A Course of Pure Mathematics (Cambridge Mathematical Library)

There are few textbooks of mathematics as well-known as Hardy's Pure Mathematics. Since its publication in 1908, this classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. In its pages, Hardy combines the enthusiasm of the missionary with the rigour of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit. Celebrating 100 years in print with Cambridge, this edition includes a Foreword by T. W. Körner, describing the huge influence the book has had on the teaching and development of mathematics worldwide. Hardy's presentation of mathematical analysis is as valid today as when first written: students will find that his economical and energetic style of presentation is one that modern authors rarely come close to.

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Physics A General Course – Savelyev

In this post we will see the three volume Physics – A General Course by I. V. Savelyev.

I have done everything in my power to acquaint students with the basic ideas and methods of physics and to teach them how to think physically. This is why the book is not encyclopedic in its nature. It is mainly devoted to explaining the meaning of physical laws and showing how to apply them consciously. What I have tried to achieve is a deep knowledge of the fundamental principles of physics rather than a shallower acquaintance with a wide range of questions.

While using the book, try not to memorize the material formalistically and mechanically, but logically, i.e. memorize the material by thoroughly understanding it. I have tried to present physics not as a science for “cramming”, not as a certain volume of information to be memorized, but as a clever, logical, and attractive science.

Notwithstanding my desire to reduce the size, I considered it essential to include a number of mathematical sections in the course: on vectors, linear differential equations, the basic concepts of the theory of probability, etc. This was done to impart a “physical” tinge to the relevant concepts and relations. In addition, the mathematical “inclusions” make it possible to go on with the physics even if, as is often the case, the relevant material has not yet been covered in a mathematics course.

The present course is intended above all for higher technical schools with an extended syllabus in physics. The material has been arranged, however, so that the book can be used as a teaching aid for higher technical schools with an ordinary syllabus simply by omitting some section.

The books were translated from the Russian by G. Leib and were first publised in 1980, this copy is the third reprint in 1989.

Volume 1 (Download)

Volume 2 (Download)

Volume 3 (Download)

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Senior Physics 1 – Kikoin, Kikoin

About the book

This book is the second in the series the first one being Junior Physics. There is a second volume in this series which we do not have now. This book covers fundamentals of motion, its laws, forces in nature and conservation laws also. There is a section on Practical work at the end of the book.

The book was translated from the Russian by Natalia Wadhwa. And was first published by Mir in 1987.

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The Nine Colours of The Rainbow – Steinhaus

About the book (from the front jacket)

Have you ever stopped to think how many colours there are in a rainbow? Seven or, perhaps, nine as the title of the book suggests? It appears, there are many more and still the title is correct. Why so?

The book will tell you what is visible and invisible light, how it helps man to acquaint himself with his environment, investigate it, penetrate into the mysteries of matter and space. You will also find out how man learned to see in the dark, transmit images over long distances and record processes occurring within millionth fractions of a second. The book contains a wealth of other information on the latest achievements in science and technology.

The author, Alexander Steinhaus, is a Soviet specialist in electronics and TV. Many years of industrial experience served as a fertile ground for his literary career on which he embarked with ardour. He has written many sci-fic articles, some stories and a few books, among which are “The Nine Colours of the Rainbow”, “A Factory Without Men”, and others. At present A. Steinhaus is working at a large sci-fic book on television.

The book was translated from the Russian by David Sobolfy and was published by Mir in 1966.

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Fundamentals of Physics – Ivanov

About the book:

The book being of­fered by the author differs from other existing books on the subject in its nontraditional approach to the course of phys­ics. The principle underlying the preparation of this course can be summarized as follows:  “From atom to matter”.

What prompted the author to adopt this approach? In­deed, the creation of new materials with unusual mechani­cal, thermal, electrical, magnetic, and optical properties requires a microscopic approach to the problem and a clear understanding of the practical significance of the approach “from atom to matter”. This means that the scientists and industrial workers engaged in fields like physical materials science, nuclear and semiconductor engineering, laser
…

This book is intended for those who wish to acquire a deeper knowledge of physical phenomena. It can be used by students of physics and mathematical schools, as well as by those who have finished school and are engaged in self- education. A good deal of the material may be useful to teachers delivering lectures on various topics of physics.

…

This is not a textbook, but rather a helpbook that should be used in conjunction with the standard textbooks. Nor is the book intended for a light reading; you have to use a pen and paper, think, analyze, and even compute whenever it is necessary. We shall describe physics here in the way re­ searchers understand it today.

Physics essentially deals with the fundamental laws of nature. The progress being made at present in all branches of natural science is due, as a rule, to the introduction of physical concepts and techniques in them. This is besides the fact that a knowledge of physical sciences is essential for new industrial ventures lying at the root of technical progress. Physics is fast becoming an important element in the modern civilization.

The book was published by Mir in 1989 and was translated from the Russian by R. S. Wadhwa.

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Semiconductors: Testing and Adjusting – Green, Shokalsky

In this post, we will look at the book Semiconductors: Testing and Adjusting by G. Green and A Shokalsky.

About the book:

The book describes the working of many electronic devices and methods of testing them. Since the book was written in the early 70s, some of the technology presented in the book may be outdated.

