Differential Forms with Applications to the Physical Sciences
Title | Differential Forms with Applications to the Physical Sciences PDF eBook |
Author | Harley Flanders |
Publisher | Courier Corporation |
Total Pages | 226 |
Release | 2012-04-26 |
Genre | Mathematics |
ISBN | 0486139611 |
"To the reader who wishes to obtain a bird's-eye view of the theory of differential forms with applications to other branches of pure mathematics, applied mathematic and physics, I can recommend no better book." — T. J. Willmore, London Mathematical Society Journal. This excellent text introduces the use of exterior differential forms as a powerful tool in the analysis of a variety of mathematical problems in the physical and engineering sciences. Requiring familiarity with several variable calculus and some knowledge of linear algebra and set theory, it is directed primarily to engineers and physical scientists, but it has also been used successfully to introduce modern differential geometry to students in mathematics. Chapter I introduces exterior differential forms and their comparisons with tensors. The next three chapters take up exterior algebra, the exterior derivative and their applications. Chapter V discusses manifolds and integration, and Chapter VI covers applications in Euclidean space. The last three chapters explore applications to differential equations, differential geometry, and group theory. "The book is very readable, indeed, enjoyable — and, although addressed to engineers and scientists, should be not at all inaccessible to or inappropriate for ... first year graduate students and bright undergraduates." — F. E. J. Linton, Wesleyan University, American Mathematical Monthly.
Differential Forms with Applications to the Physical Sciences by Harley Flanders
Title | Differential Forms with Applications to the Physical Sciences by Harley Flanders PDF eBook |
Author | |
Publisher | Elsevier |
Total Pages | 322 |
Release | 1963-01-01 |
Genre | Mathematics |
ISBN | 9780080955186 |
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Differential Forms and Applications
Title | Differential Forms and Applications PDF eBook |
Author | Manfredo P. Do Carmo |
Publisher | Springer Science & Business Media |
Total Pages | 124 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642579515 |
An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.
Differential Forms
Title | Differential Forms PDF eBook |
Author | Harry Flanders |
Publisher | |
Total Pages | 0 |
Release | 1963 |
Genre | Differential forms |
ISBN |
Tensors, Differential Forms, and Variational Principles
Title | Tensors, Differential Forms, and Variational Principles PDF eBook |
Author | David Lovelock |
Publisher | Courier Corporation |
Total Pages | 400 |
Release | 2012-04-20 |
Genre | Mathematics |
ISBN | 048613198X |
Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.
Differential Forms and Connections
Title | Differential Forms and Connections PDF eBook |
Author | R. W. R. Darling |
Publisher | Cambridge University Press |
Total Pages | 288 |
Release | 1994-09-22 |
Genre | Mathematics |
ISBN | 9780521468008 |
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.
Global Analysis
Title | Global Analysis PDF eBook |
Author | Ilka Agricola |
Publisher | American Mathematical Soc. |
Total Pages | 362 |
Release | 2002 |
Genre | Differential forms |
ISBN | 0821829513 |
The final third of the book applies the mathematical ideas to important areas of physics: Hamiltonian mechanics, statistical mechanics, and electrodynamics." "There are many classroom-tested exercises and examples with excellent figures throughout. The book is ideal as a text for a first course in differential geometry, suitable for advanced undergraduates or graduate students in mathematics or physics."--BOOK JACKET.