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Editor’s Preface to the Russian Edition

Author’s Preface to the First Edition

Chapter 1. Convective Diffusional Transfer
1-1. Basic Analytical Relations
1-2. Differential Transfer Equations
1-3. Thermodynamics of Transfer Processes
1-4. Multicomponent Mixtures
1-5. Derivation of Transfer Equations on the Basis of the Kinetic Theory of Gases
1-6. Transfer Equations for Asymmetric Fluids
1-7. Hydrodynamics of a Vortex Structure Fluid
1-8. Inhomogeneous Turbulence Heat Transfer
1-9. Elements of Nonlinear Thermomechanics in Continua
1-10. Distinguishing Features of Rheological Hydrodynamics
1-11. On Hyperbolic Heat- and Mass-Transfer Equations

Chapter 2. Heat Conduction
2-1. Differential Equation of Heat Conduction
2-2. Initial and Boundary Conditions
2-3. Heat Consumption Calculation Methods
2-4. Methods of Solving Heat-Conduction Problems
2-5. Steady-State Temperature Field
2-6. Solution of Steady-State Problems by the Conformal Mapping Technique
2-7. One-Dimensional Unsteady-State Field (Plate, Cylinder)
2-8. Temperature Waves
2-9. Boundary Conditions of the Fourth Kind
2-10. Two- and Three-Dimensional Problems

Chapter 3. Convective Heat Transfer
3-1. Heat and Mass Transfer in a Flow past a Flat Plate
3-2. Simultaneous Heat and Mass Transfer in a Laminar Flow past a Flat Plate
3-3. Heat and Mass Transfer in Pipe Flows and in Flows past Complex Geometries
3-4. Simultaneous Turbulent Heat and Mass Transfer
3-5. Free Convection
3-6. Thermoconvective Waves

Chapter 4. Conjugate Heat-Transfer Problems
4-1. Physical Basis of Conjugate Heat-Transfer Problems
4-2. Conjugation Number
4-3. Approximate Solution of Problems for a Plate in a Laminar Flow
4-4. Exact Solutions of Heat-Transfer Problems for a Plate (with a Heat Source) in Compressible Gas Flow
4-5. Asymmetric Problems without a Heat Source
4-6. Internal Conjugate Problems
4-7. Unsteady-State Heat Transfer with Laminar Flow of Incompressible Fluid in Plane and Circular Tubes
4-8. Conjugate Heat-Transfer Problem with Turbulent Fluid Flow

Chapter 5. Transport Phenomena in Capillary-Porous Bodies
5-1. Structural Properties
5-2. Thermodynamics of Surface Effects
5-3. Averaging Rules
5-4. Thermodynamic Properties of Moisture Transfer
5-5. Molecular-Kinetic Method
5-6. Heat Conduction in Capillary-Porous and Disperse Materials
5-7. Moisture Transfer in Porous Materials
5-8. Application of Capillary-Porous Materials in Space Engineering
5-9. Transfer Effects under Conditions of Weightlessness
5-10. Heat Pipes

Chapter 6. Analytical Heat and Mass Diffusion Theory
6-1. Differential Heat- and Mass-Transfer Equations
6-2. Differential Moisture-Transfer Equations in Drying Processes
6-3. Generalized System of Differential Heat- and Mass-Transfer Equations
6-4. Mass Transfer Similarity Numbers
6-5. Solution of Heat- and Mass-Transfer Equations at Generalized Boundary Conditions
6-6. Boundary Conditions of the Third Kind
6-7. Differential Equations of Filtration Through Porous Materials
6-8. Diffusion Through Porous Materials
6-9. Hyperbolic Differential Heat- and Mass-Transfer Equations and Their Solutions

References

Index

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A Practical Course In Chemical Technology by I. P. Muklyonov (Ed.)

Posted on September 24, 2026 by The Mitr

The course in chemical technology taught at chemical colleges and departments consists of three parts: lectures, practical studies, and laboratory work. A combination of these three teaching methods provides students with a sound foundation for studying any discipline of chemical technology.

This course is primarily aimed at presenting the basic laws of chemical technology, applicable to most chemical processes, as well as processes in the metallurgical, silicate, pulp and paper, and fuel processing industries. Studying the basic types of chemical processes—homogeneous and heterogeneous, non-catalytic and catalytic, electrochemical—and the associated reactors is combined with an analysis of concrete processes of greatest importance to the national economy. Particular attention is given to typical processes embodying the major aspects of chemical technology. The lectures and laboratory work also cover the structural materials used in the manufacture of chemical reactors.

In the 3rd Russian edition, emphasis is placed on the analysis of automated and computerized reactors, as well as new methods and instruments employed in the investigation of material properties. Thus, students performing laboratory work better assimilate the facts presented in lectures, acquire skills for controlling industrial processes with the aid of advanced instrumentation and computers, learn analytical procedures, and improve their techniques for processing experimental results.

In a laboratory, students carry out the first (according to the syllabus) experiment. Each work covers practically all stages of experimental procedures. First of all, students learn about the subject from the textbook in chemical technology, the present practical course, and the literature recommended at the end of each work. Then, they go through the safety rules to be observed in a chemical laboratory (see Appendix, p. 425) and the instructions for the work being carried out. After a briefing by the instructor (colloquium), students are assigned to conduct the experiment. Students then become familiar with the experimental setup, check whether it is assembled correctly, activate individual units, and calibrate some instruments.