The book was translated from the Russian by George Roberts and was first published by Mir in 1972.

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Fundamentals of Theoretical Physics – Savelyev

In this post we will see the two volume set titled Fundamentals of Theoretical Physics by I. V. Savelyev. Previously we have seen Physics A General Course by the same author.

The book being offered to the reader is a logical continuation of the author’s three-volume general course of physics. Everything possible has been done to avoid repenting what has been set out in the three-volume course. Particularly. the experiments underlying the advancing of physical ideas are not treated, and some of the results obtained are not discussed.

The book has been conceived as a training aid for students of non- theoretical specialities of higher educational institutions. I had in mind readers who would like to grasp the main ideas and methods of theoretical physics without delving into the details that are of interest only for a specialist. This book will be helpful for physics instructors at higher schools, and also for everyone interested in the subject but having no time to become acquainted with it (or re- store it in his memory) according to fundamental manuals.

The books were translated from the Russian by G. Leib and was first published in 1982.

Fundamentals of Theoretical Physics Vol 1 (Download)

Fundamentals of Theoretical Physics Vol 2 (Download)

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Electricity And Man – Manoilov

About the book:

“… Life on Earth originated and developed in

interaction with electromagnetic fields. Electricity is

inherent in the living in its most complicated form – the

vital activity of man. Scientists have done much in

studying this amazing interaction of electricity and the

animate but much in nature is still concealed, much

must be analyzed and understood. This book will help

to widen the reader’s understanding of the interaction

of electricity and the living organism, although it makes

no claim to exhaust the subject … “

The book was translated from the Russian by George Kittell and was published by Mir in 1978.

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Elementary Textbook on Physics Vol 3 – Landsberg

About the book:

Volume 3 covers aspects of wave motion, oscillations, optics and atomic and modern physics. These topics include:

Basic Concepts. Mechanical Vibrations. Acoustic Vibrations. Electric Oscillations. Wave Phenomena. Interference of Waves. Electromagnetic Waves. Light Phenomena: General. Photometry and Lighting Engineering. Basic Laws of Geometrical Optics. Application of Reflection and Refraction of Light to Image Formation. Optical Systems and Errors. Optical Instruments. Interference of Light. Diffraction of Light. Physical Principles of Optical Holography. Polarization of Light. Transverse Nature of Lightwaves. Electromagnetic Spectrum. Velocity of Light. Dispersion of Light and Colours of Bodies. Spectra and Spectral Regularities. Effects of Light. Atomic Structure. Radioactivity. Atomic Nuclei and Nuclear Power. Elementary Particles. New Achievements in Elementary Particle Physics.

About the series (from Front Jacket and Preface):
Elementary Textbook on Physics first appeared in 1948-52 under the editorship of Academician G.S. Landsberg (1890-1957) and immediately became popular with students preparing for entrance examinations in physics. The success of the book was due very much to the fact that each section was written by a specialist. Contributors to the book included the scientists S.E. Khaikin, M.A. Isakovich, M.A. Leontovich, D.I. Sakharov (Vol. 1), S.G. Kalashnikov (Vol. 2), S.M. Rytov, M.M. Sushchinskii (with the participation of I.A. Yakovlev), F.S. Landsberg-Baryshanskaya, and F.L. Shapiro (Vol. 3).

These three volumes form a course on elementary physics that has become very popular in the Soviet Union. Each sectioh was written by an authority in the appropriate field, while the overall unity and editing was supervised by Academician G.S. Landsberg (1890-1957). This textbook has gone through ten Russian editions and a great deal of effort went into the last edition to introduce SI units and change the terminology and notation for the physical units.

A feature of this course is the relatively small number of formulas and mathematical manipulations. Instead, attention was focussed on explaining physical phenomena in such a way as to combine scientific rigour and a form understandable to school children. Another aspect of the text is the technological application of the physical laws.

These features make the text a world-class textbook.

For students preparing to enter universities and colleges to study physics, and for those it high schools specialising in physics.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1989.

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Elementary Textbook on Physics Vol 2 – Landsberg

About the book:

Volume 2 covers aspects of basic aspects of electricity and magnetism. These topics include:

Electric Charges. Electric Field. Direct Current. Thermal Effect of Current. Electric Current in Electrolytes. Chemical and Thermal Generators. Electric Current in Metals. Electric Current in Gases. Electric Current in Semiconductors. Basic Magnetic Phenomena. Magnetic Field. Magnetic Field of Current. Magnetic Field of the Earth. Forces Acting on Current- Carrying Conductors in Magnetic Field. Electromagnetic Induction. Magnetic Properties of Bodies. Alternating Current. Electric Machines: Generators, Motors and Electromagnets.

About the series (from Front Jacket and Preface):
Elementary Textbook on Physics first appeared in 1948-52 under the editorship of Academician G.S. Landsberg (1890-1957) and immediately became popular with students preparing for entrance examinations in physics. The success of the book was due very much to the fact that each section was written by a specialist. Contributors to the book included the scientists S.E. Khaikin, M.A. Isakovich, M.A. Leontovich, D.I. Sakharov (Vol. 1), S.G. Kalashnikov (Vol. 2), S.M. Rytov, M.M. Sushchinskii (with the participation of I.A. Yakovlev), F.S. Landsberg-Baryshanskaya, and F.L. Shapiro (Vol. 3).

