebraical introduction 265
§ 60. Integration of simple fractions 274
§ 61. Ostrogradskij’s method 277

Chapter 17. INTEGRATION OF THE SIMPLE RATIONAL AND TRANSCENDENTAL FUNCTIONS 282

§ 62. Integration of functions of the type R(x,\sqrt[n]{\frac{ax+b}{cx+d}}) 282
§ 63. Integration of functions of the type R (x, \sqrt{ax^{2}+ bx +c}) 284
§ 64. Primitives of binomial differentials 287
§ 65. Integration of trigonometrical differentials 289
§ 66. Integration of differentials containing exponential
functions 294

Chapter 18. NUMERICAL INFINITE SERIES 297

§ 67. Fundamental concepts 297
§ 68. Series with constant signs 305
§ 69. Series with variable signs 316
§ 70. Operations with series 320
§ 71. Infinite products 326

Chapter 19. INFINITE SERIES OF FUNCTIONS 333

§ 72. Region of convergence of a series of functions 333
§ 73. Uniform convergence 335
§ 74. The continuity of the sum of a functional series 340
§ 75. Term-by-term integration and differentiation of series 344

Chapter 20 POWER SERIES AND SERIES OF POLYNOMIALS 351

§ 76. Region of convergence of a power series 351
§ 77. Uniform convergence and its consequences 357
§ 78. Expansion of functions into power series 361
§ 79. Series of polynomials 369
§ 80. Theorem of Weierstrass 372

Chapter 21. TRIGONOMETRICAL SERIES 377

§ 81. Fourier coefficients 377
§ 82. Average approximation 383
§ 83. Dirichlet-Liapunov theorem on closed trigonometrical systems 388
§ 84. Convergence of Fourier series 394
§ 85. Generalised trigonometrical series 396

Chapter 22. DIFFERENTIATION OF FUNCTIONS OF SEVERAL VARIABLES 400

§ 86. Continuity of functions of several independent variables 400
§ 87. Two-dimensional continuum 403
§ 88. Properties of continuous functions 408
§ 89. Partial derivatives 410
§ 90. Differentials 413
§ 91. Derivatives in arbitrary directions 419
§ 92. Differentiation of composite and implicit functions 422
§ 93. Homogeneous functions and Euler theorem 427
§ 94. Partial derivatives of higher orders 429
§ 95. Taylor’s formula for functions of two variables 433
§ 96. Extrema 438

Chapter 23. SOME SIMPLE GEOMETRICAL APPLICATIONS OF DIFFERENTIAL CALCULUS 443

§ 97. Equations of tangent and normal to a plane curve 443
§ 98. Tangential line and normal plane to a curve in space 446
§ 99. Tangential and normal planes to a surface 448
§ 100. Direction of convexity and concavity of a curve 451
§ 101. Curvature of a plane curve 453
§ 102. Tangential circle 458

Chapter 24. IMPLICIT FUNCTIONS 462

§ 103. The simplest problem 462
§ 104. The general problem 469
§ 105. Ostrogradskij’s determinant 475
§ 106. Conditional extremum 483

Chapter 25. GENERALISED INTEGRALS 491

§ 107. Integrals with infinite limits 491
§ 108. Integrals of unbounded functions 504

Chapter 26. INTEGRALS OF PARAMETRIC FUNCTIONS 514

§ 109. Integrals with finite limits 514
§ 110. Integrals with infinite limits 526
§ 111. Examples 535
§ 112. Euler’s integrals 541
§ 113. Stirling’s formula 548

Chapter 27. DOUBLE AND TRIPLE INTEGRALS 557

§ 114. Measurable plane figures 557
§ 115. Volumes of cylindrical bodies 567
§ 116. Double integral 571
§ 117. Evaluation of double integrals by means of two simple integrations 576
§ 118. Substitution of variables in double integrals 584
§ 119. Triple integrals 590
§ 120. Applications 593

Chapter 28. CURVILINEAR INTEGRALS 602

§ 121. Definition of a plane curvilinear integral 602
§ 122. Wark of a plane field of force 610
§ 123. Green’s formula 612
§ 124, Application to differentials of functions of two variables 617
§ 125. Curvilinear integrals in space 622

Chapter 29. SURFACE INTEGRALS 626

§ 126. The simplest case 626
§ 127. General definition of surface integrals 630
§ 128. Ostrogradskij’s formula 637
§ 129. Stoke’s formula 642
§ 130. Elements of the field theory 647

CONCLUSION – Short historical sketch 653

INDEX 665

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A Course of Higher Mathematics (Vols. 1 – 5) – Smirnov

Posted on January 2, 2022 by The Mitr

In this post, we will see the six volume A Course of Higher Mathematics by V. I. Smirnov.

About the Course

Volume I Elementary Calculus is primarily concerned with differential and integral calculus. Particular emphasis is given to functional relationships in the theory of limits. The book also treats series, functions of several variables and complex numbers.

Volume 2 Advanced Calculus: This volume is primarily concerned with advanced calculus. Covered are ordinary differential equations, linear differential equations, multiple and line integrals, vector analysis and field theory, and the mathematics necessary for the discussion of problems in classical field theory.

Volume 3, Part 1 Linear Algebra: The first part of Volume III gives a full account of the two branches of modern algebra — linear algebra and the theory of groups —which are most frequently used in theoretical physics.