The next stage is an experimental study of the effect of some process parameters on the course of the process. Some assignments involve the analysis of the effect of temperature, concentrations, time, and other factors within a broad range, enabling students to plot the process characteristics as a function of a particular variable. Students make the necessary calculations using the experimental results and write a report, including the statement of the problem and purpose of the work, process flow sheet calculations and plots based on the experimental results, and conclusions. An assignment must be stated in such a manner as to enable students to complete the experiment within six hours. Every student must carry out laboratory works from all six chapters, while particular assignments are given depending on his or her specialization.

Translated from the Russian by V. Vopyan

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Preface

Chapter 1. Noncatalytic Processes
Laboratory Work 1. Production of Phosphoric Fertilizers by Acid Decomposition of Natural Phosphates
Laboratory Work 2. Carbonization of Ammoniacal Brine
Laboratory Work 3. Froth-Bed Gas Absorption
Laboratory Work 4. Polycondensation of Dichloroethane and Sodium Polysulphide (Production of Polysulphide Rubbers or Thiokols)
Laboratory Work 5. The Kinetics of Sulphide Ore Roasting
Laboratory Work 6. The Kinetics of Dicalcium Silicate Formation
Laboratory Work 7. Coal Carbonization
Laboratory Work 8. Low-Temperature Carbonization
Laboratory Work 9. Pyrolysis of Petroleum Products
Laboratory Work 10. Studying the Oxidation Rate of Metals at Elevated Temperatures
Laboratory Work 11. Manufacture and Testing of Plastics

Chapter 2. Catalytic Processes
Laboratory Work 12. Catalytic Cracking of Petroleum Products
Laboratory Work 13. Contact Oxidation of Sulphur Dioxide
Laboratory Work 14. Oxidation of Ammonia
Laboratory Work 15. Dehydrogenation of Ethylbenzene
Laboratory Work 16. Catalytic Dehydrogenation of Alkylbenzenes
Laboratory Work 17. Dehydration and Dehydrogenation of Ethanol in the Production of Butadiene
Laboratory Work 18. Copolycondensation of Phenol and Formaldehyde
Laboratory Work 19. Catalytic Processes of Formaldehyde Production
A. Conversion of Methanol
B. Incomplete Oxidation of Methane
C. Conversion of Dimethyl Ether in a Fluidized Catalyst Bed
Laboratory Work 20. Esterification of Alcohols with Carboxylic Acids

Chapter 3. Automated and Computerized Apparatus
Laboratory Work 21. Automated Absorption Plants
Laboratory Work 22. Performance Analysis of Liquid-Phase Reactors
Laboratory Work 23. Optimization of a Contact Plant of Sulphuric Acid, Operating on a Double Contact-Double Absorption Principle
Laboratory Work 24. Analysis of Heterogeneous Catalytic Processes on an Automated Continuous-Circulation Plant
Laboratory Work 25. Analysis of Reactor Models
A. Continuous Tubular Reactor
B. Batch Perfectly Mixed Reactor
C. Continuous Perfectly Mixed Reactor and a Cascade of Reactors

Chapter 4. Electrochemical Processes
Laboratory Work 26. Electrolysis of Sodium Chloride Solution
Laboratory Work 27. Electrolysis of Lead Chloride Melt
Laboratory Work 28. Chromium Plating of Metals

Chapter 5. Preparation of Raw Materials and Material Analysis Techniques
Laboratory Work 29. Flotation
Laboratory Work 30. Water Treatment
Laboratory Work 31. Determination of Dispersity, Density of Solid Loose Materials, Density and Viscosity of Liquids
Laboratory Work 32. Analysis of the Porous Structure of Solids
A. Analysis of Porous Structure Using an Adsorption Vacuum System with a Quartz Spring Balance
B. Analysis of Secondary Structure of Porous Solids by Mercury Porometry
C. Determination of Specific Surface by the Low-Temperature Nitrogen Sorption Method
D. Determination of Specific Surface in a Chromatographic Vacuum
Laboratory Work 33. Analysis of Sorbent and Catalyst Structure by Electron Microscopy
Laboratory Work 34. Thermal Analysis
Laboratory Work 35. Analysis of Solid Materials by Infrared Spectroscopy
A. Location of the Maxima of the Main Absorption Bands in the Spectra of Known Compounds
B. Qualitative Analysis of a Mixture of Inorganic Salts by Infrared Spectra
C. Determination of the Structure of Inorganic Compounds from Infrared Spectra
Laboratory Work 36. Gas Analysis
Laboratory Work 37. Chromatographic Analysis of Multicomponent Gas and Liquid Mixtures
A. Effect of the Sample Injection Technique on the Accuracy of Analysis Results
B. Separation of Methane-Air Mixture
C. Qualitative and Quantitative Analysis of a Mixture of Aromatic Hydrocarbons
D. Analysis of a Mixture of Alkyl and Alkylene Benzenes
E. Separation and Quantitative Analysis of Mixtures Containing O₂, N₂, CO, CH₄, and CO₂

Appendix

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Foundations Of The Non Linear Theory Of Elasticity by V. V. Novozhilov

Posted on September 23, 2026 by The Mitr

This book is based on a course of lectures given by the author in 1947 in the Mathematical-Mechanical Department of Leningrad National University. It is devoted to the exposition of the theory of elasticity without any assumptions restricting the magnitude of elongations, displacements, or angles of rotation. It also examines, in a general formulation, the connection between stresses and strains in an isotropic elastic body.

