Dover Books on Physics Series

An eminent electrical engineer and authority on linear system theory presents this advanced treatise, which approaches the subject from the viewpoint of classical dynamics and covers Fourier methods. This volume will assist upper-level undergraduates and graduate students in moving from introductory courses toward an understanding of advanced network synthesis. 1963 edition.

The most important work ever produced in the field of physiological optics, this classic is a model of scientific method and logical procedure, and it remains unmatched in its thorough and accessible approach. This is the third in a three-volume republication of the definitive English translation of Handbuch der Physiologischen Optik, originally published by The Optical Society of America in 1924 and containing everything that was known about physiological optics up until that time. The substratum consists of the data that Helmholtz furnished in the two nineteenth-century German editions that appeared during his lifetime. These volumes also contain extensive supplementary matter that Nagel, Gullstrand, and Kries incorporated in the third German edition of 1911, as well as significant new material prepared for the 1924 English translation by C. Ladd-Franklin, Gullstrand, and Kries, with copious annotations by James P. C. Southall that brought the work up to date with current research. Volumes I and II discuss the dioptrics of the eye and the sensations of vision;Volume III examines the perceptions of vision. Its topics include eye movements; the monocular field of vision; direction of vision; perception of depth; binocular vision; and many other highly important topics. Appendixes cover later findings on spatial configuration in vision and the theory of binocular instruments. Indexes for all three volumes are organized by subject and author.

Based on the ideas of Einstein and Minkowski, this concise treatment is derived from the author's many years of teaching the mathematics of relativity at the University of Michigan. Geared toward advanced undergraduates and graduate students of physics, the text covers old physics, new geometry, special relativity, curved space, and general relativity. Beginning with a discussion of the inverse square law in terms of simple calculus, the treatment gradually introduces increasingly complicated situations and more sophisticated mathematical tools. Changes in fundamental concepts, which characterize relativity theory, and the refinements of mathematical technique are incorporated as necessary. The presentation thus offers an easier approach without sacrifice of rigor.

This introductory text emphasizes Feynman's development of path integrals and its application to wave theory for particles. Suitable for undergraduate and graduate students of physics, the well-written, clear, and rigorous text was written by two of the nation's leading authorities on quantum physics. A solid foundation in quantum mechanics and atomic physics is assumed. Early chapters provide background in the mathematical treatment and particular properties of ordinary wave motion that also apply to particle motion. The close relation of quantum theory to physical optics is stressed. Subsequent sections emphasize the physical consequences of a wave theory of material properties, and they offer extensive applications in atomic physics, nuclear physics, solid state physics, and diatomic molecules. Four helpful Appendixes supplement the text.

"If ever a field needed a definitive book, it is the study of turbulence; if ever a book on turbulence could be called definitive, it is this book." — Science Written by two of Russia's most eminent and productive scientists in turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. The first volume begins with an outline of laminar and turbulent flow. The remainder of the book treats a variety of aspects of turbulence: its statistical and Lagrangian descriptions, shear flows near surfaces and free turbulence, the behavior of thermally stratified media, and diffusion. Volume Two continues and concludes the presentation. Topics include spectral functions, homogeneous fields, isotropic random fields, isotropic turbulence, self-preservation hypotheses, spectral energy transfer, the Millionshchikov hypothesis, acceleration fields, equations for higher moments and the closure problem, and turbulence in a compressible fluid. Additional subjects include general concepts of the local structure of turbulence at high Reynolds numbers, the theory of fully developed turbulence, the propagation of electromagnetic and acoustic waves through a turbulent medium, and the twinkling of stars. The book closes with a discussion of the functional formulation of the problem of turbulence, presenting the equations for the characteristic functional and methods for their solution.

Nobel laureate's classic exposition of the theory of radiant heat in terms of the principle of quantum action. Topics include Kirchoff's law, black radiation, Maxwell's radiation pressure, entropy, and much more. Few modern introductions to the theory of heat radiation can match this book for precision, care, and attention to details of proof. 1914 edition. Bibliography.