Volume 3, Part II Complex Variables – Special Functions: The second part of Volume III is primarily concerned with the theory of complex variables. It presents a complete picture of the aspects of the theory which are of most direct interest to applied mathematicians.

Volume 4 Integral and Partial Differential Equations: This volume begins with full accounts of the theory of integral equations and with the calculus of variations. Included are the fundamental theory of partial differential equations and systems of equations in which characteristics plays a central role.

Volume 5 Integration and Functional Analysis: The final volume presents the theory of integration and elements of functional analysis. Although functional analysis has become a very abstract discipline, its general results can be used to derive the solution of particular problems in classical analysis and in applied mathematics.

The course was translated by D. E. Brown and edited by I. N. Sneddon and was first published in 1964.

Credits to the Original uploaders.

Volume 1 here.

Volume 2 here.

Volume 3 Part 1 here.

Volume 3 Part 2 here.

Volume 4 here.

Volume 5 here.

 

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Happy New Year and 2021 in Review

Posted on January 2, 2022 by The Mitr

Happy New Year to All!

Hope this year is better than the last,

The last one went on very very fast..

Thank you for being with us over the years!

Here are some stats from the last year and resolutions for the next..

Views and Visitors

We had a little over 300,000 views this year with about 64 k unique visitors.

Places

As for the reach except for a few countries mostly from central-western Africa, we have covered almost all the globe. Of course most of our visitors are from India, but I am happy that we reached out to these many places and people!

 

Posts

For almost last three months or so, we have made at least one post a day – hope we are able to continue this next year too.

Resolutions

  1. to try to post at least one post a day for every day of the new year – we do have enough books to do this!
  2. There are about 250 books to be scanned, will try to finish in a workshop mode with some friends – will keep you posted.
  3. Get the printing of books done – I am guilty for this to happen, we had made the post  regarding printing last April and its still in production hell (as they call it). We hope to sort this one out before this April (Keep fingers crossed).
  4. Create LaTeX versions of more books ( a few are in pipeline) will keep you posted.
  5. Purchase new physical copies (getting rarer by the day). We might need your help in this – will post updates later.

Anyways hoping that this year is good for all of us!

Posted in books, meta | Tagged , , , | 1 Comment

Continued Fractions – Khinchin

Posted on January 1, 2022 by The Mitr

In this post, we will see the book Continued Fractions by A. Ya. Khinchin.

About the book

The late Alexander J. Khinchin was born in Russia in 1894. One of the founders of the Soviet school of probability theory, Khinchin was made a full professor at Moscow University in 1922 and held that position until his death. His teaching skill is discernible in the clear and straightforward presentation of his subject. Designed for use as an expository text in the university curriculum, the book is basically of an elementary nature, the author confining his attention to continued fractions with positive-integral elements. The essentials needed for applications in probability theory, mechanics, and, especially, number theory are given and the real number system is constructed from continued fractions. The last chapter is somewhat more advanced and deals with the metric, or probability, theory of continued fractions. This first English translation is based on the third edition of the text which was issued in 1961.

The book was translated from Russian by Scripta Technica and was published in 1964.

Credits to original uploader.

You can get the book here.

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Contents

Chapter I. Properties of the Apparatus 1

1. Introduction 1
2. Convergents 3
3. Infinite continued fractions 8
4. Continued fractions with natural elements 12

Chapter II. The Representation of Numbers by Continued Fractions 16

5. Continued fractions as an apparatus for representing real numbers 16
6. Convergents as best approximations 20
7. The order of approximation 28
8. General approximation theorems 34
9. The approximation of algebraic irrational numbers and Liouville’s transcendental numbers 45
10. Quadratic irrational numbers and periodic continued fractions 47

Chapter III. The Measure Theory of Continued Fractions 51

11. Introduction 51
12. The elements as functions of the number represented 52
13. Measure-theoretic evaluation of the increase in the elements 60
14. Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation 65
15. Gauss’s problem and Kuz’min’s theorem 71
16. Average values 86
95 Index

 

 

 

 

 

 

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The Fox Plays The Bear A Trick – Creanga

Posted on December 31, 2021 by The Mitr

In this post, we will see the book The Fox Plays The Bear A Trick by Ion Creanga.

The Angry Bear

The Sly Fox

 

About the book

This little book will tell you the story of a sly fox who tricks a big angry bear!

The book was translated from Moldovian by D. Melenchuk and was illustrated by W. Brinzey. The book was published by Kishinev Literatura Artistica, Moldova in 1983. A detailed review can be found here.

All credits to Guptaji.

You can get the book here (cleaned) and here.

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Please do help if you can!

Posted on December 31, 2021 by The Mitr

Internet Archive Needs Your Help!

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Melasia And The Bear by Marko Vovchok

Posted on December 30, 2021 by The Mitr

In this post, we will see the book Melasia And The Bear by Marko Vovchok.

About the book

This little book tells us the story of a little brave girl Melasia who faces a bear alone!

The book was translated from Russian by Mary Skrypnyk and was illustrated by Valentine Ulyanova. The book was published  by Veselka Publishers, Kiev in 1980.

All credits to Guptaji.

You can get the book here (cleaned) and here.

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Write to us: mirtitles@gmail.com

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Add new entries to the detailed book catalog here.

 

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