Translated from the First (1948) Russian Edition by F. Bagemihl, H. Komm, W. Seidel

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Contents

Preface

Chapter I. The Geometry of Strain
§ 1. Coordinates
§ 2. The Angles Determining the Directions of the Coordinate Lines
§ 3. Strain Components
§ 4. Transformation of Strain Components Under Change of Axes
§ 5. Principal Axes of Strain
§ 6. Transformation of the Parameters e_r and u Under Change of Coordinate Axes
§ 7. Geometrical Meaning of the Parameters
§ 8. Fibers Preserving Direction Under Deformation
§ 9. Invariants of Strain and Rotation
§ 10. The General Picture of the Deformation in the Neighborhood of an Arbitrary Point of the Body
§ 11. Change in Volume
§ 12. On the Magnitude of Elongations and Shears
§ 13. The Theory of Small Deformations
§ 14. The Case of Small Deformations and Small Angles of Rotation
§ 15. The Transition to the Equations of the Classical Theory
§ 16. On the Transition to Curvilinear Coordinates

Chapter II. The Equilibrium of an Element of Volume of a Body
§ 17. Stresses
§ 18. Formulas for Transformation of Stress Components Under Change of Coordinate System
§ 19. Conditions for Equilibrium of an Elementary Parallelepiped Isolated From a Deformed Body
§ 20. Transformation of the Equations of Equilibrium of an Element of Volume to the Cartesian Coordinates of the Points of the Body Before Its Deformation
§ 21. Simplification of the Equations of Equilibrium in the Case of Small Elongations and Shears
§ 22. Simplification of the Equations of Equilibrium for Small Rotations
§ 23. Transition to the Classical Equations of Equilibrium
§ 24. Transition to Curvilinear Coordinates

Chapter III. Strain Energy, Boundary Conditions, Stress-Strain Law
§ 25. Strain Energy
§ 26. The Principle of Virtual Displacements
§ 27. Derivation of the Differential Equations of Equilibrium of a Deformed Isotropic Body from the Principle of Virtual Displacements
§ 28. The Relation Between Stress and Strain Components
§ 29. Boundary Conditions
§ 30. The Simplification of the Derived Equations in the Case of a Small Deformation
§ 31. Hooke’s Law
§ 32. On the Applicability of Equations (III.38) to Elastic-Plastic Deformations
§ 33. On the Simplest Variants of Nonlinear Stress-Strain Relations
§ 34. Conclusion

Chapter IV. Formulation of Elastic Problems in Terms of Stresses
§ 35. Two Further Forms for the Equations of Equilibrium of a Volume Element
§ 36. Simplification of Equations (IV.7) and (IV.8) for Small Deformations
§ 37. Still Another Form of the Boundary Conditions
§ 38. Simplification of Equations (IV.7) and (IV.8) for Small Angles of Rotation
§ 39. The Generalization of Saint-Venant’s Relations to the Case of Large Rotations and Strains
§ 40. Simplification of the Equations (IV.26) for Small Deformations
§ 41. On the Formulation of the Problems of the Theory of Elasticity in Terms of Stresses and Strains

Chapter V. The Problem of Elastic Stability
§ 42. Nonuniqueness of Solutions in the Theory of Elasticity
§ 43. The Differential Equations Which Determine the Critical Loads
§ 44. Boundary Conditions of the Problem of Elastic Stability
§ 45. Energy Criterion for the Determination of Critical Loads

Chapter VI. On the Deformation of Flexible Bodies
§ 46. Deformation of Plates
§ 47. Two-Dimensional Deformation of an Infinitely Long Strip
§ 48. Deformation of Shells
§ 49. On the Nature of Kirchhoff’s Assumptions
§ 50. Deformation of Rods (First Approximation)
§ 51. Deformation of Rods (Second Approximation)
§ 52. Pure Torsion
§ 53. The Final Expressions for the Strain Components of a Thin Rod
§ 54. Conclusion

Bibliography

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Anton Pavlovich Chekhov by Vladimir Yermilov

Posted on September 22, 2026 by The Mitr

A biography of great Russian author Antov Pavlovich Chekhov.
Translated from the Russian by Ivy Litvinov
Designed by Y. Gannushkin

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Introductory Mathematics For Engineers – Lectures In Higher Mathematics by A D. Myškis

Posted on September 21, 2026 by The Mitr

Prof. Myškis’ Lectures on Higher Mathematics is a textbook designed to cover key mathematical concepts for engineering students and technical colleges. It emphasises fundamental ideas and their practical applications in specialised fields, presented in an intuitive and accessible manner without unnecessary pedantry. The book focuses on building understanding through intuitive explanations of mathematical concepts and making their applications straightforward. It is intended for engineering students but is also suitable for home study and self-improvement.