Undergraduates in engineering and the physical sciences receive a thorough introduction to perturbation theory in this useful and accessible text. Students discover methods for obtaining an approximate solution of a mathematical problem by exploiting the presence of a small, dimensionless parameter — the smaller the parameter, the more accurate the approximate solution. Knowledge of perturbation theory offers a twofold benefit: approximate solutions often reveal the exact solution's essential dependence on specified parameters; also, some problems resistant to numerical solutions may yield to perturbation methods. In fact, numerical and perturbation methods can be combined in a complementary way. The text opens with a well-defined treatment of finding the roots of polynomials whose coefficients contain a small parameter. Proceeding to differential equations, the authors explain many techniques for handling perturbations that reorder the equations or involve an unbounded independent variable. Two disparate practical problems that can be solved efficiently with perturbation methods conclude the volume. Written in an informal style that moves from specific examples to general principles, this elementary text emphasizes the "why" along with the "how"; prerequisites include a knowledge of one-variable calculus and ordinary differential equations. This newly revised second edition features an additional appendix concerning the approximate evaluation of integrals.

Developed from a classic undergraduate course on the study of the motion of bodies, this volume stresses the history of science as well as relevant physics and mathematics. R. Catesby Taliaferro developed a well-attended and much-revered course during his 20-year tenure at Notre Dame. He left among his papers the unfinished manuscript for this text, which has now been completed and prepared for publication by a group of his former students and colleagues. Suitable for undergraduates and beginning graduate students of physics and the history of science, this volume begins with an exploration of ancient Greek celestial mechanics and the seventeenth-century scientific revolution incited by Kepler's work. Subsequent chapters examine vector spaces and their applications, elementary differential geometry, particle dynamics, displacement and kinematics, theories of light, and the special theory of relativity.

How do we know that molecules really exist? An important clue came from Brownian movement, a concept developed in 1827 by botanist Robert Brown, who noticed that tiny objects like pollen grains shook and moved erratically when viewed under a microscope. Nearly 80 years later, in 1905, Albert Einstein explained this "Brownian motion" as the result of bombardment by molecules. Einstein offered a quantitative explanation by mathematically estimating the average distance covered by the particles over time as a result of molecular bombardment. Four years later, Jean Baptiste Perrin wrote Brownian Movement and Molecular Reality, a work that explains his painstaking measurements of the displacements of particles of a resin suspended in water — experiments that yielded average displacements in excellent accord with Einstein's theoretical prediction. The studies of Einstein and Perrin provided some of the first concrete evidence for the existence of molecules. Perrin, whose name is familiar to all who employ his methods for calculations in molecular dynamics, received the 1926 Nobel Prize in physics. In this classic paper, he introduced the concept of Avogadro's number, along with other groundbreaking work. Originally published in the French journal Annates de chimie et de physique, it was translated into English by Frederick Soddy to enduring influence and acclaim.

No branch of classical physics is older in its origins yet more modern in its applications than acoustics. Courses on acoustics very naturally begin with a study of vibrations, as a preliminary to the introduction of the wave equations. Both vibrations and waves, of course, are vastly important to all branches of physics and engineering. But it is very helpful to students to gain an understanding of mechanical waves before trying to comprehend the more subtle and abstract electromagnetic ones. This undergraduate-level text opens with an overview of fundamental particle vibration theory, and it proceeds to examinations of waves in air and in three dimensions, interference patterns and diffraction, and acoustic impedance, as illustrated in the behavior of horns. Subsequent topics include longitudinal waves in different gases and waves in liquids and solids; stationary waves and vibrating sources, as demonstrated by musical instruments; reflection and absorption of sound waves; speech and hearing; sound measurements and experimental acoustics; reproduction of sound; and miscellaneous applied acoustics. Supplementary sections include four appendixes and answers to problems. Introduction. Appendixes. List of Symbols. References. Index. Answers to Problems.

This classic study, available for the first time in paperback, clearly demonstrates how quantum theory is a natural development of wave theory, and how these two theories, once thought to be irreconcilable, together comprise a single valid theory of light. Aimed at students with an intermediate-level knowledge of physics, the book first offers a historical introduction to the subject, then covers topics such as wave theory, interference, diffraction, Huygens' Principle, Fermat's Principle, and the accuracy of optical measurements. Additional topics include the velocity of light, relativistic optics, polarized light, electromagnetic theory, and the quantum theory of radiation. The more difficult mathematics has been placed in appendixes, or in separated paragraphs in small type, intended to be omitted on first reading. Examples and/or references follow each chapter to assist the student in absorbing the material and to suggest additional resources.

