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Sorry for the long hiatus in posting over last few months.

We will begin with new posts in the new year, have several new titles to post! Till then hold on.

In this post, we will look at the book *Integral Equations In Elasticity* by V. Z. Parton, P. I. Perlin.

**About the book**

This book presents the fundamentals of the theory of regular and singular integral equations in the case of one and two variables. The general principles of the theory of approximate methods are considered as well as their application for the efficient solution of both regular and singular integral equations. The necessary information is given on the three-dimensional and two-dimensional equations of the theory of elasticity including the formulation of boundary value problems. The book contains the derivation and analysis of various integral equations of the plane problem for both fundamental boundary value problems and mixed problems, and also for bodies with cuts. In the three-dimensional case the construction and analysis of integral equations are carried out for the first and second fundamental problems.

Emphasis is placed on efficient methods for solving integral equations for the plane and three-dimensional problems of elasticity. Examples are given illustrating the advantages of a particular approach. The book is appended with an extensive list of references giving comprehensive information of the subject of investigation.

The emphasis on numerical methods for the solution of integral equations for elastostatic problems corresponds to the author’s conviction that this approach has considerable promise, particularly with the advent of the nearest-generation computers.

The scope of the book is limited to elastostatic problems though the extension of the methods described to dynamic problems apparently involves no fundamental difficulties.

The book was translated from the Russian by ???? and was published by Mir in 1982.

Many thanks to *Akbar Azimi* for the scans.

**Contents **

Preface to the English Edition 7

Preface to the Russian Edition 8

On the Formation of Integral Equation Methods in the Theory of Elasticity by D. I. Sherman 10