The author, Prof. Anatoly Myškis, D.Sc., is well known not only for his original research but also for his equally original approach to the teaching of higher mathematics. He is one of the founders of the theory of differential equations with retarded argument.

His publications include Linear Differential Equations with Retarded Argument, Elements of Applied Mathematics (co-author), and Special Courses in Mathematics for Technical Colleges.

Translated from the Russian by V. M. Volosov, D. Sc.

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Contents

Chapter I. Variables and Functions
§ 1. Quantities

Concept of a Quantity
Dimensions of Quantities
Constants and Variables
Number Scale. Slide Rule
Characteristics of Variables

§ 2. Approximate Values of Quantities
6. The Notion of an Approximate Value
7. Errors
8. Writing Approximate Numbers
9. Addition and Subtraction of Approximate Numbers
10. Multiplication and Division of Approximate Numbers. General Remarks

§ 3. Functions and Graphs
11. Functional Relation
12. Notation
13. Methods of Representing Functions
14. Graphs of Functions
15. The Domain of Definition of a Function
16. Characteristics of Behaviour of Functions
17. Algebraic Classification of Functions
18. Elementary Functions
19. Transforming Graphs
20. Implicit Functions
21. Inverse Functions

§ 4. Review of Basic Functions
22. Linear Function
23. Quadratic Function
24. Power Function
25. Linear-Fractional Function
26. Logarithmic Function
27. Exponential Function
28. Hyperbolic Functions
29. Trigonometric Functions
30. Empirical Formulas

Chapter II. Plane Analytic Geometry
§ 1. Plane Coordinates

Cartesian Coordinates
Some Simple Problems Concerning Cartesian Coordinates
Polar Coordinates

§ 2. Curves in Plane
4. Equation of a Curve in Cartesian Coordinates
5. Equation of a Curve in Polar Coordinates
6. Parametric Representation of Curves and Functions
7. Algebraic Curves
8. Singular Cases

§ 3. First-Order and Second-Order Algebraic Curves
9. Curves of the First Order
10. Ellipse
11. Hyperbola
12. Relationship Between Ellipse, Hyperbola and Parabola
13. General Equation of a Curve of the Second Order

Chapter III. Limit. Continuity
§ 1. Infinitesimal and Infinitely Large Variables

Infinitesimal Variables
Properties of Infinitesimals
Infinitely Large Variables

§ 2. Limits
4. Definition
5. Properties of Limits
6. Sum of a Numerical Series

§ 3. Comparison of Variables
7. Comparison of Infinitesimals
8. Properties of Equivalent Infinitesimals
9. Important Examples
10. Orders of Smallness
11. Comparison of Infinitely Large Variables

§ 4. Continuous and Discontinuous Functions
12. Definition of a Continuous Function
13. Points of Discontinuity
14. Properties of Continuous Functions
15. Some Applications

Chapter IV. Derivatives, Differentials, Investigation of the Behaviour of Functions
§ 1. Derivative

Some Problems Leading to the Concept of a Derivative
Definition of Derivative
Geometrical Meaning of Derivative
Basic Properties of Derivatives
Derivatives of Basic Elementary Functions
Determining Tangent in Polar Coordinates

§ 2. Differential
7. Physical Examples
8. Definition of Differential and Its Connection with Increment
9. Properties of Differential
10. Application of Differentials to Approximate Calculations

§ 3. Derivatives and Differentials of Higher Orders
11. Derivatives of Higher Orders
12. Higher-Order Differentials

§ 4. V. H.ospital’s Rule
13. Indeterminate Forms of the Type 0/0
14. Indeterminate Forms of the Type ∞/∞

§ 5. Taylor’s Formula and Series
15. Taylor’s Formula
16. Taylor’s Series

§ 6. Intervals of Monotonicity. Extremum
17. Sign of Derivative
18. Points of Extremum
19. The Greatest and the Least Values of a Function

§ 7. Constructing Graphs of Functions
20. Intervals of Convexity of a Graph and Points of Inflection
21. Asymptotes of a Graph
22. General Scheme for Investigating a Function and Constructing Its Graph

Chapter V. Approximating Roots of Equations. Interpolation
§ 1. Approximating Roots of Equations

Introduction
Cut-and-Try Method. Method of Chords. Method of Tangents
Iterative Method
Formula of Finite Increments
5*. Small Parameter Method

§ 2. Interpolation
6. Lagrange’s Interpolation Formula
7. Finite Differences and Their Connection with Derivatives
8. Newton’s Interpolation Formulas
9. Numerical Differentiation

Chapter VI. Determinants and Systems of Linear Algebraic Equations
§ 1. Determinants

Definition
Properties
Expanding a Determinant in Minors of Its Row or Column

§ 2. Systems of Linear Algebraic Equations
4. Basic Case
5. Numerical Solution
6. Singular Case

Chapter VII. Vectors
§ 1. Linear Operations on Vectors

Scalar and Vector Quantities
Addition of Vectors
Zero Vector and Subtraction of Vectors
Multiplying a Vector by a Scalar
Linear Combination of Vectors

§ 2. Scalar Product of Vectors
6. Projection of Vector on Axis
7. Scalar Product
8. Properties of Scalar Product

§ 3. Cartesian Coordinates in Space
9. Cartesian Coordinates in Space
10. Some Simple Problems Concerning Cartesian Coordinates

