Resultaten voor 'richard courant'

1. Richard Courant
2. K O Friedrichs

Theoretical Studies on the Flow Through Nozzles and Related Problems

1. Eleazer Bromberg
2. Richard Courant
3. K O Friedrichs

Mathematical Theory of the Influence of a Dome on the Directivity Pattern of Sound Beams, Part 4

1. Eleazer Bromberg
2. Richard Courant
3. K O Friedrichs

Mathematical Theory of the Influence of a Dome on the Directivity Pattern of Sound Beams, Part 4

1. Richard Courant
2. K O Friedrichs

Theoretical Studies on the Flow Through Nozzles and Related Problems

1. Richard , Courant
2. Fritz , John

Introduction to Calculus and Analysis

The new Chapter 1 contains all the fundamental properties of linear differential forms and their integrals. These prepare the reader for the introduction to higher-order exterior differential forms added to Chapter 3. Also found now in Chapter 3 are a new proof of the implicit function theorem by successive approximations and a discus­ sion of numbers of critical points and of indices of vector fields in two dimensions. Extensive additions were made to the fundamental properties of multiple integrals in Chapters 4 and 5. Here one is faced with a familiar difficulty: integrals over a manifold M, defined easily enough by subdividing M into convenient pieces, must be shown to be inde­ pendent of the particular subdivision. This is resolved by the sys­ tematic use of the family of Jordan measurable sets with its finite intersection property and of partitions of unity. In order to minimize topological complications, only manifolds imbedded smoothly into Euclidean space are considered. The notion of "orientation" of a manifold is studied in the detail needed for the discussion of integrals of exterior differential forms and of their additivity properties. On this basis, proofs are given for the divergence theorem and for Stokes's theorem in n dimensions. To the section on Fourier integrals in Chapter 4 there has been added a discussion of Parseval's identity and of multiple Fourier integrals.

1. Richard Courant
2. David Hilbert

Methods of Mathematical Physics, Volume 1

Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.