Methods of Mathematical Physics

Cambridge Mathematical Library

by Harold Jeffreys, Bertha Jeffreys

This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter.

730 pages, Kindle Edition

Published November 18, 1999

About the author

Sir Harold Jeffreys, FRS (22 April 1891 – 18 March 1989) was an English mathematician, statistician, geophysicist, and astronomer. His book Theory of Probability, which first appeared in 1939, played an important role in the revival of the Bayesian view of probability.

Jeffreys was born in Fatfield, Washington, County Durham, England. He studied at Armstrong College in Newcastle upon Tyne, then part of the University of Durham, and with the University of London External Programme.

At the University of Cambridge he taught mathematics, then geophysics and finally became the Plumian Professor of Astronomy.

He married another mathematician and physicist, Bertha Swirles (1903–1999), in 1940 and together they wrote Methods of Mathematical Physics.

One of his major contributions was on the Bayesian approach to probability (also see Jeffreys prior), as well as the idea that the Earth's planetary core was liquid. He was knighted in 1953.

By 1924 Jeffreys had developed a general method of approximating solutions to linear, second-order differential equations, including the Schrödinger equation. Although the Schrödinger equation was developed two years later, Wentzel, Kramers, and Brillouin were apparently unaware of this earlier work, so Jeffreys is often neglected when credit is given for the WKB approximation.

Jeffreys received the Gold Medal of the Royal Astronomical Society in 1937, the Royal Society's Copley Medal in 1960, and the Royal Statistical Society's Guy Medal in Gold in 1962. In 1948, Jeffreys received the Prix Charles Lagrange from the Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique.

From 1939 to 1952 he was established as Director of the International Seismological Summary further known as International Seismological Centre.

The textbook Probability Theory: The Logic of Science, written by the physicist and probability theorist Edwin T. Jaynes, is dedicated to Jeffreys. The dedication reads, "Dedicated to the memory of Sir Harold Jeffreys, who saw the truth and preserved it."

It is only through an appendix to the third edition of Jeffreys' book Scientific Inference that we know about Mary Cartwright's method of proving that the number π is irrational.

Honors/awards:

Fellow, Royal Society, 1925
Adams Prize, 1927 (Constitution of the Earth)
Gold Medal, Royal Astronomical Society, 1937
Buchan Prize, Royal Meteorological Society, 1929
Murchison Medal of Geological Society (Great Britain) 1939
Victoria Medal, Royal Geographical Society, 1941
Lagrange Prize, Brussels Academy, 1948
Royal Medal, 1948
William Bowie Medal, American Geophysical Union, 1952
Knighted, 1953
Copley Medal, Royal Society, 1961
Vetlesen Prize, 1962