Ideal as an elementary introduction to equilibrium statistical mechanics, this volume covers both classical and quantum methodology for open and closed systems. Introductory chapters familiarize readers with probability and microscopic models of systems, while additional chapters describe the general derivation of the fundamental statistical mechanics relationships. The final chapter contains 16 sections, each dealing with a different application, ordered according to complexity, from classical through degenerate quantum statistical mechanics. Key features include an elementary introduction to probability, distribution, functions, and uncertainty prior to a discussion of statistical mechanics; a review of the concept and significance of energy, together with a discussion of various models of physical systems. A series of appendixes contains helpful information on Gaussian integrals, the error function, the entropy constant, solutions to problems, and other subjects. A background in integral calculus is assumed, but because material is presented at a reasonable level of complexity, even readers not familiar with quantum mechanics can make use of at least two-thirds of this book. Index. 5 Appendixes. Problems at ends of chapters. Over 100 text figures.

"Should be widely read by practicing physicists, chemists and materials scientists." — Philosophical Magazine In this comprehensive and innovative text, Professor Harrison (Stanford University) offers a basic understanding of the electronic structure of covalent and ionic solids, simple metals, transition metals, and their compounds. The book illuminates the relationships of the electronic structures of these materials and shows how to calculate dielectric, conducting, and bonding properties for each. Also described are various methods of approximating electronic structure, providing insight and even quantitative results from the comparisons. Dr. Harrison has also included an especially helpful "Solid State Table of the Elements" that provides all the parameters needed to estimate almost any property of any solid, with a hand-held calculator, using the techniques developed in the book. Designed for graduate or advanced undergraduate students who have completed an undergraduate course in quantum mechanics or atomic and modern physics, the text treats the relation between structure and properties comprehensively for all solids rather than for small classes of solids. This makes it an indispensable reference for all who make use of approximative methods for electronic-structure engineering, semiconductor development and materials science. The problems at the ends of the chapters are an important aspect of the book. They clearly show that the calculations for systems and properties of genuine and current interest are actually quite elementary. Prefaces. Problems. Tables. Appendixes. Solid State Table of the Elements. Bibliography. Author and Subject Indexes. "Will doubtless exert a lasting influence on the solid-state physics literature." — Physics Today

Though James Clerk Maxwell (1831–1879) is best remembered for his epochal achievements in electricity and magnetism, he was wide-ranging in his scientific investigations, and he came to brilliant conclusions in virtually all of them. As James R. Newman put it, Maxwell "combined a profound physical intuition, an exquisite feeling for the relationship of objects, with a formidable mathematical capacity to establish orderly connections among diverse phenomena. This blending of the concrete and the abstract was the chief characteristic of almost all his researches." Maxwell's work on heat and statistical physics has long been recognized as vitally important, but Theory of Heat, his own masterful presentation of his ideas, remained out of print for years before being brought back in this new edition. In this unjustly neglected classic, Maxwell sets forth the fundamentals of thermodynamics clearly and simply enough to be understood by a beginning student, yet with enough subtlety and depth of thought to appeal also to more advanced readers. He goes on to elucidate the fundamental ideas of kinetic theory, and — through the mental experiment of "Maxwell's demon" — points out how the Second Law of Thermodynamics relies on statistics. A new Introduction and notes by Peter Pesic put Maxwell's work into context and show how it relates to the quantum ideas that emerged a few years later. Theory of Heat will serve beginners as a sound introduction to thermal physics; advanced students of physics and the history of science will find Maxwell's ideas stimulating, and will be delighted to discover this inexpensive reprint of a long-unavailable classic.