These three volumes form a course on elementary physics that has become very popular in the Soviet Union. Each sectioh was written by an authority in the appropriate field, while the overall unity and editing was supervised by Academician G.S. Landsberg (1890-1957). This textbook has gone through ten Russian editions and a great deal of effort went into the last edition to introduce SI units and change the terminology and notation for the physical units.

A feature of this course is the relatively small number of formulas and mathematical manipulations. Instead, attention was focussed on explaining physical phenomena in such a way as to combine scientific rigour and a form understandable to school children. Another aspect of the text is the technological application of the physical laws.

These features make the text a world-class textbook.

For students preparing to enter universities and colleges to study physics, and for those it high schools specialising in physics.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1988.

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Elementary Textbook on Physics Vol 1 – Landsberg

About the book:

Volume 1 covers aspects of basic mechanics and fluid mechanics (both statics and dynamics), heat and molecular physics. These topics include:

Kinematics. Dynamics. Statics. Work and Energy. Curvilinear Motion. Motion in Noninertial Reference Systems and inertial Forces. Hydrostatics. Aerostatics. Fluid Dynamics. Thermal Expansion of Solids and Liquids. Work. Heat. Law of Energy Conservation. Molecular Theory. Properties of Gases. Properties of Liquids. Properties of Solids. Transition from Solid to Liquid State. Elasticity and Strength. Properties of Vapours. Physics of the Atmosphere. Heat Engines.

About the series (from Front Jacket and Preface):

Elementary Textbook on Physics first appeared in 1948-52 under the editorship of Academician G.S. Landsberg (1890-1957) and immediately became popular with students preparing for entrance examinations in physics. The success of the book was due very much to the fact that each section was written by a specialist. Contributors to the book included the scientists S.E. Khaikin, M.A. Isakovich, M.A. Leontovich, D.I. Sakharov (Vol. 1), S.G. Kalashnikov (Vol. 2), S.M. Rytov, M.M. Sushchinskii (with the participation of I.A. Yakovlev), F.S. Landsberg-Baryshanskaya, and F.L. Shapiro (Vol. 3).

These three volumes form a course on elementary physics that has become very popular in the Soviet Union. Each sectioh was written by an authority in the appropriate field, while the overall unity and editing was supervised by Academician G.S. Landsberg (1890-1957). This textbook has gone through ten Russian editions and a great deal of effort went into the last edition to introduce SI units and change the terminology and notation for the physical units.

A feature of this course is the relatively small number of formulas and mathematical manipulations. Instead, attention was focussed on explaining physical phenomena in such a way as to combine scientific rigour and a form understandable to school children. Another aspect of the text is the technological application of the physical laws.

These features make the text a world-class textbook.

For students preparing to enter universities and colleges to study physics, and for those it high schools specialising in physics.

The book was translated from the Russian by Natalia Wadhwa and was first published by Mir in 1988.

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Elementary Physics: Problems and Solutions – Gurskii

The book is intended for those preparing for university entrance examinations in physics. The contents and sequence of topics are in keeping with the requirements for such examinations. The few sections beyond the entrance examination programme are marked by circles. In view of the introduction of the elements of higher mathematics to the high-school curriculum, some problems have also been illustrated using differential calculus. The author has endeavoured to present the basic principles of school physics in a compact form to help the candidates revise the entire course in the shortest possible time. All sections have been illustrated with problems to give a better understanding of the subject. Each problem and its solution is followed by one or more exercises on the same topic, the exercises corresponding to problems that have been solved in the text are assigned the same number.Those intending to use this book independently are advised to attempt the exercises after going through the theoretical part. The relevant solved problems should be consulted if difficulties are encountered while solving the exercises. After this, the exercise should be tried again, and if there is more than one exercise bearing the same number, another exercise (preferably the last one) should be tackled. In most cases, the last exercises in a series are the most difficult.

The book was translated from Russian by Natalia Wadhwa and was first published in 1987.

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Problems in Theoretical Physics – Grechko, Sugakov, Tomasevich, Fedorchenko

About the book:

From the Front Jacket

This book is a collection of problems covering mechanics, electrodynamics, nonrelativistic quantum mechanics, !statistical physics and thermodynamics. Each Section opens with a brief outline of the main laws and relationships used to solve the problems. Also information about the needed mathematical apparatus is included. Along with answers there are guides to solving the more complicated problems. SI units are used throughout the book. Problems in Theoretical Physics is intended for physics majors at universities and other institutions of higher learning. Some of the problems are specifically for students majoring in theoretical physics. Certain ones can be used in the physics and mathematics departments of teachers colleges.

From the Preface

The text draws largely on the Course of Theoretical Physics by L. D. Landau and E. M. Lifshitz, but also makes use of other textbooks and handbooks recommended for the university course in theoretical physics. Some of the problems have been taken from published problem books listed at the end of this book, but many are original. The student will be able to solve the problems if he has a good knowledge of the fundamentals of theoretical physics, which are briefly outlined in each section of this book.

