Classical Electrodynamics and Theory of Relativity

Excerpts are presented from a graduate course on Classical Electrodynamics held during the spring semester of 2000 at the Institute of Physics, Guanajuato State University, Mexico

These are lectures on General Theory of Relativity that were given to students of the Mathematical Faculty of the Higher School of Economics in Moscow.

The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of electromagnetism the general laws are expressed as geometric (coordinate-free) relations between quantities on a four-dimensional spacetime manifold. Based on these laws, and exterior calculus on metric spaces, we derive fields and relations th...

This work is an introduction to modern mathematical physics. We begin with Maxwell laws and vector calculus, pass next to consider the action and the Feynman integral in quantum mechanics, next relativity and differential geometry to formulate the electromagnetic laws in intrinsic form. Next we see gravitation to study the covariant derivative. We end with the electromagnetic bundle U(1). It contains the know-how + the know-why. The text is written in Spanish. 340 pps.

Lecture notes written for a one-semester course in mathematical relativity aimed at mathematics and physics students. Not meant as an introduction to general relativity, but rather as a complementary, more advanced text.

The present technical notes offer a brief summary of the essential points of electromagnetism at the undergraduate physics level. Some problems are presented at the end of each section; those with solutions are marked with an asterisk.

This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book with the motivation of geometrical or pictorial way of thinking. This note is an effort of teaching differential geometry and shows its wide applicability to relativity theory. The problems in this lecture note may be useful to the students

In this article we present pictorially the foundation of differential geometry which is a crucial tool for multiple areas of physics, notably general and special relativity, but also mechanics, thermodynamics and solving differential equations. As all the concepts are presented as pictures, there are no equations in this article. As such this article may be read by pre-university students who enjoy physics, mathematics and geometry. However it will also greatly aid the intuit...

In this article we show that Einstein covariance principle provides a wide opportunity in the solutions of different problems of theoretical physics. Here we apply covariance principle in some problems of classical electrodynamics and kinetics. Extension of this approach in the other fields is obvious.

We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's equations. They are expressed in terms of the field strengths $(E,{\cal B})$, the excitations $({\cal D},H)$, and the sources $(\rho,j)$. This fundamental set of four microphysical equations has to be supplemented by somewhat less general ...