With unusual depth and clarity, it covers the problem of the foundations of geometry, the theory of time, the theory and consequences of Einstein's relativity including: relations between theory and observations, coordinate definitions, relations between topological and metrical properties of space, the psychological problem of the possibility of a visual intuition of non-Euclidean structures, and many other important topics in modern science and philosophy. While some of the book utilizes mathematics of a somewhat advanced nature, the exposition is so careful and complete that most people familiar with the philosophy of science or some intermediate mathematics will understand the majority of the ideas and problems discussed. Partial CONTENTS: I. The Problem of Physical Geometry. Universal and Differential Forces. Visualization of Geometries. Spaces with non-Euclidean Topological Properties. Geometry as a Theory of Relations. II. The Difference between Space and Time. Simultaneity. Time Order. Unreal Sequences. Ill. The Problem of a Combined Theory of Space and Time. Construction of the Space-Time Metric. Lorentz and Einstein Contractions. Addition Theorem of Velocities. Principle of Equivalence. Einstein's Concept of the Problems of Rotation and Gravitation. Gravitation and Geometry. Riemannian Spaces. The Singular Nature of Time. Spatial Dimensions. Reality of Space and Time.

Geared toward research students in physics and chemistry, this text introduces the three main uses of group theory in quantum mechanics: (1) to label energy levels and the corresponding eigenstates; (2) to discuss qualitatively the splitting of energy levels, starting from an approximate Hamiltonian and adding correction terms; and (3) to aid in the evaluation of matrix elements of all kinds. "The theme," states author Volker Heine, "is to show how all this is achieved by considering the symmetry properties of the Hamiltonian and the way in which these symmetries are reflected in the wave functions." Early chapters cover symmetry transformations, the quantum theory of a free atom, and the representations of finite groups. Subsequent chapters address the structure and vibrations of molecules, solid state physics, nuclear physics, and relativistic quantum mechanics. A previous course in quantum theory is necessary, but the relevant matrix algebra appears in an appendix. A series of examples of varying levels of difficulty follows each chapter. They include simple drills related to preceding material as well as extensions of theory and further applications. The text is enhanced with 46 illustrations and 12 helpful appendixes.

This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence and stresses the global aspects of cosmology. Suitable for independent study as well as for courses in differential geometry, relativity, and cosmology. 1979 edition.

This incisive text provides a basic undergraduate-level course in modern optics for students in physics, technology and engineering. The first half of the book deals with classical physical optics; the second principally with the quantum nature of light. Chapters 1 and 2 treat the propagation of light waves, including the concepts of phase and group velocities, and the vectorial nature of light. Chapter 3 applies the concepts of partial coherence and coherence length to the study of interference, and Chapter 4 takes up multiple-beam interference and includes Fabry-Perot interferometry and multilayer-film theory. Diffraction and holography are the subjects of Chapter 5, and the propagation of light in material media (including crystal and nonlinear optics) are central to Chapter 6. Chapters 7 and 8 introduce the quantum theory of light and elementary optical spectra, and Chapter 9 explores the theory of light amplification and lasers. Chapter 10 briefly outlines ray optics in order to introduce students to the matrix method for treating optical systems and to apply the ray matrix to the study of laser resonators. Many applications of the laser to the study of optics are integrated throughout the text. The author assumes students have had an intermediate course in electricity and magnetism and some advanced mathematics beyond calculus. For classroom use, a list of problems is included at the end of each chapter, with selected answers at the end of the book.

"The Cosmic Code can be read by anyone. I heartily recommend it!" — The New York Times Book Review "A reliable guide for the nonmathematical reader across the highest ridges of physical theory. Pagels is unfailingly lighthearted and confident." — Scientific American "A sound, clear, vital work that deserves the attention of anyone who takes an interest in the relationship between material reality and the human mind." — Science 82 This is one of the most important books on quantum mechanics ever written for general readers. Heinz Pagels, an eminent physicist and science writer, discusses and explains the core concepts of physics without resorting to complicated mathematics. The two-part treatment outlines the history of quantum physics and addresses complex subjects such as Bell's theorem and elementary particle physics, drawing upon the work of Bohr, Gell-Mann, and others. Anecdotes from the personal documents of Einstein, Oppenheimer, Bohr, and Planck offer intimate glimpses of the scientists whose work forever changed the world.

Suitable for upper-level undergraduates and graduate students, this text explores the most exact methods used in the theory of figures of equilibrium. It also examines problems concerning the figures of celestial bodies, including invariable or varying figures, zonal rotation, systems composed of fluid and rigid parts, and more. 1958 edition.