Notation 19

**Chapter 1 ELEMENTS OF THE THEORY OF ONE-DIMENSIONAL AND MULTIDIMENSIONAL INTEGRAL EQUATIONS **

1. Analytic Theory of a Resolvent 21

2. Cauchy-type Integral 35

3. Riemann Boundary Value Problem 48

4. Singular Integral Equations 52

5. Riemann Boundary Value Problem in the Case of Discontinuous Coefficients and Unclosed Contours 64

6. Singular Integral Equations in the Case of Discontinuous Coefficients and Unclosed Contours 71

7. Two-dimensional Singular Integrals 75

8. Two-dimensional Singular Integral Equations 89

**Chapter II APPROXIMATE METHODS FOR SOLVING INTEGRAL EQUATIONS **

9. General Principles of the Theory of Approximate Methods 98

10. Method of Successive Approximations 105

11. Mechanical Quadrature Method for Regular Integral Equations 111

12. Approximate Methods for Solving Singular Integral Equations 114

13. Approximate Methods for Solving Singular Integral ^

Equations (Continued) 120

**Chapter III FUNDAMENTAL PRINCIPLES OF THE MATHEMATICAL THEORY OF ELASTICITY **

14. Three-dimensional Problem 137

15. Plane Problem 137

16. Bending of Thin Plates 143

17. On Singular Solutions of Elastic Equations 148

**Chapter IV INTEGRAL EQUATIONS FOR TWO-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY **

18. Muskhelishvili’s Integral Equations 155

19. Sherman-Lauricella Integral Equations 159

20. Sherman-Lauricella Integral Equations (Continued) 164

21. Multiply (Doubly) Connected Regions 168

22. Problems of the Theory of Elasticity for Piecewise Homogeneous Bod ies 171

**Chapter V SOME SPECIAL TOPICS OF TWO-DIMENSIONAL ELASTICITY **

23. Problems of the Theory of Elasticity for Bodies with Cuts 175

24. Integral Equations for Mixed (Contact) Problems 179

25. Problems of the Theory of Elasticity for Bodies Bounded by Piecewise Smooth Contours 182

26. Method of Linear Relationship 186

27. Method of Linear Relationship (Continued) 189

**Chapter VI INTEGRAL EQUATIONS FOR FUNDAMENTAL THREE-DIMENSIONAL PROBLEMS OF THE THEORY OF ELASTICITY **

28. Generalized Elastic Potentials 199

29. Regular and Singular Integral-Equations for Fundamental Three-dimensional Problems 206

30. Extension of the Fredholm Alternatives to Singular Integral Equations of the Theory of Elasticity 215

31. Spectral Properties of Regular and Singular Integral Equations. Method of Successive Approximations 217

32. Differential Properties of Solutions of Integral Equations and Generalized Elastic Potentials 223

33. Approximate Methods of Solving Integral Equations for Fundamental Three-dimensional Problems 224

34. Problems of the Theory of Elasticity for Bodies Bounded by Several Surfaces 239

35. Three-dimensional Problems of the Theory of Elasticity for Bodies with Gut 244

36. Piecewise Homogeneous Bodies 253

37. Solution of Problems of the Theory of Elasticity for Bodies Bounded by Piecewise Smooth Surfaces 262

38. Mixed (Contact) Problems 269

Conclusion 274

References 277

Author Index 299

Subject Index 302

In this post, we will see the book *Plugging Materials and the Cementing of Wells* by A. Bulatov.

**About the book:**

This textbook, translated from the third Russian edition, is intended for students at technical schools specializing in the drilling of oil and gas wells. The book outlines the techniques of cementing oil and gas wells, based on current scientific developments and experience gained in applying advanced methods by the Soviet oil-industry specialists, and offers a description of cementing outfit, plugging cements, and chemicals used for their

treatment. It also surveys the properties of plugging mixtures (slurries) and cement stone under a variety of geological and technical conditions.One of the merits of the text is that it describes the composition of plugging cements and techniques employed in their preparation, which is of great importance in training technical personnel at oil fields.

The book will be of particular value in countries where oil is being produced with the participation of the Soviet specialists and with use of the Soviet-made equipment.

The book was translated from the Russian by *S. Kittell* and was published by Mir in 1985 (Second Edition).

Many thanks to *Akbar Azimi* for the scans.

**Contents**

Preface. 8

Introduction. 9

Chapter I. Methods of Casing Cementing. 13

1.1. Primary Cementing Methods. 13

1.2. Secondary (Remedy) Cementing Methods. 22

Chapter 2. Technology of Cementing Wells. 21

2.1. Flow Properties of Slurries. 24

2.2. Idea of Slurry Flow. 28

2.3. Preparation of Well Bore for Casing and Cementing. 30

2.4. Determining Well Bore Configuration and Volume. 35

2.5. Improving the Quality of Well Cementing. 38

2.6. Technological Parameters. 39

2.7. Spacer (Displacement) Fluids. 42

Chapter 3. Cementing Units and Cement Mixers. 44

3.1. Cementing Units. 44

3.2. Cementing Units of Special Construction. 55

3.3. Improvement of Cementing Units. 57

3.4. Citnent Mixers. 59

3.5. Cementing Process Control Station and Self-Propelled Manifold Unit.68

3.6. Cementing Process Calculations. 71

Chapter 4. Cementing Conditions and Requirements for the Quality of Cement Slurries and Stone. 85

