Download Differential Geometry for Physicists and Mathematicians: by Jose G Vargas PDF

By Jose G Vargas

This can be a ebook that the writer needs were to be had to him while he was once scholar. It displays his curiosity in figuring out (like specialist mathematicians) the main proper arithmetic for theoretical physics, yet within the kind of physicists. which means one isn't dealing with the examine of a set of definitions, comments, theorems, corollaries, lemmas, and so forth. yet a story the same as a narrative being instructed that doesn't bog down sophistication and deep effects.

It covers differential geometry a long way past what common relativists understand they should comprehend. And it introduces readers to different components of arithmetic which are of curiosity to physicists and mathematicians, yet are mostly neglected. between those is Clifford Algebra and its makes use of along side differential kinds and relocating frames. It opens new learn vistas that extend the subject material.

In an appendix at the classical idea of curves and surfaces, the writer slashes not just the most proofs of the normal technique, which makes use of vector calculus, yet even present remedies that still use differential varieties for a similar objective.

Readership: Physicists and mathematicians engaged on differential geometry.

Show description

Read Online or Download Differential Geometry for Physicists and Mathematicians: Moving Frames and Differential Forms: From Euclid Past Riemann PDF

Similar differential geometry books

Differential Geometry: Theory and Applications (Contemporary Applied Mathematics)

This booklet provides the elemental notions of differential geometry, similar to the metric tensor, the Riemann curvature tensor, the basic varieties of a floor, covariant derivatives, and the basic theorem of floor conception in a self-contained and available demeanour. even though the sector is frequently thought of a classical one, it has lately been rejuvenated, due to the manifold functions the place it performs a vital position.

Compactifications of Symmetric and Locally Symmetric Spaces (Mathematics: Theory & Applications)

Introduces uniform buildings of many of the recognized compactifications of symmetric and in the community symmetric areas, with emphasis on their geometric and topological constructions rather self-contained reference geared toward graduate scholars and learn mathematicians attracted to the purposes of Lie idea and illustration thought to research, quantity conception, algebraic geometry and algebraic topology

An Introduction to Multivariable Analysis from Vector to Manifold

Multivariable research is a crucial topic for mathematicians, either natural and utilized. except mathematicians, we think that physicists, mechanical engi­ neers, electric engineers, structures engineers, mathematical biologists, mathemati­ cal economists, and statisticians engaged in multivariate research will locate this e-book super helpful.

Extra info for Differential Geometry for Physicists and Mathematicians: Moving Frames and Differential Forms: From Euclid Past Riemann

Sample text

N = A1i1 A2i2 . . Anin ω i1 ∧ ω i2 ∧ . . ∧ ωin = |Aji |ω 1 ∧ ω 2 ∧ . . 3) where |Aji | is the determinant of the matrix whose elements are the Aji ’s. If (ω i ) = (dy i ) and (ω i ) = (dxi ), Eq. 3) becomes dy 1 ∧ dy 2 ∧ . . ∧ dy n = J(∂y/∂x)dx1 ∧ dx2 ∧ . . 4) where J(∂y/∂x) is the Jacobian. But we have as well dx1 ∧ dx2 ∧ . . ∧ dxn = J(∂x/∂y)dy 1 ∧ dy 2 ∧ . . ∧ dy n . 5) From these expressions, there is no way to tell which 3−form, whether dx1 ∧ dx2 ∧ . .

Dy n = J(∂y/∂x)dx1 ∧ dx2 ∧ . . 4) where J(∂y/∂x) is the Jacobian. But we have as well dx1 ∧ dx2 ∧ . . ∧ dxn = J(∂x/∂y)dy 1 ∧ dy 2 ∧ . . ∧ dy n . 5) From these expressions, there is no way to tell which 3−form, whether dx1 ∧ dx2 ∧ . .

A pair of region and coordinate assignment is called a chart. The region in the chart of Cartesian coordinates in the plane is the whole plane. And the region in the chart for the system of polar coordinates is the plane punctured at the chosen origin of the system. The inverse of a coordinate function will certainly take us from the coordinates to the points on the manifold represented by those coordinates. Let us call them inverse coordinate functions. e the number of components needed to represent their points in the manner prescribed.

Download PDF sample

Rated 4.72 of 5 – based on 36 votes