This foundational text is written for students who want to go beyond the perceptual stage of music to learn how musical sound is created and perceived. It surveys a wide range of topics related to acoustics, beginning with a brief history of the art and science of music. Succeeding chapters explore the general principles of sound, musical scales, the primary ways in which sound can be generated, the characteristics of instruments, the use of mechanical and electronic recording devices, hi-fi stereophonic and quadraphonic sound, the design of electronic musical instruments, and architectural acoustics. Comprehensive yet accessible, Physics and Music includes over 300 diagrams, photographs, and tables. Each chapter concludes with questions, problems, and projects, in addition to references for further study. 1980 edition.

Lasers play an increasingly important role in a variety of detection techniques, making inelastic light scattering a tool of growing value in the investigation of dynamic and structural problems in chemistry, biology, and physics. Until the initial publication of this work, however, no monograph treated the principles behind current developments in the field.This volume presents a comprehensive introduction to the principles underlying laser light scattering, focusing on the time dependence of fluctuations in fluid systems; it also serves as an introduction to the theory of time correlation functions, with chapters on projection operator techniques in statistical mechanics. The first half comprises most of the material necessary for an elementary understanding of the applications to the study of macromolecules, or comparable sized particles in fluids, and to the motility of microorganisms. The study of collective (or many particle) effects constitutes the second half, including more sophisticated treatments of macromolecules in solution and most of the applications of light scattering to the study of fluids containing small molecules.With its wide-ranging discussions of the many applications of light scattering, this text will be of interest to research chemists, physicists, biologists, medical and fluid mechanics researchers, engineers, and graduate students in these areas.

A wide-ranging collection of problems and solutions related to quantum mechanics, this text will be useful to students pursuing an advanced degree in physics. Topics include one-dimensional motion, tunnel effect, commutation relations, Heisenberg relations, spreading of wave packets, operators, angular momentum, spin, central field of force, motion of particles in a magnetic field, atoms, scattering, creation and annihilation operators, density matrix, relativistic wave equations, and many other subjects. Suitable for advanced undergraduates and graduate students of physics, this third edition was edited by Dirk ter Haar, a Fellow of Magdalen College and Reader in Theoretical Physics at the University of Oxford. This enlarged and revised edition includes additional problems from Oxford University Examination papers. The book can be used either in conjunction with another text or as advanced reading for anyone familiar with the basic ideas of quantum mechanics. 1975 edition.

This classic of modern physics includes a vast array of approximation methods, mathematical tricks, and physical pictures that are also useful in the application of quantum mechanics to other fields. Students and professionals will find it an essential reference for calculations pertaining to hydrogen-like and helium-like atoms and their comparison with experimental results. In-depth explorations of the Dirac theory of the electron and of radiative effects include brief accounts of relevant experiments. The specific application of general field-theoretic results to atomic systems also receives a thorough examination. Author Hans A. Bethe (1906–2005), Professor of Physics at Cornell University, won the Nobel Prize in Physics in 1967. Co-author Edwin E. Salpeter is James Gilbert White Distinguished Professor of the Physical Sciences at Cornell University.

The crucial significance of symmetry to the development of group theory and in the fields of physics and chemistry cannot be overstated, and this well-organized volume provides an excellent introduction to the topic. The text develops the elementary ideas of both group theory and representation theory in a progressive and thorough fashion, leading students to a point from which they can proceed easily to more elaborate applications. The finite groups describing the symmetry of regular polyhedral and of repeating patterns are emphasized, and geometric illustrations of all main processes appear here — including more than 100 fully worked examples. Designed to be read at a variety of levels and to allow students to focus on any of the main fields of application, this volume is geared toward advanced undergraduate and graduate physics and chemistry students with the requisite mathematical background.