4.1. Temperature and Pressure In Wells. 86

4.2. Stratal Waters. 88

4.3. Requirements to the Quality ot Plugging Mixture and Stone. 89

Chapter 5. Composition and Basic Properties of Portland Cement. 97

5.1. Classification of Plugging (Oil-Well) Cements and Mixtures. 97

5.2. Plugging Portland Cement. 99

5.3. Clinker Composition. 99

5.4. Quantitative Characteristics of Clinker. 101

5.5. Saturation Coefficient and Moduli of Portland Cement. 101

5.6. Estimated and Actual Mineralogical Composition of Portland Cement Clinker. 102

5.7. Brief Information on the Technology of Portland Cement Production. 104

5.8. Properties of Dry Cement Flour. 106

5.9. Active Mineral Additives io Binders. 107

5.10. Heat Liberation During Hardening of Plugging Mixtures. 108

Chapter 6. Properties of Cement Slurry and Cement Stone. 123

6.1. Sedimentation Stability of Cement Slurries. 123

6.2. Water Loss of Cement Slurry. 124

6.3. Thickening of Cement Slurry. 126

6.4. Setting Time of Cement Slurries. 127

6.5. Density of Cement Slurry. 129

6.6. Intemingling of Mud Fluids and Plugging Mixtures. 129

6.7. Contraction Effect in Hydration of Cement and in Hardening of Cement Slurry. 131

6.8. Mechanical Strength of Cement Stone. 132

6.9. Permeability of Cement Stone. 135

6.10. Adhesion of Cement Stone to Casing String Metal and to Rocks. 137

6.11. Changes in Volume of Plugging Cements (Slurries and Stone). 138

Chapter 7. Plugging Cement. 142

7.1. Definition and Composition of Plugging Cement. 142

7.2. Specifications for Granulated Coke-Smelting Blast-Furnace Slags. 143

7.3. Specifications for Plugging Cement. 143

7.4. Acceptance Rules. 144

7.5. Test Methods. 145

7.6. Transportation and Storage. 159

7.7. Determining the Permeability of Cement Stone. 159

Chapter 8. Adjusting the Properties of Cement Slurry and Cement Stone. 162

8.1. Cement Setting Retardants. 162

Chapter 9. Plugging Cements for High-Temperature Wells. 169

9.1. Cement-Sand Slurries. 169

9.2. Choice of Sand. 171

9.3. Proportioning of Cement-Sand Slurries. 173

9.4. Permeability of Cement-Sand Stone. 175

9.5. Slag-Sand Cements. 176

9.6. Setting Time and Mechanical Strength of Slag-Sand Slurries and Stone. 178

9.7. Slag-Sand Cements for Wells with Bottom-Hole Temperatures above 200 °C and Pressures up to 100 MPa. 182

9.8. Slag-Sand Cements with Sand of Natural Size. 182

9.9. Plugging Cements Based on Ferromanganese Slag. 184

9.10. Jointly Ground Slag-Sand Cements. 184

9.11. Separate and Combined Effects of Temperature and Pressure on Properties of Slag Slurries. 185

9.12. Effect of Storage Time on Properties ot Slag Cements. 185

9.13. Water Loss of Slag Slurries. 186

9.14. Adhesion of Slag Cements to Metal. 187

9.15. Slag Portland Cement. 187

9.16. Lime-Sand Slurries. 189

9.17. Belite-SIlica Cement. 190

Chapter 10. Cements for Low-Density Slurries and Weighted Cements. 191

10.1. Lightened Plugging Mixtures with Finely Ground Silica Additives. 197

10.2. Lightened Slag Slurries. 198

10.3. Weighted Cement Slurries. 200

10.4. Weighted Slag Slurries. 204

10.5. Aerated Cement Slurries. 204

Chapter 11. Cement Slurries Prepared with Concentrated Saline Solutions (Brines) 208

11.1. Dissolution of Saliferous Rocks in Plugging Mixtures. 209

11.2. Preparation of Salinized (Brine) Plugging Mixtures. 210

11.3. Effect of Salts on Pheological Properties of Plugging Mixtures. 212

11.4. Water Loss of Salinized (Brine) Plugging Mixtures. 213

11.5. Adhesion of Cement Stone to Salts. 214

11.6. Corrosion of Plugging Cement Stone. 214

11.7. Features Specific to Cementing of Wells in Permafrost Areas. 215

Chapter 12. Plugging Materials for Controlling Loss of Circulation. 219

12.1. Plugging Mixtures for Controlling Loss of Circulation in Drilling. 220

12.2. Quick-Setting Mixtures. 221

12.3. Gel-Cements. 223

12.4. Features Specific to the Setting of Quick-Taking Plugging Mixtures. Selection of Mixtures for Concrete Conditions. 223

Chapter 13. Special Plugging Cements and Mixtures. 225

13.1. Corrosion-Proof Plugging Cements. 225

13.2. Expanding Plugging Cements. 230

13.3. Gypsum as a Plugging Material. 231

13.4. Hydrophobic Cements. 233

13.5. Oil-Cement Slurries. 233

13.6. Organic and Organic-Mineral Materials for Cementing Wells. 235

Chapter 14. Facilities and Structures for Transporting, Mixing, and Storage of Plugging Materials. 248

