March 7, 2017

From Pythagoras to Einstein by K. O. Friedrichs

By K. O. Friedrichs

The most thread operating via this just a little unorthodox method of the designated concept of relativity is the Pythagorean theorem. it sounds as if in its most simple geometric shape within the very starting of this monograph. Then it reappears in algebraic apparel, is additional converted and eventually reinterpreted to play the function of 1 of the most characters within the certain idea of relativity.

The first 4 chapters are simply available to school sophmores or juniors. the rest a part of the e-book could be a little tricky for college students who by no means studied physics, even supposing the writer really employs in simple terms the thought of influence and presupposes no heritage in physics. simply by the vector geometry brought previous, he leads the reader from the effect dialog legislation to the recognized formulation e=mc2.

Show description

Read Online or Download From Pythagoras to Einstein PDF

Similar mathematical physics books

Table of Integrals, Series, and Products, Seventh Edition

A section demanding to decipher first and foremost, yet as soon as I acquired used to it this is often the easiest math reference publication i have ever had. i'm going to by no means desire one other one until I put on this one out (not most probably. .. critical binding) and if I do i'm going to need to get an analogous publication back. attention-grabbing background printed within the introductions to past types.

Functional Integration: Action and Symmetries

Sensible integration effectively entered physics as course integrals within the 1942 Ph. D. dissertation of Richard P. Feynman, however it made no feel in any respect as a mathematical definition. Cartier and DeWitt-Morette have created, during this ebook, a clean method of sensible integration. The e-book is self-contained: mathematical rules are brought, built, generalised and utilized.

Variational Methods in Mathematical Physics (Texts and Monographs in Physics)

This textbook is a accomplished advent to variational equipment. Its unifying point, in line with applicable strategies of compactness, is the examine of serious issues of functionals through direct tools. It indicates the interactions among linear and nonlinear useful research. Addressing specifically the pursuits of physicists, the authors deal with intimately the variational difficulties of mechanics and classical box theories, writing on neighborhood linear and nonlinear boundary and eigenvalue difficulties of significant periods of nonlinear partial differential equations, and giving newer effects on Thomas-Fermi thought and on difficulties related to severe nonlinearities.

Computational Physics: Problem Solving with Computers

This moment variation raises the universality of the former version via delivering all its codes within the Java language, whose compiler and improvement equipment can be found at no cost for primarily all working structures. moreover, the accompanying CD presents some of the similar codes in Fortran ninety five, Fortran seventy seven, and C, for much more common program, in addition to MPI codes for parallel functions.

Additional resources for From Pythagoras to Einstein

Example text

P \ The result is proved by induction based on the proof of (ii) above. x k • Remark Wedge multiplication is commutative except when both factors are of odd order, in which case it is anticommutative. 2 Let (e') (i = 1 , . e. V*. Then a basis for A (V„) (l«p«n) is the set (e''A... Ae'"), where l^i, < . . < i «n, and A {V ) has dimension ( ). 1 that a basis for the space V*jf^ of covariant tensors of order ρ is (e' ®.. ®e>') (/',,.. ,j = l,.. ,«) is the basis of V* corresponding to the basis (e/) of V„.

We are thus led to define the exterior or wedge product ωΛσ by x s (p + qVplq] ωΛσ = ——— ίί(ω®σ) . The numerical factor is introduced to avoid clumsy factors later, but conventions vary in this respect. e. a scalar, we put ωΛσ = σΛω = ωσ. Let («,•) be a given basis of V„. Then the components of ωΛσ are determined as follows. 2 (P + QV(ωΛσ),- .. , , ^ = (ωΛσ)(ί,,.. ,e J = ip 1 *ί(ω®σ)(

The integer ρ is known as the d e g r e e of the form. Let S be a p-forme V * ^ . /, = 5μ,... , i = 1 , . . , n); p when p>n, certain indices must be repeated and the tensor is zero. e. a 1-form as defined earlier. The number of independent non-zero components of a p-form to is the number of ways of selecting ρ distinct indices from the set 1 , . . e. Sec. 2] — p-forms —. The components ω. , where the indices are taken in their natural p\(n-p)\ order, are known as the proper components of ω. Since antisymmetry is preserved by addition and scalar multiplication, the set of all p-forms is a vector space denoted by \ (V^, which is a subspace of V * ^ (sometimes written as 3 (V„)).

Download PDF sample

Rated 4.28 of 5 – based on 30 votes