§ 4. Vector Product of Vectors
11. Orientation of Surface and Vector of Area
12. Vector Product
13. Properties of Vector Product
14*. Pseudovectors

§ 5. Products of Three Vectors
15. Triple Scalar Product
16. Triple Vector Product

§ 6. Linear Spaces
17. Concept of Linear Space
18. Examples
19. Dimension of Linear Space
20. Concept of Euclidean Space
21. Orthogonality

§ 7. Vector Functions of Scalar Argument. Curvature
22. Vector Variables
23. Vector Functions of Scalar Argument
24. Some Notions Related to the Second Derivative
25. Osculating Circle
26. Evolute and Evolvent

Chapter VIII. Complex Numbers and Functions
§ 1. Complex Numbers

Complex Plane
Algebraic Operations on Complex Numbers
Conjugate Complex Numbers
Euler’s Formula
Logarithms of Complex Numbers

§ 2. Complex Functions of a Real Argument
6. Definition and Properties
7*. Applications to Describing Oscillations

§ 3. The Concept of a Function of a Complex Variable
8. Factorization of a Polynomial
9*. Numerical Methods of Solving Algebraic Equations
10. Decomposition of a Rational Fraction into Partial Rational Fractions
11*. Some General Remarks on Functions of a Complex Variable

Chapter IX. Functions of Several Variables
§ 1. Functions of Two Variables

Methods of Representing
Domain of Definition
Linear Function
Continuity and Discontinuity
Implicit Functions

§ 2. Functions of Arbitrary Number of Variables
6. Methods of Representing
7. Functions of Three Arguments
8. General Case
9. Concept of Field

§ 3. Partial Derivatives and Differentials of the First Order
10. Basic Definitions
11. Total Differential
12. Derivative of Composite Function
13. Derivative of Implicit Function

§ 4. Partial Derivatives and Differentials of Higher Orders
14. Definitions
15. Equality of Mixed Derivatives
16. Total Differentials of Higher Order

Chapter X. Solid Analytic Geometry
§ 1. Space Coordinates

Coordinate Systems in Space
2*. Degrees of Freedom

§ 2. Surfaces and Curves in Space
3. Surfaces in Space
4. Cylinders, Cones and Surfaces of Evolution
5. Curves in Space
6. Parametric Representation of Surfaces in Space. Parametric Representation of Functions of Several Variables

§ 3. Algebraic Surfaces of the First and the Second Orders
7. Algebraic Surfaces of the First Order
8. Ellipsoid
9. Hyperboloids
10. Paraboloids
11. General Review of Algebraic Surfaces of the Second Order

Chapter XI. Matrices and Their Applications
§ 1. Matrices

Definitions
Operations on Matrices
Inverse Matrix
Eigenvectors and Eigenvalues of a Matrix
The Rank of a Matrix

§ 2. Linear Mappings
6. Linear Mapping and Its Matrix
7. Transformation of the Matrix of a Linear Mapping When the Basis Is Changed
8. The Matrix of a Mapping Relative to the Basis Consisting of Its Eigenvectors
9. Transforming Cartesian Basis
10. Symmetric Matrices

§ 3. Quadratic Forms
11. Quadratic Forms
12. Simplification of Equations of Second-Order Curves and Surfaces

§ 4. Non-Linear Mappings
13*. General Notions
14*. Non-Linear Mapping in the Small
15*. Functional Relation Between Functions

Chapter XII. Applications of Partial Derivatives
§ 1. Scalar Field

Directional Derivative. Gradient
Level Surfaces
Implicit Functions of Two Independent Variables
Plane Fields
Envelope of One-Parameter Family of Curves

§ 2. Extremum of a Function of Several Variables
6. Taylor’s Formula for a Function of Several Variables
7. Extremum
8. The Method of Least Squares
9*. Curvature of Surfaces
10. Conditional Extremum
11. Extremum with Unilateral Constraints
12*. Numerical Solution of Systems of Equations

Chapter XIII. Indefinite Integral
§ 1. Elementary Methods of Integration

Basic Definitions
The Simplest Integrals
The Simplest Properties of an Indefinite Integral
Integration by Parts
Integration by Change of Variable (by Substitution)

§ 2. Standard Methods of Integration
6. Integration of Rational Functions
7. Integration of Irrational Functions Involving Linear and Linear-Fractional Expressions
8. Integration of Irrational Expressions Containing Quadratic Trinomials
9. Integrals of Binomial Differentials
10. Integration of Functions Rationally Involving Trigonometric Functions
11. General Remarks

Chapter XIV. Definite Integral
§ 1. Definition and Basic Properties

Examples Leading to the Concept of Definite Integral
Basic Definition
Relationship Between Definite Integral and Indefinite Integral
Basic Properties of Definite Integral
Integrating Inequalities

§ 2. Applications of Definite Integral
6. Two Schemes of Application
7. Differential Equations with Variables Separable
8. Computing Areas of Plane Geometric Figures
9. The Arc Length of a Curve
10. Computing Volumes of Solids
11. Computing Area of Surface of Revolution

§ 3. Numerical Integration
12. General Remarks
13. Formulas of Numerical Integration

