This second edition updates the classic text for applied mathematics. Its clarity, scope, and content as well as its sheer mathematical elegance make it essential for students of physics or engineering. Part I of the two-volume series covers types of fields, equations governing fields, fields and the variational principle, functions of a complex variable, ordinary differential equations, integral representations, boundary conditions and eigenfunctions, Green's functions, and integral equations. Problem sets and helpful tables conclude each chapter. AUTHORS: Herman Fesbach received his Ph.D. in physics from MIT and was on the MIT physics faculty for more than 50 years. From 1967-73, he was the Director of MIT's Center for Theoretical Physics, and from 1973-83, he was Chairman of the Physics Department. Philip M. Morse earned his Ph.D. in physics from Princeton University in 1929 and later joined the faculty of MIT. In 1956 he launched MIT's Operations Research Center, directing it until 1968, and he was a major figure in originating the field of operations research. Michio Masujima studied physics and mathematics at MIT and Stanford University. He received his Ph.D. in mathematics from MIT in 1983 and worked for many years at the NEC Fundamental Research Laboratory in Japan, where he was in charge of computational physics, and later as a lecturer at the NEC Junior Technical College, where he was responsible for the subjects of mathematics and physics.