The book was translated from the Russian by Eugene Yankovsky and was published by Mir in 1977.

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Essays About the Universe – Vorontsov-Vel’yaminov

This book by a prominent Soviet astronomer and imaginative interpreter of the history and latest knowledge of astronomy, an age-old science that has come through two shattering decades of exciting discovery and research, can be dubbed a popular encyclopaedia of astronomy. It is a vivid and fascinating account of almost all the celestial bodies with which astronomy is concerned: planets, comets, meteors, the Sun and stars, gaseous and dust nebulae, quasars, black hole., etc. The tome is lavishly illustrated throughout with a mixture of photographs and specially commissioned artwork in full colour. The book will appeal to the general reader with no astronomical and mathematical background, fascinated by the wonders of the Space Age.

The book has two major sections, the first deals with Solid matter, that is the planets (minor and major), comets and meteors. The second part deals with the gaseous state which includes stars, nebulae, galaxies, interstellar matter. Mathematics is avoided as much as possible with the main emphasis on explaining the physical meaning of the concepts and their implications to the reader. The book covers an impressively wide range of topics in astronomy starting from the basics to topics of cutting-edge research.

The book was translated from the Russian by Alexander Repyev and was published by Mir 1985.
Note: The book is large in size (~ 190 MB). It took some time to scan it, as I had to scan individual pages because of their large size almost A4 in size. Unfortunately, before the optimisation of the images could be completed, I lost all the raw images to a disk crash. Hence I have uploaded the pdf that could be salvaged. You might notice some inconsistencies in the pages here and there. There are some amazing full-page illustrations, one of my favourites is one explaining the meteor path for different observers.

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Albert Einstein’s Philosophical views and the Theory of Relativity – Gribanov

This book presents the first integral treatment of the philosophical views of Albert Einstein and their influence on the origin and inter­pretation of the theory of relati­vity. It brings out the specific features of the philosophical com­ prehension of the theory of relativity m the world and Soviet literature, and analyses the influence of the new relativistic physical ideas in enriching and developing the tradi­tional philosophical categories of matter, space, time, and motion.

The book was first published by Progress Publishers in 1987 and was translated from the Russian by H. Campbell Creighton. The book was designed by Vyacheslav Serebryakov.

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The Forces of Nature – Grigoryev, Myakishev

About the book:

This book is a popular description of the unity of the forces of nature for the general reader.
At present, all interactions between bodies in nature are thought to be ultimately due to the interaction of elementary particles and involve only four types of forces: universal gravitation, or gravitational forces, electromagnetic forces, nuclear forces and the so- called weak interactions.
This book describes the principal properties of these four types of force and their “sphere of action”, that is, the part they play in diverse natural processes that range from galaxies to the atomic nucleus and the mutual transformations of elementary particles. It includes the latest achievements of physics and gives a picture of the unresolved problems that confront science today.

About the authors:

The authors of this book are Candidates of Physico-mathematical sciences Vladimir Grigoryev and Gennady Myakishev. In 1948 they graduated from the Physics Department of Moscow University and completed their graduate studies in 1951. At present both are Associate Professors of the Moscow University Physics Department.
V. Grigoryev has published over twenty papers on problems of quantum field theory and has been particularly interested in particle formation via high- energy collisions. G. Myakishev has written a number of works on electronics and problems of the methodology of science, several elementary numerous textbooks on physics and articles for popular-science magazines.

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Elements Of Applied Mathematics – Zeldovich, Myskis

This book is not a textbook in the ordinary sense of the word but rather a reader in the mathematical sciences. Using simple examples taken from physics and a variety of mathematical problems, we have tried to introduce the reader to a broad range of ideas and methods that are found in present-day applications of mathematics to physics, engineering and other fields. Some of these ideas and methods (such as the use of the delta function, the principle of superposition, obtaining asymptotic expressions, etc.) have not been sufficiently discussed in the ordinary run of mathematics textbooks for non-mathematicians, and so this text can serve as a supplement to such textbooks. Our aim has been to elucidate the basic ideas of mathematical methods and the general laws of the phenomena at hand. Formal proofs, exceptions and complicating factors have for the most part been dropped. Instead we have strived in certain places to go deeper into the physical picture of the processes.

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Theory of Angular Momentum – Yutsis, Levinson, Vanagas

The principal results obtained up to 1935 in the quantum-mechanical theory of angular momentum are contained in chapter III of Condon and Shortley’s “Theory of Atomic Spectra” /1949/. Since then, owing to the ideas of Wigner /1931,1937/ and Racah /1942/, the theory has been enriched by the algebra of noncommuting tensor operators and the theory of y-coefficients. This has considerably increased its computational possibilities and has broadened the scope of its applications. Among the branches of theoretical physics where the methods of the theory of angular momentum are widely applied today we might mention the theory of atomic and nuclear spectra, the scattering of polarized particles in nuclear reactions, the theory of genealogical coefficients, etc. (a bibliography of the applications may be found in Edmonds’ book /1957/).