§ 4. Improper Integrals
14. Integrals with Infinite Limits of Integration
15. Basic Properties of Integrals with Infinite Limits of Integration
16. Other Types of Improper Integral
17*. Gamma Function
18*. Beta Function
19*. Principal Value of Divergent Integral

§ 5. Integrals Dependent on Parameters
20*. Proper Integrals
21*. Improper Integrals

§ 6. Line Integrals
22. Line Integrals of the First Type
23. Line Integrals of the Second Type
24. Conditions for a Line Integral of the Second Type to Be Independent of the Path of Integration

§ 7. The Concept of Generalized Function
25*. Delta Function
26*. Application to Constructing Influence Function
27*. Other Generalized Functions

Chapter XV. Differential Equations
§ 1. General Notions

Examples
Basic Definitions

§ 2. First-Order Differential Equations
3. Geometric Meaning
4. Integrable Types of Equations
5*. Equation for Exponential Function
6. Integrating Exact Differential Equations
7*. Singular Points and Singular Solutions
8*. Equations Not Solved for the Derivative
9*. Method of Integration by Means of Differentiation

§ 3. Higher-Order Equations and Systems of Differential Equations
10. Higher-Order Differential Equations
11*. Connection Between Higher-Order Equations and Systems of First-Order Equations
12*. Geometric Interpretation of System of First-Order Equations
13*. First Integrals

§ 4. Linear Equations of General Form
14. Homogeneous Linear Equations
15. Non-Homogeneous Equations
16*. Boundary-Value Problems

§ 5. Linear Equations with Constant Coefficients
17. Homogeneous Equations
18. Non-Homogeneous Equations with Right-Hand Sides of Special Form
19*. Euler’s Equations
20*. Operators and the Operator Method of Solving Differential Equations

§ 6. Systems of Linear Equations
21. Systems of Linear Equations
22*. Applications to Testing Lyapunov Stability of Equilibrium State

§ 7. Approximate and Numerical Methods of Solving Differential Equations
23. Iterative Method
24*. Application of Taylor’s Series
25. Application of Power Series with Undetermined Coefficients
26*. Bessel’s Functions
27*. Small Parameter Method
28*. General Remarks on Dependence of Solutions on Parameters
29*. Methods of Minimizing Discrepancy
30*. Simplification Method
31. Euler’s Method
32. Runge-Kutta Method
33. Adams Method
34. Milne’s Method

Chapter XVI. Multiple Integrals
§ 1. Definition and Basic Properties of Multiple Integrals

Some Examples Leading to the Notion of a Multiple Integral
Definition of a Multiple Integral
Basic Properties of Multiple Integrals
Methods of Applying Multiple Integrals
Geometric Meaning of an Integral over a Plane Region

§ 2. Two Types of Physical Quantities
6*. Basic Example. Mass and Its Density
7*. Quantities Distributed in Space

§ 3. Computing Multiple Integrals in Cartesian Coordinates
8. Integral over Rectangle
9. Integral over an Arbitrary Plane Region
10. Integral over an Arbitrary Surface
11. Integral over a Three-Dimensional Region

§ 4. Change of Variables in Multiple Integrals
12. Passing to Polar Coordinates in Plane
13. Passing to Cylindrical and Spherical Coordinates
14*. Curvilinear Coordinates in Plane

Chapter XVII. [Heading not present in the supplied contents]

§ 5. Fourier Transformation
32*. Fourier Transform
33*. Properties of Fourier Transforms
34*. Application to Oscillations of Infinite String

Chapter XVIII. Elements of the Theory of Probability
§ 1. Random Events and Their Probabilities

Random Events
Probability
Basic Properties of Probabilities
Theorem of Multiplication of Probabilities
Theorem of Total Probability
6*. Formulas for the Probability of Hypotheses
Disregarding Low-Probability Events

§ 2. Random Variables
8. Definitions
9. Examples of Discrete Random Variables
10. Examples of Continuous Random Variables
11. Joint Distribution of Several Random Variables
12. Functions of Random Variables

§ 3. Numerical Characteristics of Random Variables
13. The Mean Value
14. Properties of the Mean Value
15. Variance
16*. Correlation
17. Characteristic Functions

§ 4. Applications of the Normal Law
18. The Normal Law as the Limiting One
19. Confidence Interval
20. Data Processing

Chapter XIX. Computers
§ 1. Two Classes of Computers

Analogue Computers
Digital Computers

§ 2. Programming
3. Number Systems
4. Representing Numbers in a Computer
5. Instructions
6. Examples of Programming

Appendix. Equations of Mathematical Physics
1*. Derivation of Some Equations
2*. Some Other Equations
3*. Initial and Boundary Conditions

§ 2. Method of Separation of Variables
4*. Basic Example
5*. Some Other Problems

Bibliography

Name Index

Subject Index

List of Symbols

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Engineering Thermodynamics by V.A. Kirillin; V.V. Sychev; A.E. Sheindlin

Posted on September 20, 2026 by The Mitr

Although many Soviet and foreign textbooks in engineering thermodynamics already exist, the authors have decided to write a new textbook for university students in power engineering, heat physics, and applied physics departments. We have done so for the following reasons.