14.1. Plugging Cement Storage Regulations.252

14.2. Arrangement, Operating Principle, and Technical Data of Railwayside Mechanized Plugging Cement Store. 254

14.3. GROZNEFT Installation for Preparing Dry Plugging Mixtures. 258

14.4. KRASNODARNEFTEGAZ Installation for Preparing Plugging Mixtures. 259

14.5. Laboratory Control over Plugging Materials. 260

Chapter 15. Organization of Cementing Jobs. Complications and Safety Engineering in Cementing of Wells. 268

15.1. Organization of Cementing Jobs 268

15.2. Complications in Cementing of Wells. 272

15.3. Accident Prevention in Handling Free-Flowing and Dusty Materials. 278

15.4. Accident Prevention in Cementing Jobs. 280

15.5. Safety in Handling Radioactive Isotopes. 282

15.6. Safety Regulations to be Observed when Working in Gaseous Environment and Handling Chemicals.283

15.7. Safety Regulations to be Observed when Working in Winter Time. 283

15.8. General Safety Rules. 284

Chapter 16. Cementing Quality Check. 285

Index 292

Posted in engineering, geology, mir books, mir publishers, soviet, technology
Tagged casing, cement, cementing, civil, construction, engineering, gas wells, mirtitles, mixtures, oil fields, oil wells, plugging, portland, process, quality, slurry, technology, wells
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In this post, we will see the book *Linear Algebra with Elements of Analytic Geometry* by A.S. Solodovnikov, G.A. Toropova.

**About the book**

This study aid follows the course on linear algebra with elementary analytic geometry and is intended for technical school students specializing in applied mathematics. The text deals with the elements of analytic geometry, the theory of matrices and determinants, systems of linear equations, vectors, and Euclidean spaces. The material is presented in an informal manner. Many interesting examples will help the reader to grasp the material easily.

The book was translated from the Russian by Tamara Baranovskaya and was published by Mir in 1990.

Original colour scan by Folkscanomy Mathematics.