The only book known to us giving an exposition of the algebra of noncommuting tensor operators and j-coefficients is Edmonds’ “Angular Momentum in Quantum Mechanics” /1957/, which may serve as an excellent textbook for a first acquaintance with the subject. However, the exposition of the theory of j-coefficients and transformation matrices given in this book is not complete. This may constitute an impediment when the apparatus is employed m more complicated cases. The present
book fills this gap.

The writing of this book began before Edmonds’ book appeared in print. The authors have utilized nearly all results known to them in the given field. Among these a certain place is occupied by the results obtained by a group of workers under the
direction of one of the present authors (A. Yutsis), the remaining two authors (I. Levmson and V. Vanagas) being the principal participants. The book corresponds to the content of the first part of a course, “Methods of Quantum-Mechanical Atomic Calculations”, given by the senior author to students of theoretical physics at the
Vilnius State University im. V. Kapsukas over the last two years.

We found it worthwhile to use the elegant and powerful methods of group theory in our exposition. To avoid encumbering the book with elements of group theory we have assumed that the reader is already acquainted with linear representations of the three-dimensional rotation group. The reader who is unfamiliar with this may refer to the books by G.Ya. Lyubarskii*/1957/ and I. M, Gel’fand et al. /1958/.

We begin with the well-known theory of vector addition of two angular momenta (chapter I), turning next to the addition of an arbitrary number of angular momenta (chapter II), The following chapters (III- VI) are devoted to quantities of the theory of angular momentum where an important place is occupied by the graphical method which IS convenient for various calculations. The last chapter (VII) deals with the method of noncommuting tensor operators. Material of a supplementary character is given in the appendices.

We have cited a number of unpublished works some of which were not available to us. References to these were based on other published works. We apologise in advance for any resulting inaccuracy.

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Operations Research – Wentzel

The aim of this book is to present in a widely appealing form the sub­ject matter and methods of operations research
(OR), a managerial tool designed to increase the effectiveness of mana­gerial decisions as an ob­jective supplement to the subjective assessment.
With no confinement to an exclusive area of practice, the discussion in the book is focused on the methodological as­pects which are common to all OR problems is simple and requires wherever they might ap­pear. Therefore the main emphasis is placed on such methodological treatises as problem formulation, model development, and assessment of computational results, rather than on mathematical rigor.
In writing this text the author — a well known Soviet mathematician and popular novelist – employed her many-year experience in govern­mental OR projects and lectureship at the Mos­cow Institute of Trans­portation Engineering to give a vivid presentation of the relevant methods of mathematical pro­gramming, game theory, queueing models, and decision analysis. The mathematics of the book is simple and requires only expertise in probability theory. The book is devoted primarily to the practitioners who are novices to the subject.
It will be interesting to students, engineers, managerial staff and all those involved in deci­sion making.

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A Modern Handbook of Physics – Yavorsky and Detlaf

The basic sciences and physics, in particular, are of prime importance today in the training of engineers for the various branches of the national economy. This has led to fundamental changes in recent years in the teaching of physics in engineering institutes, and to the students of other educational institutions in which they do not major in physics. The scope and scientific level of physics courses have been substantially supplemented and cover the main trends in the development of modern physics. Consequently, the physics textbooks for engineering students have inevitably become three-volume editions of almost fifteen hundred pages. The need has arisen, in this connection, for a concise handbook on this subject.

The aim of the authors was to fulfill this need. In scope and depth this handbook includes all of the definitions, formulas and information covered in the most comprehensive and up-to-date physics courses of engineering institutes
and the physics departments of universities and colleges. Physical laws are concisely formulated, all the necessary explanations are given and, in many cases, derivations as well. Though it plays a vital role in the teaching of physics, experimental material has been omitted. This is due only to a lack of space. All the units and symbols comply with the requirements of the SI Units of physical quantities and systems of units are listed and dealt with in a short appendix.

This handbook is designed primarily for engineering students, as well as college and university students studying, but not majoring in physics. It can be used to advantage by engineers and graduate students, as well as by instructors and lecturers of intermediate schools and colleges.

Mathematical knowledge required in using the handbook is within the scope of the ordinary mathematics courses of engineering institutes. The detailed index and the numerous cross references, indicating the chapter, section and subsection, are of aid in finding any required information.

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Straight Lines and Curves – Vasilyev, Gutenmacher

The authors N. B. Vasilyev and V. L. Gutenmacher are professors of mathematics at Moscow University. N. B. Vasilyev works in the field of the application of mathematical methods to biology, while V. I. Gutenmacher works in the field of mathematical methods used in the analysis of economic models.

In addition to their scientific work, they have both written many articles and books for high school and university students, and have worked with the Correspondence Mathematics School, which draws its pupils from all over the Soviet Union. They have worked on the committee organizing the “mathematical olympiad” problem competitions, which have greatly stimulated interest in mathematics among young people in the Soviet Union. They regularly contribute to the magazine “Kvant” (“Quantum”), a remarkable educational magazine devoted to mathematics and physics. This book contains a wealth of material usually found in geometry courses, and takes a new look at some of the usual theorems.

It deals with paths traced out by moving points, sets of points satisfying given geometrical conditions, and problems on finding maxima and minima. The book contains more than 200 problems which lead the reader towards some important areas of modern mathematics, and will interest a wide range of readers whether they be high school or university students, teachers, or simply lovers of mathematics.