With improved instruction in thermodynamics in most higher educational institutions, the authors feel a more thorough presentation of basic problems is necessary. Of primary importance is an understanding of the fundamental concepts and methods of thermodynamics for analysing various physical phenomena.

Clearly, a modern course in engineering thermodynamics must reflect today’s and even tomorrow’s level of technology. Therefore, it is difficult to conceive of a modern textbook in thermodynamics which does not present the different methods of converting heat directly into electric power, modern methods of analysing the efficiency of the cycles of heating plants, the thermodynamics of dissociated and ionised gases, and other problems.

Since the authors consider it unjustified to include in courses of engineering thermodynamics problems relating to statistical physics and the molecular-kinetic theories of gases, we will limit ourselves to a short discussion of the statistical aspects of the second law of thermodynamics.

Although, as a rule, institutes of power engineering do not offer a special course in chemical thermodynamics, modern heat engineering involves many processes accompanied by chemical reactions, dissociation, and ionisation. The authors consider it necessary, therefore, to devote a special chapter to a short presentation of chemical thermodynamics to give the reader an idea of the methods applied in a thermodynamic description of chemical processes.

All numerical examples are given in the SI system (the unit to measure energy is the joule, and the unit to measure pressure is the pascal). As a general rule, along with their values in the SI system, the values of energy have also been indicated in calories (and pressure, in kgf/cm²).

The authors will be grateful for criticism and will take it into consideration in future work on the book.

Translated from the Russian by S. Semyonov

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Contents

Preface
Preface to the English edition

Introduction
Thermodynamics and its method
Properties of state
Concept of a thermodynamic process
Ideal gas Ideal gas laws
Concept of mixtures Mixtures of ideal gases
Concept of heat capacity

The first law of thermodynamics
Heat Joule’s experiment Equivalence of heat and work
Law of conservation and conversion of energy
Internal energy and external work
Mathematical statement of the first law of thermodynamics
Enthalpy
Mathematical statement of the first law of thermodynamics for processes of flow

The second law of thermodynamics
Cycles Concept of thermal efficiency Heat sources
Reversible and irreversible processes
Statements of the second law of thermodynamics
The Carnot cycle Carnot’s theorem
The thermodynamic temperature scale

Entropy
Change of entropy in irreversible processes
Combined mathematical statement of the first and second laws of thermodynamics
Entropy and thermodynamic probability
Reversibility and work

Differential equations of thermodynamics
Basic methods
Maxwell’s relations
Partial derivatives of internal energy and enthalpy
Heat capacities

Equilibrium in thermodynamic systems and phase changes
Homogeneous and heterogeneous thermodynamic systems
Thermodynamic equilibrium
Conditions of stability and equilibrium for an isolated homogeneous system
Conditions for phase equilibrium
Phase changes
The Clausius-Clapeyron equation
Phase stability
Phase changes at unequal phase pressures
Phase changes under curved surfaces

Thermodynamic properties of substances
Thermal and caloric properties of solids
Thermal and caloric properties of liquids
Andrews’ experiment The critical point Van der Waals’ equation
Thermal and caloric properties of real gases Equation of state for real gases
Thermodynamic properties of substances on the change-of-phase line Two-phase systems
Properties of substance at the critical point
Methods of calculating the entropy of substance
Thermodynamic diagrams of state for substances
Thermodynamic properties of substance in a metastable state

Basic thermodynamic processes
The isochoric process
The isobaric process
The isothermal process
The adiabatic process
Polytropic processes
Throttling The Joule-Thomson effect
Joule expansion (expansion into a vacuum)
Mixing
Compression processes

Fluid flow processes
Basic flow equations
Velocity of sound
Flow through convergent nozzles
Transonic range The Laval nozzle
Adiabatic flow with friction
General regularities of flow The influence inversion law
Adiabatic stagnation temperature

Methods to analyse the efficiency of thermopower plants
Cycle efficiency
Comparison methods for thermal efficiencies of reversible cycles
Method of efficiencies in the analysis of irreversible cycles
Entropy calculation method for the loss of availability in irreversible cycles
Exergy calculation method for availability losses

Gas power cycles
Cycles of reciprocating internal combustion engines
Gas-turbine cycles
Reaction-engine cycles

Vapour power cycles
The Carnot cycle
The Rankine cycle
Rankine cycle analysis allowing for irreversibilities

Reheat cycle

Regenerative cycle

Binary cycles

Thermification cycles

Cycles of direct-energy conversion systems

Thermoelectric generator cycle

The cycle of a thermionic converter

MHD-generator cycle

Refrigeration cycles

Reverse heat cycles and processes
Refrigeration installations

Air-compression refrigeration cycle

Vapour-compression refrigeration cycle

Steam-jet refrigeration cycle

Absorption refrigeration cycle

Thermoelectric refrigeration cycle

Heat pump
Principle of operation

Liquefaction of gases

Humid air

Basic concepts

I-d diagram for humid air

Fundamentals of chemical thermodynamics

Thermochemistry
Hess’s law
Kirchhoff’s equation

Chemical equilibrium and the second law of thermodynamics

Equilibrium constant and degree of dissociation

The Nernst heat theorem

Conclusion

Bibliography

Name index

Subject index

Posted in books, chemistry, engineering, mir books, mir publishers | Tagged thermodynamics, engineering, entropy, statistical physics, soviet literature, thermodynamic systems, laws of thermodynamics, thermodynamic processes | 4 Comments