"A remarkable work which will remain a document of the first rank for the historian of mechanics." — Louis de Broglie In this masterful synthesis and summation of the science of mechanics, Rene Dugas, a leading scholar and educator at the famed Ecole Polytechnique in Paris, deals with the evolution of the principles of general mechanics chronologically from their earliest roots in antiquity through the Middle Ages to the revolutionary developments in relativistic mechanics, wave and quantum mechanics of the early 20th century. The present volume is divided into five parts: The first treats of the pioneers in the study of mechanics, from its beginnings up to and including the sixteenth century; the second section discusses the formation of classical mechanics, including the tremendously creative and influential work of Galileo, Huygens and Newton. The third part is devoted to the eighteenth century, in which the organization of mechanics finds its climax in the achievements of Euler, d'Alembert and Lagrange. The fourth part is devoted to classical mechanics after Lagrange. In Part Five, the author undertakes the relativistic revolutions in quantum and wave mechanics. Writing with great clarity and sweep of vision, M. Dugas follows closely the ideas of the great innovators and the texts of their writings. The result is an exceptionally accurate and objective account, especially thorough in its accounts of mechanics in antiquity and the Middle Ages, and the important contributions of Jordanus of Nemore, Jean Buridan, Albert of Saxony, Nicole Oresme, Leonardo da Vinci, and many other key figures. Erudite, comprehensive, replete with penetrating insights, AHistory of Mechanics is an unusually skillful and wide-ranging study that belongs in the library of anyone interested in the history of science.

"A great delight to read." — Physics Today Among the most fertile areas of modern physics, many-body theory has produced a wealth of fundamental results in all areas of the discipline. Unfortunately the subject is notoriously difficult and, until the publication of this book, most treatments of the topic were inaccessible to the average experimenter or non-specialist theoretician. The present work, by contrast, is well within the grasp of the nonexpert. It is intended primarily as a "self-study" book that introduces one aspect of many-body theory, i.e. the method of Feynman diagrams. The book also lends itself to use as a reference in courses on solid state and nuclear physics which make some use of the many-body techniques. And, finally, it can be used as a supplementary reference in a many-body course. Chapters 1 through 6 provide an introduction to the major concepts of the field, among them Feynman diagrams, quasi-particles and vacuum amplitudes. Chapters 7 through 16 give basic coverage to topics ranging from Dyson's equation and the ladder approximation to Fermi systems at finite temperature and superconductivity. Appendixes summarize the Dirac formalism and include a rigorous derivation of the rules for diagrams. Problems are provided at the end of each chapter and solutions are given at the back of the book. For this second edition, Dr. Mattuck, formerly of the H. C. Orsted Institute and the University of Copenhagen, added to many chapters a new section showing in mathematical detail how typical many-body calculations with Feynman diagrams are carried out. In addition, new exercises were included, some of which gave the reader the opportunity to carry out simpler many-body calculations himself.  new chapter on the quantum field theory of phase transitions rounds out this unusually clear, helpful and informative guide to the physics of the many-body problem.

In addition to being among the twentieth century’s major scientific figures, Sir James Jeans (1877–1946) was also one of the greatest modern science expositors. His classic introduction to mechanics endures as a clear and concise presentation of first principles. Although brief, it encompasses a remarkably wide selection of topics. Its subjects include rest and motion, force and the laws of motion, forces acting on a single particle, statics of systems of particles, statics of rigid bodies, center of gravity, work, motion of a particle under constant forces, motion of systems of particles, motion of a particle under a variable force, motion of rigid bodies, and generalized coordinates. Within each chapter, the author carefully explains the most elementary concepts (such as velocity, acceleration, Newton’s laws, friction, moments, and kinetic energy), and he illustrates them with examples. Ideal for beginning physics students or for more advanced readers in need of refreshment, the text emphasizes the fundamental physical principles rather than mathematics or applications. So clearly written that it can be read and understood outside the classroom, it features hundreds of fully worked illustrative examples and test exercises.

An internationally famous physicist and electrical engineer, the author of this text was a pioneer in the investigation of gravitational waves. Joseph Weber's General Relativity and Gravitational Waves offers a classic treatment of the subject. Appropriate for upper-level undergraduates and graduate students, this text remains ever relevant. Brief but thorough in its introduction to the foundations of general relativity, it also examines the elements of Riemannian geometry and tensor calculus applicable to this field. Approximately a quarter of the contents explores theoretical and experimental aspects of gravitational radiation. The final chapter focuses on selected topics related to general relativity, including the equations of motion, unified field theories, Friedman's solution of the cosmological problem, and the Hamiltonian formulation of general relativity. Exercises. Index.

A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.