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Física. Electricidad, magnetismo y óptica

Este libro es el segundo volumen de un texto sobre introducción a la física para alumnos que estudien seriamente ciencias físicas, ciencias de la vida e ingeniería. Aquellos que sigan este curso deberán haber estudiado previamente geometría, álgebra y trigonometría; el cálculo diferencial e integral, el álgebra y la trigonometría son también requisitos previos para el segundo volumen. El primer volumen cubre la mecánica y la termodinámica; el segundo estudia la electricidad y el magnetismo, la luz y la óptica. Tenemos en preparación un tercer volumen sobre física moderna y mecánica cuántica. La organización del contenido es esencialmente clásica con excepciones.

Una característica excepcional para un libro de esta naturaleza es la inclusión de abundante material histórico, no como mera deferencia al pasado o patriotismo científico, sino más bien para que el alumno actual de física conozca el crecimiento orgánico de nuestro conocimiento. Además, una característica poco corriente ne este texto es la inclusión de métodos orientados por ordenadores, calculadores de mano programables y microprocesadores. Por último, este volumen contiene 187 ejemplos resueltos que deben considerarse como parte integral del texto. 

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A Problem Book in Real Analysis (Problem Books in Mathematics)

Education is an admirable thing, but it is well to remember from time to time that nothing worth knowing can be taught. Oscar Wilde, “The Critic as Artist,” 1890. Analysis is a profound subject; it is neither easy to understand nor summarize. However, Real Analysis can be discovered by solving problems. This book aims to give independent students the opportunity to discover Real Analysis by themselves through problem solving. ThedepthandcomplexityofthetheoryofAnalysiscanbeappreciatedbytakingaglimpseatits developmental history. Although Analysis was conceived in the 17th century during the Scienti?c Revolution, it has taken nearly two hundred years to establish its theoretical basis. Kepler, Galileo, Descartes, Fermat, Newton and Leibniz were among those who contributed to its genesis. Deep conceptual changes in Analysis were brought about in the 19th century by Cauchy and Weierstrass. Furthermore, modern concepts such as open and closed sets were introduced in the 1900s. Today nearly every undergraduate mathematics program requires at least one semester of Real Analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of this book is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, we hope that learning analysis becomes less taxing and thereby more satisfying.

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Introduction to Real Analysis

This text provides the fundamental concepts and techniques of real analysis for students in all of these areas. It helps one develop the ability to think deductively, analyze mathematical situations, and extend ideas to a new context. Like the first three editions, this edition maintains the same spirit and user-friendly approach with additional examples and expansion on Logical Operations and Set Theory. There is also content revision in the following areas: Introducing point-set topology before discussing continuity, including a more thorough discussion of limsup and limimf, covering series directly following sequences, adding coverage of Lebesgue Integral and the construction of the reals, and drawing student attention to possible applications wherever possible.

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Relativity: The Special and the General Theory

Time's 'Man of the Century', Albert Einstein is the unquestioned founder of modern physics. His theory of relativity is the most important scientific idea of the modern era. In this short book Einstein explains, using the minimum of mathematical terms, the basic ideas and principles of the theory which has shaped the world we live in today. Unsurpassed by any subsequent books on relativity, this remains the most popular and useful exposition of Einstein's immense contribution to human knowledge.Einstein presents his views on the special and general theory of relativity and the universe as a whole.

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Challenging Mathematical Problems with Elementary Solutions, Vol. II

Volume II of a two-part series, this book features 74 problems from various branches of mathematics. Ranging from relatively simple to extremely difficult, their topics include points and lines, topology, convex polygons, theory of primes, nondecimal counting, and other subjects. Suitable for students, teachers, and any lover of mathematics. Complete solutions.

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The USSR Olympiad problem book_ selected problems and theorems of elementary mathematics

This book contains 320 unconventional problems in algebra, arithmetic, elementary number theory, and trigonometry. Most of the problems first appeared in competitive examinations sponsored by the School Mathematical Society of the Moscow State University and the Mathematical Olympiads held in Moscow. Although most of the problems presuppose only high school mathematics, they are not easy; some are of uncommon difficulty and will challenge the ingenuity of any research mathematician. Nevertheless, many are well within the reach of motivated high school students and even advanced seventh and eighth graders.
The problems are grouped into twelve separate sections. Among these are: the divisibility of integers, equations having integer solutions, evaluating sums and products, miscellaneous algebraic problems, the algebra of polynomials, complex numbers, problems of number theory, distinctive inequalities, difference sequences and sums, and more.
Complete solutions to all problems are given; in many cases, alternate solutions are detailed from different points of view. Solutions to more advanced problems are given in considerable detail. Moreover, when advanced concepts are employed, they are discussed in the section preceding the problems. Useful in a variety of ways in high school and college curriculums, this challenging volume will be of particular interest to teachers dealing with gifted and advanced classes.

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Challenging Mathematical Problems with Elementary Solutions, Vol. I

Volume I of a two-part series, this book features a broad spectrum of 100 challenging problems related to probability theory and combinatorial analysis. The problems, most of which can be solved with elementary mathematics, range from relatively simple to extremely difficult. Suitable for students, teachers, and any lover of mathematics. Complete solutions.

