The Structure of Scientific Revolutions

Vector Analysis. Curved Coordinates, Tensors. Determinants and Matrices. Group Theory. Infinite Series. Functions of a Complex Variable I. Functions of a Complex Variable II. Differential Equations. Sturm-Liouville Theory. Gamma-Factrial Function. Bessel Functions. Legendre Functions. Special Functions. Fourier Series. Integral Transforms. Integral Equations. Calculus of Variations. Nonlinear Methods and Chaos.

Mathematical Methods for Physicists

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Exactly solved models in statistical mechanics

: This reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental problem is to appropriately decompose the domain R of a function g (x,y) of two variables. This problem starts by describing the physical situation which produces images: assume that a three-dimensional world is observed by an eye or camera from some point P and that g1(rho) represents the intensity of the light in this world approaching the point sub 1 from a direction rho. If one has a lens at P focusing this light on a retina or a film-in both cases a plane domain R in which we may introduce coordinates x, y then let g(x,y) be the strength of the light signal striking R at a point with coordinates (x,y); g(x,y) is essentially the same as sub 1 (rho) -possibly after a simple transformation given by the geometry of the imaging syste. The function g(x,y) defined on the plane domain R will be called an image. What sort of function is g? The light reflected off the surfaces Si of various solid objects O sub i visible from P will strike the domain R in various open subsets R sub i. When one object O1 is partially in front of another object O2 as seen from P, but some of object O2 appears as the background to the sides of O1, then the open sets R1 and R2 will have a common boundary (the 'edge' of object O1 in the image defined on R) and one usually expects the image g(x,y) to be discontinuous along this boundary. (JHD)

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Optimal approximations by piecewise smooth functions and associated variational problems

One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons For hydrogen and the analcgous ions He+, Li++, etc, the calculations can be performed exactly, both in Schrodinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron More specifically, the calculations are exact for a single electron in a fixed Coulomb potential Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment

Quantum Mechanics of One- and Two-Electron Atoms

This classic work has been a unique resource for thousands of mathematicians, scientists and engineers since its first appearance in 1902 Never out of print, its continuing value lies in its thorough and exhaustive treatment of special functions of mathematical physics and the analysis of differential equations from which they emerge The book also is of historical value as it was the first book in English to introduce the then modern methods of complex analysis This fifth edition preserves the style and content of the original, but it has been supplemented with more recent results and references where appropriate All the formulas have been checked and many corrections made A complete bibliographical search has been conducted to present the references in modern form for ease of use A new foreword by Professor SJ Patterson sketches the circumstances of the book's genesis and explains the reasons for its longevity A welcome addition to any mathematician's bookshelf, this will allow a whole new generation to experience the beauty contained in this text

A Course of Modern Analysis

This classic book is a encylopaedic and comprehensive account of the classical theory of analytical dynamics. The treatment is rigorous yet readable, starting from first principles with kinematics before moving to equations of motion and specific and explicit methods for solving them, with chapters devoted to particle dyanmics, rigid bodies, vibration, and dissipative systems. Hamilton's principle is introduced and then applied to dynamical systems, including three-body systems and celestial mechanics. Very many examples and exercisies are supplied throughout.

A treatise on the analytical dynamics of particles and rigid bodies

1. Complex numbers 2. The theory of convergence 3. Continuous functions and uniform convergence 4. The theory of Riemann integration 5. The fundamental properties of analytic functions 6. The theory of residues 7. The expansion of functions in infinite series 8. Asymptotic expansions and summable series 9. Fourier series and trigonometrical series 10. Linear differential equations 11. Integral equations 12. The gamma function 13. The zeta function of Riemann 14. The hypergeometric function 15. The Legendre function 16. The confluent hypergeometric functions 17. Bessel functions 18. The equations of mathematical physics 19. Mathieu functions 20. Elliptic functions 21. The theta functions 22. Jacobian elliptic functions 23. Ellipsoidal harmonics and Lame's equation.

A course of modern analysis; an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions

A history of the theories of aether and electricity

Market: Physicists, interested lay readers, and historians of science. This survey of the history of electrodynamics provides insight into the revolutionary advances made in physics during 19th and the first quarter of the 20th centuries. The first volume covers the theories of classical physics from the time of Plato to the end of the 19th century. The second volume examines the origins of the discoveries that paved the way for modern physics with the emphasis on special relativity, quantum theories, general relativity, matrix mechanics, and wave mechanics.

Edmund Taylor Whittaker

Papers

A Course of Modern Analysis

A treatise on the analytical dynamics of particles and rigid bodies

A course of modern analysis; an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions

A history of the theories of aether and electricity

A history of the theories of aether and electricity