**CONTENTS**

Preface 8

Part One. ANALYTIC GEOMETRY 10

Chapter 1. VECTORS IN THE PLANE AND IN SPACE. CARTESI AN COORDINATE SYSTEM 10

1.1. Vectors 10

1.2. Vector Basis in the Plane and in Space 20

1.3. Cartesian Coordinate System on a Straight Line, in the Plane, and in Space 28

Exercises to Chapter 1 35

Chapter 2. RECTANGULAR CARTESIAN COORDINATES. SIMPLE PROBLEMS IN ANALYTIC GEOMETRY 37

2.1. Projection of a Vector on an Axis 37

2.2. Rectangular Cartesian Coordinate System 40

2.3. Scalar Product of Vectors 47

2.4. Polar Coordinates 54

Exercises to Chapter 2 55

Chapter 3. DETERMINANTS 57

3.1. Second-Order Determinants. Cramer’s Rule 57

3.2. Third-Order Determinants 60

3.3. n-th-Order Determinants 62

3.4. Transposition of a Determinant 67

3.5. Expansion of a Determinant by Rows and Columns 69

3.6. Properties of nth-Order Determinants 71

3.7. Minors. Evaluation of nth-Order Determinants 77

3.8. Cramer’s Rule for an n x n System 82

3.9. A Homogeneous n x n System 86

3.10. A Condition for a Determinant to Be Zero 91

Exercises to Chapter 3 95

Chapter 4. THE EQUATION OF A LINE IN THE PLANE. A STRAIGHT LINE IN THE PLANE 100

4.1. The Equation of a Line 100

4.2. Parametric Equations of a Line 105

4.3. A Straight Line in the Plane and Its Equation 107

4.4. Relative Position of Two Straight Lines in the Plane 122

4.5. Parametric Equations of a Straight Line 124

4.6. Distance Between a Point and a Straight Line 125

4.7. Half-Planes Defined by a Straight Line 127

Exercises to Chapter 4 128

Chapter 5. CONIC SECTIONS 131

5.1. The Ellipse 131

5.2. The Hyperbola 140

5.3. The Parabola 148

Exercises to Chapter 5 153

Chapter 6. THE PLANE IN SPACE 156

6.1. The Equation of a Surface in Space. The Equation of a Plane 156

6.2. Special Forms of the Equation of a Plane 163

6.3. Distance Between a Point and a Plane. Angle Between Two Planes 168

6.4. Half-Spaces 169 Exercises to Chapter 6 171

Chapter 7. A STRAIGHT LINE IN SPACE 174

7.1. Equations of a Line in Space. Equations ofa Straight Line 174

7.2. General Equations of a Straight Line 178

7.3. Relative Position of Two Straight Lines 183

7.4. Relative Position of a Straight Line anda Plane 186

Exercises to Chapter 7 189

Chapter 8. QUADRIC SURFACES 192

8.1. The Ellipsoid 192

8.2. The Hyperboloid 195

8.3. The Paraboloid 198

Part Two. LINEAR ALGEBRA 202

Chapter 9. SYSTEMS OF LINEAR EQUATIONS 203

9.1. Elementary Transformations of a System of Linear Equations 203

9.2. Gaussian Elimination 205

Exercises to Chapter 9 216

Chapter 10. VECTOR SPACES 218

10.1. Arithmetic Vectors and Operations with Them 218

10.2. Linear Dependence of Vectors 222

10.3. Properties of Linear Dependence 227

10.4. Bases in Space R^n 230

10.5. Abstract Vector Spaces 233

Exercises to Chapter 10 239

Chapter 11. MATRICES 241

11.1. Rank of a Matrix 242

11.2. Practical Method for Finding the Rank of a Matrix 245

11.3. Theorem on the Rank of a Matrix 247

11.4. Rank of a Matrix and Systems of Linear Equations 249

11.5. Operations with Matrices 250

11.6. Properties of Matrix Multiplication 253

11.7. Inverse of a Matrix 255

11.8. Systems of Linear Equations in Matrix Form 259

Exercises to Chapter 11 263

Chapter 12. EUCLIDEAN VECTOR SPACES 266

12.1. Scalar Product. Euclidean Vector Spaces 266

12.2. Simple Metric Concepts in Euclidean Vector Spaces 269

12.3. Orthogonal System of Vectors. Orthogonal Basis 271

12.4. Orthonormal Basis 274

Exercises to Chapter 12 275

Chapter 13. AFFINE SPACES. CONVEX SETS AND POLYHEDRONS 277

13.1. The Affine Space A^n 277

13.2. Simple Geometric Figures in A^n 279

13.3. Convex Sets of Points in A^n. Convex Polyhedrons 282

Exercises to Chapter 13 286

Index 288

In this post we will see the book *Problems On The Equations Of Mathematical Physics* by *M. M. Smirnov*.

About the book

The aim of the present collection of problems is to illustrate the theory of partial differential equations as it is given in various textbooks.

The problems of this collection are divided in three paragraphs. The first paragraph contains introductory excercizes on the reduction of partial differential equations to canonical form. The second paragraph deals mainly with problems, the general solution of which can be formed by means of the method of characteristics e.g. Cauchy’s (or also Goursat’s) and mixed problems.In the third paragraph the most important method is presented, namely the separation of variables. This is done for mixed problems (for hyperbolic and parabolic equations) and for boundary value problems (elliptic equations).

The solutions of all excercizes are given. Most of the problems are accompanied by an explanation of the solution method used: so that this problem book can also be used for self study.

The book was published by Nordoff in 1967 and was translated from the Russian by W. I. M. Wils.

CONTENTS

**Part I. Problems 7**

**1. Reduction of partial differential equations with two independent variables to canonical form 7**

1. Equations of hyperbolic type 7

2. Equations of parabolic type 8

3. Equations of elliptic type 8

**2. The method of characteristics 9**

**3. Separation of variables 23**

1. Equations of hyperbolic type 26

2. Equations of parabolic type 33

3. Equations of elliptic type 38

**Part.II. Solutions and hints 43**

Posted in books, mathematics, physics, problem books, soviet
Tagged canonical form, cauchy's method, elliptic, hyperbolic, mathematical physics, mathematics, method of characteristics, parabolic, partial differential equations, physics, problems and solutions, reduction, separation of variables
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