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The Stanford Mathematics Problem Book: With Hints and Solutions

This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. 1974 edition.

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Calculus: Basic Concepts for High Schools – Tarasov

The whole book is presented as a relatively free-flowing

dialogue between the AUTHOR and the READER. From one discussion

to another the AUTHOR will lead the inquisitive and receptive

READER to different notions, ideas, and theorems of calculus,

emphasizing especially complicated or delicate aspects, stressing the

inner logic of proofs, and attracting the reader’s attention to special

points. I hope that this form of presentation will help a reader of the

book in learning new definitions such as those of derivative, antiderivative, definite. integral, differential equation, etc. I also expect that

it will lead the reader to better understanding of such concepts as

numerical sequence, limit of sequence, and function. Briefly, these

discussions are intended to assist pupils entering a novel world of

calculus. And if in the long run the reader of the book gets a feeling

of the intrinsic beauty and integrity of higher mathematics or even

is appealed to it, the author will consider his mission as successfully

completed.

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Fundamentos de la teoría electromagnética, 4ta Edición – John R. Reitz

Es un libro exclusivamente teórico, aunque después de cada tema veremos una lista de ejercicios para realizar, los cuales tienen solución plasmada al final del libro. En general no hay muchos ejemplos detallados, quizás los justos. Es riguroso y elegante, ademas presenta una calidad y claridad a la hora de exponer los temas, impecable.

En concreto este libro recoge temas como: un breve repaso al análisis vectorial que será útil para comprender los desarrollos que se irán viendo, temas como electroestática, campos en medios diélectricos, un tema exclusivo para la teoría microscópica de los dieléctricos, energía electroestática, corriente eléctrica, campo magnético de corrientes estacionarias, propiedades magnéticas de la materia, teoría macroscópica del magnetismo, inducción electromagnética, energía magnética, corrientes que varían lentamente, un tema exclusivo de fisica de plasmas, otro dedicado a las propiedades electromagnéticas de los superconductores, las ecuaciones de maxwell, la propagación de ondas electromagnéticas monocromáticas, ondas monocromáticas en regiones limitadas, dispersión y campos oscilantes en medios dispersivos, emisión de radiación, electrodinámica, teoría de la relatividad especial y multitud de apéndices.

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SOLVING PROBLEMS IN GEOMETRY: INSIGHTS AND STRATEGIES (Mathematical Olympiad Series Book 10)

This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry.

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FÍSICA PARA CIENCIAS E INGENIERÍA

Cuenta con un enfoque integrador, combina el contenido con el entorno de aprendizaje actual, desde la resolución de problemas en clase hasta la tarea en línea, utiliza comentarios específicos y tutoriales. Más amigable para los estudiantes que nunca, el texto incluye nuevos ejercicios ricos en contexto, problemas conceptuales, y pedagogía educativa sólida. Las ilustraciones, tablas, cuadros, gráficas y los ejemplos detallados trabajados complementan el lenguaje conciso y las instrucciones meticulosas por las cuales Raymond A. Serway y John W. Jewett Jr. son conocidos. Además, WebAssign, el sistema de tareas más fácil de usar del mundo, le proporciona la solución definitiva a sus deberes y necesidades de evaluación para maximizar el éxito de su curso.
Características:

• Los estudiantes se enfrentan a cientos de problemas durante sus cursos de física. Un número relativamente pequeño de principios fundamentales forman la base de estos problemas.
• ¿Qué pasaría sí? La pregunta ofrece una variación de la situación planteada en el ejemplo del libro.
• Al final de cada capítulo se incluye un extenso conjunto de problemas; en total, el libro de texto impreso contiene más de 2 000 problemas.
• Describe las características principales que los instructores quisieran saber.
• Se enfatiza en argumentos físicos estructurados de forma adecuada y en estrategias efectivas para resolver problemas.
• Al mismo tiempo motivamos al estudiante mediante ejemplos prácticos que demuestren el papel de la física en otras disciplinas, como ingeniería, química y medicina.

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Sears and Zemansky's University Physics with Modern Physics

University Physics with Modern Physics 13th edition – University Physics is known for its uniquely broad, deep, and thoughtful set of worked examples–key tools for developing both physical understanding and problem-solving skills.
The Thirteenth Edition revises all the Examples and Problem-Solving Strategies to be more concise and direct while maintaining the Twelfth Edition’s consistent, structured approach and strong focus on modeling as well as math.
To help students tackle challenging as well as routine problems, the Thirteenth Edition adds Bridging Problems to each chapter, which pose a difficult, multiconcept problem and provide a skeleton solution guide in the form of questions and hints.
The text’s rich problem sets–developed and refined over six decades–are upgraded to include larger numbers of problems that are biomedically oriented or require calculus. The problem-set revision is driven by detailed student-performance data gathered nationally through MasteringPhysics®, making it possible to fine-tune the reliability, effectiveness, and difficulty of individual problems.
Complementing the clear and accessible text, the figures use a simple graphic style that focuses on the physics. They also incorporate explanatory annotations–a technique demonstrated to enhance learning.
This text is available with MasteringPhysics–the most widely used, educationally proven, and technically advanced tutorial and homework system in the world.