Quimica Orgánica by V. M. Potapov; S. N. Tatarinchik

Posted on September 19, 2026 by The Mitr

La química orgánica atraviesa un período de notable desarrollo caracterizado por el descubrimiento de nuevas sustancias con propiedades excepcionales y la creación de compuestos innovadores de aplicación práctica en diversas áreas. Este progreso se apoya en el uso de métodos modernos de investigación fundamentados en la física y en una profundización de las nociones teóricas. Sin embargo, esto plantea retos educativos, ya que es necesario condensar una gran cantidad de material en los planes de estudio. Los autores abogan por priorizar las leyes generales de la química orgánica, dejando en segundo plano el contenido puramente descriptivo, y basan su enfoque en la teoría de la estructura química de Bútlerov, complementada con una mejor comprensión de los enlaces químicos y las reacciones orgánicas. Este enfoque permite clasificar las reacciones de manera sistemática y facilitar su aprendizaje.

El libro sigue una clasificación basada en los grupos funcionales, que determinan el comportamiento químico de los compuestos orgánicos. Se abordan primero los hidrocarburos y luego sus derivados, incluyendo halogenados e hidroxílicos, destacando aquellos compuestos de relevancia práctica en la industria, agricultura y medicina. Para esta nueva edición, los autores han incorporado recomendaciones de instituciones académicas como las escuelas politécnicas de Moscú y Leningrado, ajustando el contenido al programa aprobado en 1974 para especialidades como química analítica y química de explotaciones petrolíferas. Finalmente, los autores invitan a los lectores a proporcionar observaciones críticas para mejorar la obra en futuras ediciones.

Traducido del ruso por Neiml Sosa

Todos los créditos a los cargadores originales.

Nota: La calidad del escaneo es promedio

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The Stranger by Titus Popovici

Posted on September 18, 2026 by The Mitr

A Soviet era novel of the political awakening of a young Romanian intellectual in 1944.

Translated from the Romanian by Lazar Marinescu

Illustrations: P. Nazarie

Jacket: P. Vulcanescu

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Examples And Problems To The Course Of Unit Operations Of Chemical Engineering by K. F. Pavlov; P. G. Romankou; A. A. Noskov

Posted on September 17, 2026 by The Mitr

The gaining of skill in solving practical engineering problems is very important for students of the course in unit operations. The Department of Unit Operations of Chemical Engineering at the Leningrad Technological Institute places great emphasis on this aspect, and the present book contains many examples and problems in the course that are the result of many years of instructional experience.

Great attention is devoted to the independent work of students, and problems are provided on all sections of the course:

Fundamentals of applied hydraulics
Pumps, fans, compressors
Hydromechanical separation methods
Hydrodynamics of a fluidised bed
Agitation in a liquid medium
Heat transfer in chemical apparatus
Evaporation, crystallisation
Mass transfer, absorption
Distillation and rectification
Extraction and leaching
Adsorption
Drying
Moderate and deep refrigeration
The basic formulas and equations needed for solving the problems are given at the beginning of each chapter. The appendices contain numerous reference tables and diagrams.

The present book, edited by Associate Member of the USSR Academy of Sciences, P. G. Romankov, is intended as a training aid for students of chemical engineering and related specialities in day, evening, and correspondence faculties. It will also be a useful aid in course and diploma designing.

About the Authors

Konstantin F. Pavlov (1895–1944)
Konstantin F. Pavlov was an outstanding specialist in the separation of natural and industrial gases. In 1934, he received his doctorate and the rank of professor. He headed the departments of Chemical Engineering of Inorganic Substances and General Chemical Engineering at the Leningrad Technological Institute, where, in 1936, he founded the first training laboratory in unit operations of chemical engineering in the country (now named after him).

He is the author of several training aids in chemical engineering and original research works (e.g., the rule of linearity of chemical engineering functions). During his final years, he worked in Moscow at the Institute of Physical Problems of the USSR Academy of Sciences.

Pyotr G. Romankov, D.Sc.
Professor Pyotr G. Romankov worked for many years as a chemical engineer and instructor at various chemical institutes. Since 1941, he has been the head of the Department of Unit Operations of Chemical Engineering at the Leningrad Technological Institute. Together with his pupils and collaborators, he has published over 250 scientific works, including several monographs on the theory and application of hydromechanical, heat, and mass-exchange processes of chemical engineering.

In 1964, Pyotr Romankov was elected an associate member of the USSR Academy of Sciences. He is an Honoured Scientist of the RSFSR and has received numerous government awards. He is also a Doctor honoris causa of several foreign higher educational establishments.

Anatoli A. Noskov (1904–1977)
Anatoli A. Noskov worked for many years as an engineer in gas separation under the guidance of Prof. Konstantin Pavlov. He was later invited to work at the Department of Unit Operations of Chemical Engineering at the Leningrad Technological Institute, where he advanced from lecturer to professor.

Anatoli Noskov is well known for his contributions to improving rectification processes and methods for calculating standard operations of chemical engineering.

Edited by P. G. Romankov
Associate Member, USSR Academy of Sciences

Translated from the Russian by G. Leib

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