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A Course on Integration Theory: including more than 150 exercises with detailed answers

This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included.   A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.​

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Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics

This first-year, graduate-level text and reference book covers the fundamental concepts and twenty-first-century applications of six major areas of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn't: statistical physics, optics (waves of all sorts), elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology. Growing out of a full-year course that the eminent researchers Kip Thorne and Roger Blandford taught at Caltech for almost three decades, this book is designed to broaden the training of physicists. Its six main topical sections are also designed so they can be used in separate courses, and the book provides an invaluable reference for researchers.
* Presents all the major fields of classical physics except three prerequisites: classical mechanics, electromagnetism, and elementary thermodynamics
* Elucidates the interconnections between diverse fields and explains their shared concepts and tools * Focuses on fundamental concepts and modern, real-world applications
* Takes applications from fundamental, experimental, and applied physics; astrophysics and cosmology; geophysics, oceanography, and meteorology; biophysics and chemical physics; engineering and optical science and technology; and information science and technology
* Emphasizes the quantum roots of classical physics and how to use quantum techniques to elucidate classical concepts or simplify classical calculations
* Features hundreds of color figures, some five hundred exercises, extensive cross-references, and a detailed index
* An online illustration package is available to professors.

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Improper Riemann Integrals

Improper Riemann Integrals is the first book to collect classical and modern material on the subject for undergraduate students. The book gives students the prerequisites and tools to understand the convergence, principal value, and evaluation of the improper/generalized Riemann integral. It also illustrates applications to science and engineering problems.

The book contains the necessary background, theorems, and tools, along with two lists of the most important integrals and sums computed in the text. Numerous examples at various levels of difficulty illustrate the concepts and theorems. The book uses powerful tools of real and complex analysis not only to compute the examples and solve the problems but also to justify that the computation methods are legitimate.

Enriched with many examples, applications, and problems, this book helps students acquire a deeper understanding of the subject, preparing them for further study. It shows how to solve the integrals without exclusively relying on tables and computer packages.

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Differential and Integral Calculus (R. Courant )

Mi objetivo es exhibir la estrecha conexión entre el análisis y sus aplicaciones y, sin pérdida de rigor y precisión, dar el debido crédito a la intuición como la fuente de la verdad matemática. ... Para mí, parece extremadamente importante que el estudiante sea advertido desde el principio contra un purismo presuntuoso y presumido; Este no es el menor de mis propósitos al escribir este libro.

El libro está dirigido a cualquier persona que, después de haber completado un curso ordinario de matemática escolar, desee dedicarse al estudio de las matemáticas o sus aplicaciones a la ciencia y la ingeniería, sin importar si es estudiante de una universidad o escuela técnica, maestro o ingeniero. No prometo ahorrarle al lector la molestia de pensar, pero sí trato de llevar el camino directo al conocimiento útil, y apunto a hacer que el tema sea más fácil de entender, no solo dando pruebas paso a paso, sino también arrojando luz sobre las interconexiones y propósitos del conjunto.

El principiante debe tener en cuenta que he evitado bloquear la entrada a los hechos concretos del cálculo diferencial e integral mediante debates sobre asuntos fundamentales, para los cuales aún no está preparado. En cambio, estos se recopilan en apéndices de los capítulos ... El lector también notará que el estilo general de presentación, al principio detallado, está más condensado hacia el final del libro. Sin embargo, no debe dejarse desanimar por las dificultades aisladas que puede encontrar en los capítulos finales. Tales brechas en la comprensión, si no son demasiado frecuentes, generalmente se llenan por sí mismas. [Y el señor Courant dice en el vol. II que no se espera que los estudiantes lean un libro como este secuencialmente.]

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The Quantum Theory of Fields, Volume 3: Supersymmetry

Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This third volume of The Quantum Theory of Fields presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics that is likely to be at the center of future progress in the physics of elementary particles and gravitation. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, nonperturbative results, theories of supersymmetry in higher dimensions, and supergravity. A thorough review is given of the phenomenological implications of supersymmetry, including theories of both gauge and gravitationally-mediated supersymmetry breaking. Also provided is an introduction to mathematical techniques, based on holomorphy and duality, that have proved so fruitful in recent developments. This book contains much material not found in other books on supersymmetry, some of it published here for the first time. Problems are included.

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The Quantum Theory of Fields: Volume 2, Modern Applications Paperback: Modern Applications v. 2

The Quantum Theory of Fields, first published in 1996, is a self-contained, comprehensive introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume II gives an account of the methods of quantum field theory, and how they have led to an understanding of the weak, strong, and electromagnetic interactions of the elementary particles. The presentation of modern mathematical methods is throughout interwoven with accounts of the problems of elementary particle physics and condensed matter physics to which they have been applied. Many topics are included that are not usually found in books on quantum field theory. The book is peppered with examples and insights from the author's experience as a leader of elementary particle physics. Exercises are included at the end of each chapter.

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The Quantum Theory of Fields: Volume 1, Foundations Paperback: Foundations v. 1

In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.

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